New Approaches to Melody in 1920S Musical Thought

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Sounding Lines: New Approaches to Melody in 1920s Musical Thought

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Citation Probst, Stephanie. 2018. Sounding Lines: New Approaches to Melody in 1920s Musical Thought. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences.

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 2018, Stephanie Probst

Sounding Lines: New Approaches to Melody in 1920s Musical Thought

Abstract

This dissertation identifies a new concept of melody that emerged in early twentieth- century Germany at the intersection of developments in composition, music theory, philosophy, the visual arts, and psychology. Focusing on the widespread analogy of the line, which came to encapsulate melody as an autonomous, temporally evolving yet coherently perceived musical entity, the study investigates how theorists unleashed melody from the hegemony of nineteenth- century harmony and theorized its structuring principles independently from vertical ties. Recent theories of visualization frame readings of an interdisciplinary body of sources to illuminate the ways in which the melodic line bridged physical and psychological models of music, temporal and spatial perspectives, and theories of visual and aural cognition.

The first two chapters chronicle the revival and re-conceptualization of the line in the visual arts and of melody in music around 1900 as parallel developments. Chapter I examines how modernist tendencies towards abstraction in visual-artistic practice and theory emancipated the line from its traditional representational functionality and elevated it to an expressive graphical element. By representing the temporal processes of its creation and cognition, the line came to hypostatize cognitive theories of vision and audition. In Chapter II, the example of Ernst

Toch’s String Quartet Op. 26 (1919) illustrates how melody became a structurally and perceptually salient parameter in compositions around 1920, which challenges this introduced for printers, performers, and listeners alike, and how different ideological camps contested the rightful application of linearity in music criticism.

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Chapters III and IV focus respectively on notions of the single melodic line in Toch’s

Melodielehre (1923) and the intertwining of multiple horizontal trajectories in Ernst Kurth’s

Foundations of Linear Counterpoint: Bach’s Melodic Polyphony (1917). I trace a lineage of pertinent inquiries in cognitive psychology and Gestalt theory, from Ernst Mach’s theory of sensory perception (1886/96) and Christian von Ehrenfels’s seminal “On ‘Gestalt Qualities’”

(1890/1922) to the work of Max Wertheimer (1912, 1923), and elucidate the ways in which music theorists intuited cognitive and Gestalt-theoretical principles in their linear conceptions of melody by privileging step-wise melodic progressions. Chapter V examines the music-analytical and interpretative potential of the line in graphical depictions of musical compositions by

Bauhaus-artists Wassily Kandinsky, Paul Klee, and Henrik Neugeboren.

My discussion situates an acknowledged turning point in music in a broad cultural and intellectual context. I argue that the interdisciplinary conditions undergirding linear-melodic thinking of this time continue to inform compositional and analytical models and aesthetic connotations of melody and the line today.

TABLE OF CONTENTS

Acknowledgements vii List of Figures and Table xii Note on Translations xv

Introduction: Some Points 1 Overview of Chapters 12

Chapter I. Sounding Lines 17 Between the Arts, Physics, and Psychology 19 The Genetic Line 26 Tracing Perception: From Eye Paths to the Gestalt Quality of Melody 32 Bach and Beethoven as Linear Icons 41 Musical Lines Today 51

Chapter II. The Status of Melody in the Early Twentieth Century: 57 Aesthetics, Composition, Notation, Theory From Nineteenth-Century Melodik to Twentieth-Century Melodielehre 57 The Nineteenth Century 59 Into the Twentieth Century 65 Ernst Toch and Aesthetic Debates ca. 1920 73 Defining History to Shape the Present 74 Invention (“Einfall”) 76 Theory vs. Pedagogy 79 Theory vs. “Entzauberung” 81 Harmony 84 Composing, Notating, Performing, and Listening to Linear Music in the 1920s: 86 Ernst Toch’s String Quartet No. 9 in C Major, Op. 26 (1919/20) Toch’s Op. 26 90 Expanding Notation 93 “Linearity” in Music Criticism 103

Chapter III. Melodic Wave Lines, 1821 and 1923: Towards Continuity in Ernst 113 Toch’s Tonhöhenlinie Kanne’s Wave Line 115 From Kanne’s Wave Line to Toch’s Tonhöhenlinie : A Preliminary Comparison 121 Approximating Continuity 124 The Problem of Continuity in Kanne’s Theory 124 Towards a Graphical Line in Toch’s Theory 128 Approximating Continuity in Toch’s Tonhöhenlinie 134

Chapter III (cont.) A Psychological Perspective on Music Theory: Cognition as Methodological 136 Anchor in Toch’s Melodielehre Backdrops for Toch’s Cognitive Framework 141 Ernst Mach 141 Christian von Ehrenfels 144 Other Gestalt Theorists 148 Achieving Continuity 153 The Shape of the Tonhöhenlinie as Expressive Seismograph 155 Beethoven and the Aesthetic Function of Toch’s Tonhöhenlinie 164

Chapter IV. Interweaving Lines in Ernst Kurth’s Theory of Linear Counterpoint 170 Melody as Experienced Motion 173 Gestalt-Theoretical Aspects in Kurth’s Understanding of Melodic Motion 178 Models for Kurth’s Melodic Line in the Visual Arts and Other Domains 189 Horizontality and Verticality in History: Kurth’s Music-Theoretical Intervention 198 The Linear Forms in Apparent Polyphony (“Scheinpolyphonie”) 206 The Gestalt Theory of Apparent Polyphony 219

Chapter V. Performing Music (Analysis) with Pen, Paper, and Steel: 229 Artistic Renditions of Music At The Bauhaus From Dots to the Line: Listening through Kandinsky’s Ears 233 Against the Point in Counterpoint: Lines in J.S. Bach’s Polyphonic Style 243 Performing Bach with Pen and Paper 256 Visions of Tonal Space: Examining the Organization of the Graphs 264 A Haptic Encounter with Polyphony 271 Performing and Listening Engraved 276

Conclusion: Some Threads 279 Drawing, Thinking, Composing, and Hearing Lines 282 Mapping Movement and Interpreting Lines 286

Bibliography 291

ACKNOWLEDGEMENTS

Lines tie together ideas, and ideas connect people. In writing this dissertation, and throughout my education, a tightly knit web of people have supported me as I collected, developed, and interwove ideas for this project.

At Harvard, I am particularly indebted to the three members of my dissertation committee, Suzie Clark, Alex Rehding, and Chris Hasty, for their guidance during the dissertation, for challenging me and encouraging me to find my own path as a scholar. I am grateful to Suzie for her vision and rigor, her inspiring teaching, and for her generous and holistic approach as a mentor. Alex gave much direction to this dissertation through his creative ideas and vast knowledge and has been unfailingly available with practical advice and encouragement.

I am also grateful for his help with rendering some of the more evocative samples of early twentieth-century German in fittingly colorful translations. I thank Chris for encouraging me to think outside established frames and for the long, stimulating conversations that helped me to see the bigger picture of my research.

I extend thanks to the other wonderful mentors and teachers of my graduate education, including Sindhu Revuluri and Kate van Orden at Harvard, and Bob Wason, Jonathan Dunsby,

Elizabeth Marvin, and Bob Hasegawa at Eastman. Seminars at Harvard by Ahmed Ragab in the

History of Science, and Benjamin Buchloh in the History of Art and Architecture provided new critical lenses to my thinking. I am grateful to Laura Frahm for inviting me to present early ideas of my research in her seminar on “New Media Theory,” a course that also brought media theory to bear on my project. I look back with gratitude to Marie-Agnes Dittrich, Martin Eybl,

Wolfgang Gratzer, and Birgit Lodes for encouraging me to pursue my interests in my early

vii studies in Vienna. My music teacher in high school, Gabriele Eder, was the first to stimulate and foster my curiosity in music’s essence, power, and larger contexts.

Nancy Shafman, Eva Kim, Kaye Denny, Lesley Bannatyne, and Karen Rynne make the

Music Department at Harvard such a welcoming and happy place and have been forthcoming with help on all organizational issues, sometimes even before I asked. Andy Wilson in the Music library always accommodated any special requests and generously volunteered his expertise on player piano rolls. I am very grateful for Harvard’s Oscar Straus Schafer teaching fellowship and the Barbara Natterson-Horowitz finishing grant, which have provided me the time and flexibility to finish the dissertation while abroad during the last two years.

I have benefited greatly from participating in the interdisciplinary colloquium on

“Panaesthetics” that Cécile Guédon organized at Harvard. The seminars have equipped me with a range of perspectives on inter-artistic scholarship, and my lively discussions with Cécile have left an imprint on my thinking towards both my research and the larger things in life. I am very grateful to Gurminder Bhogal, who kindly and generously read the full manuscript of this dissertation and offered expert advice and enthusiasm. I learned a lot about the art of teaching from observing Richard Beaudoin’s classes. Beyond these valuable pedagogical insights, I have appreciated conversations with him about music and the visual arts, excursions to art galleries, and his honest feedback on shared work. Richard introduced me to Orit Hilewicz, who has become another energetic and inquisitive interlocutor about our shared fascination with intersections between music and the visual arts. I am sincerely thankful for the interest in my work that Julia Kursell, Sybille Krämer, and Áine Henneghan have expressed, and the manuscripts, sources, and ideas that they have shared with me along the way.

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My “theory cohort” at Harvard—Olivia Lucas, Frederick Reece, Bill O’Hara, Danny

Walden, and Joe Fort—have been the best colleagues I could have hoped for, and their brilliance and humor made these years the more memorable. I have learned a lot from discussions, work exchange, and comic relief with Monica Hershberger, Emerson Morgan, Natasha Roule, and

Sarah Politz. I thank Manuela Meier for the friendship and for providing a home abroad; Rujing

Huang for her humor; and Elizabeth Craft for her caring advice. I am particularly grateful to

Hayley Fenn, who read a full draft of this dissertation (and many previous drafts) effectively overnight and has become an “honorary lineologist” per virtue of our conversations, in which she stimulated me with her creativity, helped me to tie together loose ends of my thoughts, and provided great friendship. Many thanks are due to Russ Manitt, whose enthusiasm made me believe in this dissertation project in the first place, and who has remained an inspiring interlocutor and critical reader along the way. It is also due to him and Scott Edwards that I got to live in the “house of musicology” on Greenville Street, where “love, light & happiness” surrounded me in many a way during these years. I look back to the house with many happy memories, including Vienna roast coffee and the camaraderie of Grace Edgar and Hanna Frey, and warm cookie deliveries and comforting meals from Caitlin Schmid and Tom Scahill.

When I first considered continuing my education in the United States, I found a fellow pioneer in Rebecca Vogels. Visiting her in New York was a formative experience, and meetings with her and Benjamin in Vienna remain highlights of my visits there. Carmel Raz was incredibly forthcoming with advice from the day I first met her and has remained a source of inspiration and motivation. At Eastman, Daphne Tan was particularly supportive in helping me navigate my first steps in American academia, and I have valued her insights and our discussions about the history of music theory and the theories of Ernst Kurth.

When life sent me to Munich, I could not have imagined a more welcoming community than the one I found at the Deutsches Museum. I am especially indebted to Rebecca Wolf for arranging for my own workspace and including me in her research group. Rebecca also put me in touch with Arne Stollberg, who has generously shared his work and ideas, which have informed in particular my inquiries in Chapter 4. I am grateful for the opportunity to present work-in- progress to the musicology colloquium of Wolfgang Rathert at the Ludwig-Maximilians-

Universität in Munich.

Across the continents, I am thankful for friends who have followed my travels and sustained me with their support across an immense distance. Julia Wikström, Toni Haas, Marlies

Haschke, Anna Derndorfer, Diane Hunger, and Johanna Privitera have been there for me with an open ear and heart. Many shared stories, holiday retreats, and meetings in places old and new with Federica Berdini have been an integral frame to this dissertation. Kathi and Johannes

Passini have provided a welcoming home in Vienna on multiple occasions, and brought great coffee to our apartment through their generous gift. In Vienna, Philadelphia, and New York, I always enjoy the company of Daniele and Stephanie Massera, and the long friendship that connects us. I am so glad that moving to Munich magically reunited me with my two roommates from Cremona, Kati Tanko and Sandra Dachsel. Meals, hiking excursions, and babysitting with and for them has provided a wonderful balance to work and made us feel instantly at home.

From colleague, friend, roommate to husband, Leon Chisholm has accompanied me along the journey of this dissertation from the very beginning, guiding the way through the genuine originality and thoroughness of his own work. His caring love, unwavering support and loyalty have carried me through and boosted my confidence when I most needed it. I thank him not only for a full round of copy-edits and for answering endless linguistic questions, but also for

x the distractions, for teaching me billiards, for walks and adventures. I am lucky that through

Leon, I have expanded my family with my generous, caring in-laws Jim and Judy, and Jill, Labi,

Nick, and Hayley, who have included me so warmly into their family.

I appreciate the love and generous support from my uncle and aunt Helmut and Uschi, and my late aunt Inge Kralupper. The maturity and judiciousness of my little cousin Matthias has offered many humbling reminders about zooming out from the small frustrations and looking ahead into the future. I am a proud big sister to my sister Maria, whose path I follow with admiration and whose musicality and dedication are inspiring. With lots of love I remember the wit and curiosity of my two grandmothers, and finishing this dissertation makes me humble to think of how much they both would have enjoyed pursuing studies themselves.

My brother Bernhard has been on my side as one of my closest confidants, who I rely on with matters big and small. I admire his intelligence and creativity and am grateful for his calm patience and the humor he shares with all of us, for his hands-on support, hand knit hats and foolproof recipes. From my father, I learned what it means to be passionate about one’s work, to set high goals, and to extend love and support. I cherish our hikes, his encouragement to do what feels right, and the confidence and trust he gives me. Finally, if I listed all the things that I owe to my mother, I would have to write another dissertation, from her intelligence and sensitivity to the love and energy that she has invested in raising us and providing us a care-free childhood full of joy and fantasy. I hope that seeing me finish this Ph.D. will make her proud of what she has helped us achieve. With gratitude, I dedicate this dissertation to my mother, father, and brother.

LIST OF FIGURES AND TABLE

Figure I.1 : Paul Klee, “active line,” Pedagogical Sketchbook 26

Figure I.2 : Wassily Kandinsky, visualization of Beethoven, Symphony No. 5, 1 st 37 movement, mm. 58–65, Point and Line to Plane

Figure I.3 : Wassily Kandinsky, visualization of Beethoven, Symphony No. 5, 1 st 39 movement, mm. 1–5, Point and Line to Plane

Figure I.4 : August Halm, analysis of J. S. Bach, B-flat minor Fugue (BWV 891), as 46 collated by Rehding

Figure I.5 : Pablo Picasso, harlequin, from Cocteau’s treatise Cock and Harlequin 50

Figure I.6 : Fabienne Verdier, “Mélodie du réel” (2014), mounted at the Pinakothek der 52 Moderne in Munich in Fall 2017

Figure I.7 : Paul Klee, “freie Linie,” from the manuscript Bildnerische Formlehre 53

Fi gure II.1 : Ernst Toch, String Quartet No. 9, Op. 26, 3 rd movement, No. 12, score 95

Figure II.2 : The same passage in the cello part, with added cue notes 96

Figure II.3 : The same passage in the viola part, with the wave line to indicate thematic 96 prominence

Figure II.4 : Ernst Toch, String Quartet No. 9, Op. 26, 3 rd movement, No. 2, score 99

Figure III.1 : Friedrich August Kanne, melodic wave line, Der Zauber der Tonkunst 113

Figure III.2 : Ernst Toch, “small wave line,” Melodielehre 113

Figure III.3 : Friedrich August Kanne, annotated wave line with C major scale 120

Figure III.4 : Friedrich August Kanne, examples of scalar fill-ins in a Lutheran melody 126

Figure III.5 : Ernst Toch, Melodielehre , Example 10 130

Figure III.6 : Ernst Toch, Melodielehre , Example 11 130

Figure III.7 : Ernst Toch, Melodielehre , Example 41 132

Figure III.8 : Ernst Toch, Melodielehre , Example 42 132

Figure III.9 : Ernst Mach, Sinnesempfindungen (1896), sketch 143

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Figure III.10 : Mach’s diagram populated with Toch’s theory of the line in aural and 143 visual cognition

Figure III.11 : Michael Polth, representation of “Gerade” Tonhöhenlinie 155

Figure III.12 : Ernst Toch, “large wave line,” Melodielehre 156

Figure III.13 : Ernst Toch, triangle of dramatic organization, adapted after Freytag’s 159 theory, Melodielehre

Figure III.14 : Ernst Toch, Melodielehre , Example 20 161

Figure III.15 : Michael Polth, analysis of Chopin, Mazurka in B-flat major, Op. 7, No. 1, 162 mm. 1–4

Figure III.16 : Ernst Toch, Tonhöhenlinie for Beethoven, Symphony No. 3, Marcia 164 funebre , mm. 36–40, Melodielehre , Example 40

Figure IV.1 : Alexander Truslit, Gestaltung und Bewegung in der Musik , Plate 2 196

Figure IV.2 : Ernst Kurth, Linear Counterpoint , Example 70 208

Figure IV.3 : J. S. Bach, Suite for Solo Cello in E-flat major (BWV 1010), Prelude, mm. 210 1–16, with added annotations

Figure IV.4 : Ernst Kurth, Linear Counterpoint , Example 114 211

Figure IV.5 : J. S. Bach, Suite for Solo Cello in D minor (BWV 1008), Prelude, mm. 25– 215 33, with added annotations

Figure IV.6 : Ernst Kurth, Linear Counterpoint , Example 119 216

Figure IV.7 : Ernst Kurth, Linear Counterpoint , Example 120 217

Figure IV.8 : Max Wertheimer, illustration of the “factor of proximity,” from 221 “Untersuchungen zur Lehre von der Gestalt”

Figure IV.9 : Max Wertheimer, illustration of the “factor of common fate,” from 222 “Untersuchungen zur Lehre von der Gestalt”

Figure IV.10 : Ernst Kurth, Linear Counterpoint , Example 182 227

Figure IV.11 : Ernst Kurth, Linear Counterpoint , Example 183 227

Figure V.1 : Henrik Neugeboren, visualization of J.S. Bach, Fugue in E-flat minor (BWV 246 853), mm. 61 ½–66

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Figure V.2 : Henrik Neugeboren, visualization of J.S. Bach, Fugue in E-flat minor (BWV 250 853), mm. 77–83

Figure V.3 : Ferruccio Busoni, edited score and annotation of J .S. Bach, Fugue in E-flat 251 minor (BWV 853), mm. 45–47

Figure V.4 : Paul Klee, Graphical translation of J.S. Bach, Sonata for Violin and 257 Harpsichord (BWV 1019), Adagio, mm. 1-2, Beiträge zur bildnerischen Formlehre

Figure V.5 : J.S. Bach, Sonata for Violin and Harpsichord (BWV 1019), Adagio, mm. 1– 258 2

Figure V.6 : Paul Klee, “Heroische Bogenstriche“ (1938) 260

Figures V.7 –9: Photographs of Henrik Neugeboren, sculpture, Leverkusen 273

Figure V.10 : J .S. Bach, Fugue in E-flat minor (BWV 853), mm. 52–55 274

Figure VI.1 : Erich Moritz von Hornbostel, annotation of “Melodiebewegung,” Chopin, 287 Waltz in D-flat major, Op. 64, No. 1, mm. 5–12, from “Melodischer Tanz”

Table II.1 : Treatises on Melody, 1874–1937 63

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NOTE ON TRANSLATIONS

All translations are my own unless otherwise noted.

INTRODUCTION : SOME POINTS

Lines seem to be everywhere, and yet they do not exist in nature. Their ubiquitous presence is a product of our minds, as dimensionally compressed reflections of the world around us. Outside our heads, lines reside on the level surfaces of their engraving, as renderings of the cognitive images we perceive. 1 Beyond this diagrammatic understanding, the line is commonly employed as both a metonym and a metaphor. For the anthropologist Tim Ingold, for instance,

“the line” variously connotes such material constitutions as threads or traces. 2 In the realm of music, both views coexist, as lines take different functions and forms of appearance, be it as graphical icons in a diagrammatic sense, or as conceptual metaphors that relate to tangible phenomena and experiences.

In these diverse capacities, the line has animated musical thought through the centuries.

But in the 1920s, German music theorists proved particularly drawn to the line, employing it to designate their new analytical frameworks. Ernst Toch’s Tonhöhenlinie , Ernst Kurth’s linearer

Kontrapunkt , and Heinrich Schenker’s Urlinie are the most prominent manifestations of this trend, among many lesser known examples. But these theoretical conceptions are only the tip of the iceberg. The line also prevailed in compositional notation, graphical analyses, and even in trans-medial artistic interpretations of music from this time. Linear metaphors served to denote

1 In recent scholarship, Sybille Krämer has promoted such an understanding of the line in many of her writings. See for instance Sybille Krämer, “Punkt, Strich, Fläche: Von der Schriftbildlichkeit zur Diagrammatik,” in Schriftbildlichkeit: Wahrnehmbarkeit, Materialität und Operativität von Notationen , ed. Sybille Krämer, Eva Cancik-Kirschbaum, and Rainer Totzke (Berlin: Akademie Verlag, 2012), 79– 100, and Sybille Krämer, “Flattening as Cultural Technique: Epistemic and Aesthetic Functions of Inscribed Surfaces,” as part of the Colloquy “Discrete/Continuous: Music and Media Theory after Kittler,” ed. Alexander Rehding, Journal of the American Musicological Society 70, no. 1 (2017): 240. 2 Tim Ingold, Lines: A Brief History (London: Routledge, 2007), and The Life of Lines (London: Routledge, 2015).

contemporary trends in composition, choreographic schemes of music performance, as well as theoretical models to analyze a variety of musical styles of the past, and they characterized both conservative and modernist aesthetic ideologies.

This dissertation asks, what motivated the widespread use of this imagery in music and related disciplines in this particular cultural-historical context? In pursuing answers, I draw out the discursive and representational potential that the line assumed in the dialogue with such disciplines as cognition, Gestalt psychology, and the visual arts. The triangular frame of music, visual culture, and psychological research not only acknowledges the fundamentally imaginary condition of the line, but also anchors my inquiry at the intersection of three disciplinary narratives. An understanding of what constituted a line—and, more specifically, a musical line— in the early twentieth century emerges only when these strains of thought are brought together.

In that vein, I start by exploring the cultural and intellectual conditions in these disciplines, to investigate how the line became a favored analogy for musical phenomena. By reviewing the formation of new theories of the line in the visual arts, I trace the ascription of a dynamic and temporal dimension to the line, itself contingent on paradigm shifts in science and philosophy. Artists and psychologists alike promoted an embodied understanding of the line, as a manifestation of the painter’s physical gesture, to be traced by the viewer. This conception mirrored the way in which music theorists talked about melody in the early twentieth century, trying to allay the tension between, on the one hand, melody’s construction of discrete tones and its transitory appearance and, on the other, its perception as a holistic entity. Their very first challenge, even at this basic level, was to correlate physical, physiological, and psychological concerns. Their inquiries not only engendered new theories of auditory and visual cognition, but also, in turn, solidified the epistemological grounds for forging an analogy between aural and

visual phenomena. 3 I argue that these conditions and the newly established definition of the line encouraged its mapping onto music, and facilitated new aesthetic interpretations of this analogy.

Melody thus emerges, in the convergence of artistic, musical, and psychological theories in the early twentieth century, as the foremost musical parameter to be depicted through a line.

This pairing of linear thought and representation and melodic construction constitutes the focus of my dissertation. I trace how melody and the line shared a parallel history of rediscovery and emancipation from traditional functional ties within their respective disciplines. With regards to music history, this contextualization at the intersection of developments in art and psychology at once fills a conspicuous gap in scholarship to date. For while the trend towards melody and linear-horizontal trajectories in music in the early twentieth century might constitute a commonplace in the histories of music and music theory, the backdrop to these developments has remained mostly unexplored.

Melody rose to renewed prominence in the early 1900s, in both music theory and compositional practice. For one, with the dissolution of common-practice harmony, composers structured their music increasingly through horizontally oriented principles. In parallel, music theorists started to usher melody out of the shadow of nineteenth-century harmony treatises. An essay by German musicologist Michael Polth observes a heightened production of treatises on melody around the turn of the twentieth century, and particularly in the 1920s. His analysis positions this phenomenon primarily within the lineage of nineteenth-century treatises on

3 I follow the definitions of analogy and metaphor as proposed by Larson: “Metaphors are cross-domain mappings, and all metaphors are analogies.” In Larson’s understanding, analogies do not necessarily entail mappings across domains. Steve Larson, Musical Forces: Motion, Metaphor, and Meaning in Music (Bloomington: Indiana University Press, 2012), 323 and 328.

harmony. 4 David Trippett’s study of the aesthetic debates on melody in the era of Richard

Wagner elucidates the stakes that theorizing melody still entailed around 1900, with melody being considered the locus of emotional expression, individuality, and originality, and the product of unconscious and effortless intuition in the genius composer’s mind.5 Trippett’s purview breaks off at the moment in which music theorists finally overcame the hurdles that he discusses. My dissertation enters at this point and asks what resources and strategies facilitated the formation of dedicated theories of melody in the 1920s.

My focus on the relationship between the line and melody not only highlights the myriad ways in which they are and have been entwined, but also lays the foundation for considerations of the potential that the line holds with regard to such musical parameters as harmonic progression and musical form. Examples of such applications might include contour graphs in a draft of Arnold Schoenberg’s compositional treatise Fundamentals of Musical Composition and in the Gedanke manuscript (1921–34), harmonic charts that his assistant Leonard Stein assigned to students at UCLA, as well as Hans Mersmann’s diagrams of musical form in Angewandte

Musikästhetik (1926). Furthermore, such investigations ought ideally to address the use of diagrammatic notational systems in composition and music analysis, as they started to become popular in the early decades of the twentieth century. Joseph Schillinger’s notational system, which he developed in the 1920s and 30s as an accompaniment to his theory of composition, would serve as a good example of this trend.

4 Michael Polth, “Zwischen Gestaltpsychologie und Funktionalität: Anmerkungen zur Melodielehre von Ernst Toch,” in Spurensicherung: der Komponist Ernst Toch (1887-1964) – Mannheimer Emigrantenschicksale , ed. Hermann Jung (Frankfurt/Main: Peter Lang, 2007), 101–19. 5 David Trippett, Wagner’s Melodies: Aesthetics and Materialism in German Musical Identity (Cambridge, UK: Cambridge University Press, 2013).

Throughout, I aim at exposing music theory’s interdisciplinary foundations and ties, by tracing specific ideas across the work not only of music theorists, but also of experts in other fields. As I elucidate, music theorists framed their interrogation of melody in psychological terms just as melody, conversely, served as a primary site for psychologists researching cognitive processes of memory, anticipation, and recognition. Similarly, visual artists explored graphical functions of the line by applying it in the representation of music just as music theorists leaned on the dynamic re-conception of the line in the visual arts when formulating their analytical perspectives. Reconstructing these constellations allows me to expand on predominant narratives in the history of music theory. In tracing methodological frames and collaborations with other disciplines that shaped music-theoretical thought, scholars such as Alexandra Hui, Youn Kim,

Alexander Rehding, Benjamin Steege, and Elizabeth West Marvin have delineated a shift around the turn of the twentieth century from an acoustic to a psychological paradigm. 6 I contribute new sources from music theory and cognitive research to substantiate this trend and connect these developments to the evolution of melody in musical thought. Moreover, I uncover how these aspirations stimulated the visual imagination of the thinkers involved, and projected music into a graphical reality.

As with the above studies, the center of attention in this dissertation will lie on German culture. Austria, Germany, and Switzerland, were the cradle not only of Gestalt theory, but also of the most prominent linear conceptions in music theory. Certainly, notions of the melodic line

6 Alexander Rehding, Hugo Riemann and the Birth of Modern Musical Thought (Cambridge, UK: Cambridge University Press, 2003), 34, captures this shift as a turn from the “age of acoustics” to the “age of psychology” in the history of music theory. See also Alexandra Hui, The Psychophysical Ear: Musical Experiments, Experimental Sounds, 1840-1910 (Cambridge, MA: MIT Press, 2012), Youn Kim, “Theories of Musical Hearing, 1863-1931: Helmholtz, Stumpf, Riemann and Kurth in Historical Context” (Ph.D. dissertation, Columbia University, 2003), Benjamin Steege, Helmholtz and the Modern Listener (Cambridge, UK: Cambridge University Press, 2012), Elizabeth West Marvin, “Tonpsychologie and Musikpsychologie: Historical Perspectives on the Study of Music Perception,” Theoria 2 (1987): 59–84.

extended far beyond this specific cultural context, as I discuss in the first chapter, but even then, their application often propagated the hegemony of German cultural heritage. As I illustrate, also in discussions in France and the United Kingdom, for instance, Johann Sebastian Bach’s polyphonic music, and the symphonies of Ludwig van Beethoven were treated as exemplars not only of the compositional styles of their eras, but also featuring particularly linear melodies.

When Bach and Beethoven enjoy a recurrent presence in this dissertation, this prevalence is representative of the esteem that they received as lodestars of linear-melodic composition and theory in the early twentieth century across national boundaries and cultural hostilities.

Besides these musical styles of the past, music theorists and critics of the 1920s also advocated for modernist compositional tendencies of their day as a noteworthy instantiation of a

“linear music.” Each of the theorists portrayed in this dissertation employed the line to advance their respective cultural-political agenda, and more often than not they clashed in debates over the appropriation of a shared cultural idol for a specific ideological program.

In addition to numerous supporting characters, I focus my analyses on the work of two

Viennese-born music theorists, Ernst Kurth (1886–1946) and Ernst Toch (1887–1964). While minor similarities between the two theorists’ biographies and writings have been noted, the comparison remains superficial. 7 I examine Kurth’s and Toch’s conceptions of the line—and their mutual relationship—in greater depth, reading them as two related though distinct approaches to the line, and analyzing their similarities and points of divergence. In the writings of both theorists, the melodic line indeed occupied a prominent position. In my analysis of their

7 Luitgard Schader, “Das Verhältnis von Ernst Tochs ‘Melodielehre’ zu Ernst Kurths ‘Grundlagen des linearen Kontrapunkts,’” Musiktheorie 18, no. 1 (2003): 51–64. Based on overlaps in Toch’s and Kurth’s educational background, and some observations about similarities in their treatises, Schader has accused Toch of leaving Kurth’s influence unacknowledged. These allegations are also perpetuated in Polth, “Zwischen Gestaltpsychologie und Funktionalität.” I attend to Schader’s arguments in detail in Chapters 2 and 3.

texts, I start by considering Toch’s notion of the Tonhöhenlinie (“pitch line”) from his

Melodielehre (1923). Concentrating on melodic formations on the musical surface, Toch observed structural features of melody across diverse, but mostly homophonic, repertoires. From this focus on the single line, I progress to examining how Kurth theorized the interweaving of multiple melodic trajectories as they develop simultaneously in Bach’s polyphonic compositions in his Grundlagen des linearen Kontrapunkts: Bachs melodische Polyphonie (Foundations of

Linear Counterpoint: Bach’s Melodic Polyphony , 1917).

The combined analysis of Toch’s and Kurth’s treatises reveals an essential—if only implicitly stated—limitation to their linear-melodic conceptions, namely the predilection for step-wise melodic progressions. In addition to investigating how this restriction played out in the treatises at hand, I demonstrate how it correlates with a Gestalt-theoretical principle that Max

Wertheimer codified in 1923 as the “factor of proximity.” 8 This psychological backdrop also undergirded other linear approaches to melody, including Heinrich Schenker’s famous Urlinie .

Schenker developed his theory of the Urlinie over a time span of more than ten years, with early remarks in the Erläuterungsausgabe of Beethoven’s piano sonata op. 101 (1921) and the first volumes of Der Tonwille (published between 1921 and 1924)—around the same time as

Toch’s and Kurth’s writings—up to the most expanded exploration of the concept in Der freie

Satz (Free Composition , 1935). 9 The impact that Schenker’s theories exerted on the formation of

8 Max Wertheimer, “Untersuchungen zur Lehre von der Gestalt. II,” Psychologische Forschung: Zeitschrift für Psychologie und ihre Grenzwissenschaften 4 (1923): 301–50. 9 Heinrich Schenker, Die letzten fünf Sonaten von Beethoven: Sonate A Dur Op. 101, Erläuterungsausgabe , Wiener Urtext Ausgabe (Vienna: Universal-Edition, 1921) and Schenker, Der Tonwille. Flugblätter (Vierteljahrschrift) zum Zeugnis unwandelbarer Gesetze der Tonkunst einer neuen Jugend dargebracht von Heinrich Schenker, 10 vols., (Vienna: Universal Edition, 1921–24), available in translation as Schenker, Der Tonwille. Pamphlets in Witness of the Immutable Laws of Music: Offered to a New Generation of Youth , ed. and trans. William Drabkin, 2 vols. (Oxford; New York: Oxford University Press, 2004), Schenker, Der freie Satz: das erste Lehrbuch der Musik , Neue musikalische

academic music theory, especially in North America, is widely known. His legacy has been studied much more extensively than either of the theorists featured in this dissertation. 10 But

Schenker’s reception soared in particular after his death, to the extent that his Urlinie is likely the first concept that comes to mind of music theorists today when triggered with the allusion of

“line.” For the aesthetic debates of the 1920s that I focus on in this dissertation, however, the figures of Kurth and Toch were much more integral. As I show, Kurth’s treatise catapulted the keyword of “linearity” into contemporary music criticism, while the work of Toch and other modernist composers incited debates about its rightful application.

Still, my inquiries into Kurth’s and Toch’s ideas and the cultural and intellectual context around them will also illuminate some important aspects of Schenker’s Urlinie . In particular, attending to the shared psychological and phenomenological conditions to these music- theoretical conceptions draws attention to some critical limitations that they entail in their selectivity of certain melodic formations over others. On this basis, I compare the different ways in which cognitive mechanisms impacted the music-analytical perspectives that these music theorists propounded and the observations that they allow for.

Theorien und Phantasien 3 (Vienna: Universal Edition, 1935). Within the panoply of scholarship on Schenker’s theory, the following in particular address pertinent historical context for notions of the Urlinie : Norman Douglas Anderson, “The Development of the Concept of ‘Line’ in the Writings of Heinrich Schenker” (M.A. thesis, University of Texas at Austin, 1983), Suzannah Clark, “The Politics of the Urlinie in Schenker’s ‘Der Tonwille’ and ‘Der Freie Satz,’” Journal of the Royal Musical Association 132, no. 1 (2007): 141–64, David Neumeyer, “The Ascending ‘Urlinie,’” Journal of Music Theory 31, no. 2 (October 1987): 275–303, Hedi Siegel, “Looking at the Urlinie,” in Structure and Meaning in Tonal Music: Festschrift in Honor of Carl Schachter , ed. L. Poundie Burstein and David Gagné (Hillsdale, NY: Pendragon Press, 2006), 79–99. 10 On the dissemination and influence of Schenker’s thought in North American academia, see for instance William Rothstein, “The Americanization of Heinrich Schenker.” In Theory Only 9, no. 1 (1986): 5–17, and David Carson Berry, “Schenkerian Theory in the United States: A Review of Its Establishment and a Survey of Current Research Topics.” Zeitschrift der Gesellschaft für Musiktheorie 2– 3, no.2 (2005): 101–37.

I intend the ideas offered here to radiate outwards to scholarship in the visual arts and in

psychology, as much as I draw on research in these disciplines. I envision this contribution in at

least three ways. First, within growing research on relations between the arts—now often termed

comparative arts—perspectives from music scholars are still noticeably underrepresented. This

holds true equally for constellations of inter-media and multimedia, as a common taxonomy

classifies the intersection between artistic media.11 In particular with the increasing tendency to couple the audio and visual in modern and contemporary art, scholars have been hard pressed to stake out the collaborations and material configurations that these transmedial couplings entail and the expertise and methodologies that they demand. Dedicated studies on “Visual Music” form only a small part of this trend, while some recent edited volumes take a more encyclopedic approach. 12

A large body of scholarship is devoted to early twentieth-century Modernism, a golden

age for inter-artistic cross-pollination, as I review in Chapter I, and in particular on the audio-

visual nexus. As one of the founding fathers of comparative arts in its modern guise, Daniel

11 Such a distinction is advocated for instance by Daniel Albright, Panaesthetics: On the Unity and Diversity of the Arts , Anthony Hecht Lectures in the Humanities (New Haven, CT: Yale University Press, 2014), 209, and Simon Shaw-Miller, Visible Deeds of Music: Art and Music from Wagner to Cage (New Haven, CT: Yale University Press, 2002). See also the writings of philosopher Jerrold Levinson on hybridity in the arts, such as Levinson, “Hybrid Art Forms,” Journal of Aesthetic Education 18, no. 4 (1984): 5–13; Levinson, Music, Art, and Metaphysics: Essays in Philosophical Aesthetics (Oxford: Oxford University Press, 2011). 12 In the vast body of literature, two rather different approaches are represented by Kerry Brougher and Olivia Mattis, Visual Music: Synaesthesia in Art and Music since 1900 (New York: Thames & Hudson, 2005), and Nicholas Cook, Analysing Musical Multimedia (Oxford: Clarendon Press, 1998). The conception of “Visual Music” goes back to painter and critic Roger Fry, who envisioned “creating a purely abstract language of form” when he coined the designation in 1912. Two comprehensive edited volumes are Tim Shephard and Anne Leonard, The Routledge Companion to Music and Visual Culture (London: Routledge, 2013), and Yael Kaduri, The Oxford Handbook of Sound and Image in Western Art (Oxford: Oxford University Press, 2016).

Albright’s extensive work takes a remarkably balanced and broad approach.13 In such volumes as

Karin von Maur’s The Sound of Painting , Peter Vergo’s The Music of Painting , or Music and

Modernism, c. 1849–1950 edited by Charlotte de Mille, and the work of Simon Shaw-Miller, the

allure of music for the visual arts is discussed primarily from the perspective of art historians. 14

Complementary views are offered in such contributions as the chapter on “Convergences: Music

and the Visual Arts” in Walter Frisch’s monograph German Modernism: Music and the Arts ,

and, with a specific focus on ornament and the arabesque in fin-de-siècle France, the work of

Gurminder Bhogal.15 Scholars like Siglind Bruhn and Orit Hilewicz, meanwhile, focus on cases

of musical ekphrasis—relating to musical compositions that take inspiration from other art

forms—and explore the challenges and potential that such compositions raise for music analysis

and critical listening. 16

Second, while many of these studies focus on examples from artistic practice, my research attends to manifestations of inter-artistic ambitions in contemporaneous theoretical discourse and explores the historical context in which these ideas originated. Here, music theory emerges as an informant to the growing research field of comparative arts. Moreover, the

13 Among Albright’s numerous books on the subject, the following are the most pertinent to my research: Albright, Untwisting the Serpent: Modernism in Music, Literature, and Other Arts (Chicago: University of Chicago Press, 2000), Panaesthetics , and Putting Modernism Together: Literature, Music, and Painting 1872-1927 (Baltimore: Johns Hopkins University Press, 2015). Albright himself designates Horace and Gotthold Ephraim Lessing as the “two patron saints to the study of comparative arts.” Albright, Untwisting the Serpent, 8. 14 Charlotte De Mille, ed., Music and Modernism, c. 1849-1950 (Newcastle upon Tyne: Cambridge Scholars, 2011), Karin von Maur, The Sound of Painting (Munich: Prestel, 1999), Peter Vergo, The Music of Painting: Music, Modernism and the Visual Arts from the Romantics to John Cage (New York: Phaidon, 2010), Simon Shaw-Miller, Visible Deeds of Music , and Eye hEar the Visual in Music (Burlington, VT: Ashgate, 2013). 15 Walter Frisch, “Convergences: Music and the Visual Arts,” chap. 3 of German Modernism: Music and the Arts (Berkeley: University of California Press, 2005), 88–137, Gurminder Kaur Bhogal, Details of Consequence: Ornament, Music, and Art in Paris (Oxford: Oxford University Press, 2013). 16 Siglind Bruhn, Musical Ekphrasis: Composers Responding to Poetry and Painting (Hillsdale, NY: Pendragon Press, 2000), Orit Hilewicz, “Listening to Ekphrastic Musical Compositions” (Ph.D. dissertation, Columbia University, 2017).

theoretical apparatus that I reconstruct from the intertwined histories in art, science, psychology, and music resonates across a range of musical practices, encompassing composing, notating, analyzing, performing, and listening. It is from that perspective that my research brings together a diverse range of sources that may at first appear heterogeneous, including theoretical and journalistic writings, artistic and analytical illustrations, compositions, paintings, and sculpture.

Third, this dissertation approaches the topic of linearity from a musical perspective. The impact of the line on European culture around the turn of the twentieth century has recently attracted renewed attention from art historians and cultural historians alike. Besides Régine

Bonnefoit’s cogent study of linear theories around Paul Klee, Sabine Mainberger’s monograph

Experiment Linie: Künste und ihre Wissenschaften um 1900 offers the most comprehensive account of the myriad ways in which the fascination with lines manifested itself at that time, from literary theories to fashion and design.17 Despite the all-encompassing title, however, music and the aural domain are strikingly underrepresented in that study, appearing only in two footnotes that promote the investigation of linear musical thought of the time as a desideratum for future scholarship. 18 My dissertation responds to this call, and integrates music and music theory as vital participants in this widespread historical phenomenon. As my research demonstrates, music was indeed an important arena for testing new conceptions of the line, exposing its representational potential as a dynamic, temporally evolving gesture.

17 Régine Bonnefoit, Die Linientheorien von Paul Klee (Petersberg: Michael Imhof, 2009), Sabine Mainberger, Experiment Linie: Künste und ihre Wissenschaften um 1900 (Berlin: Kulturverlag Kadmos, 2010). 18 Mainberger, Experiment Linie . The two footnotes related to music refer to Ernst Kurth (111n74) and Eduard Hanslick (131n141).

Overview of Chapters

The two opening chapters situate my discussion within discourses on line in the visual arts and melody in music. Chapter I asks how a line could become a sounding entity, as numerous artists and art critics invoked in their writings. I trace these notions across the visual arts, theories of time and space, theories of embodiment and cognition, Gestalt psychology, and music. My explorations take as their starting point early twentieth-century practices and theories of the line in the visual arts. I review how the trend towards abstraction emancipated the line from its traditional representational functions, such as in delineating contour and aiding the illusion of perspective, and elevated it to an independent graphical means of expression. Artist

Paul Klee’s concept of the “active line,” which generates itself through a point set in motion, epitomizes the newly gained agency of the graphical line. Moreover, Klee’s theory illustrates how the line became infused with connotations of temporality and dynamism. I argue that this potential of the line to delineate temporal processes facilitated its association with melody.

Theories of embodiment and cognition further inscribed in the line the temporal processes of its creation by the draughtsman and of its re-enactment by the viewer. The sources that I employ in this narrative moreover illuminate the widespread appropriation of the line in different national and cultural contexts across Europe, alongside the political contentions attached to it in both the visual arts and in music. To demonstrate the topicality of this historical framework for visual art today, I analyze a series of paintings titled “Mélodie du réel” by French artist Fabienne Verdier from 2014, in which the various theories I discuss converge.

Chapter II traces parallel developments in music that led to the conceptualization of melody as an independent musical parameter in the early decades of the twentieth century, traversing music theory, composition, performance, printing, and debates on musical aesthetics.

First, I review the aesthetic concerns surrounding theoretical approaches to melody in the nineteenth century and explore the extent to which these concerns persisted into the new century.

In the 1910s and 20s, most protagonists of these debates were composers, and their views reflect how melody inhabited a contentious place between conservative and avant-garde ideologies. To examine the compositional trends in the 1920s, I analyze Ernst Toch’s String Quartet Op. 26

(1919/20), which showcases the challenges of the new stylistic tendencies for performers, music printers, listeners, and critics. Finding his compositional intent thwarted by the limitations of conventional music notation, Toch resorted to graphical wave lines drawn in the instrumental parts to support the performers in rendering the horizontally stratified musical texture. The reception history of the composition in turn documents how the new compositional style required listeners and critics to adjust not only their expectations, but also their vocabulary to account for the music of their time. I conclude the chapter by surveying the ensuing prominence of the line and “linearity” as descriptive metaphors in music journals of the 1920s.

In Chapter III, I return to some of the cognitive and Gestalt-theoretical research from the turn of the twentieth century that I discussed in the opening chapter to investigate in more detail how this new epistemic framework affected linear metaphors in music theory. To demonstrate the explanatory potential afforded by these theories, I compare two music-theoretical applications of the line in Friedrich August Kanne’s “Der Zauber der Tonkunst” (“The Magic of

Music,” 1821) and Toch’s Melodielehre (1923). While the sine-shaped wave lines that the two theorists drew to represent melody look strikingly similar at first sight, I explore how they connote quite different aesthetic perspectives, each building on the respective intellectual context of their times. Specifically, while both sought to approximate the graphical continuity of the line in musical terms, I argue that the cognitive framework available to Toch opened up new

expressive possibilities in his employment of the line. I trace the formation of pertinent contributions from Ernst Mach’s theories of sensory perception (1886/96) to Christian von

Ehrenfels’s “On ‘Gestalt Qualities’” (1890/1922) and the Viennese school of psychology founded on his ideas.

I expand this contextualization within the emergence of experimental psychology in

Chapter IV, which is centered on Kurth’s 1917 treatise Grundlagen des linearen Kontrapunkts:

Bachs melodische Polyphonie (Foundations of Linear Counterpoint: Bach’s Linear Polyphony ).

Opening this monograph with the programmatic announcement to “penetrate counterpoint using the line as unit and primordial entity,” Kurth promoted a horizontally oriented understanding of polyphony that prioritized the linear coherence of its individual contrapuntal voices over a vertical-harmonic analysis.19 Focusing on the polyphonic music of Johann Sebastian Bach,

Kurth’s analyses expand on the predominantly homophonic repertoires that Toch considered in his Melodielehre . I examine how Kurth codified ever more specifically the typical forms of the lines that he derived from that repertoire, particularly in examples of “apparent polyphony”

(“Scheinpolyphonie”). The attendant objective of extracting a predetermined classification of linear melodic shapes parallels the approach of Schenker’s Urlinie and exposes resonances with

Wertheimer’s Gestalt-theoretical principles as published in 1922–23.

While these chapters chronicle how music theorists harnessed dynamic geometrical and artistic definitions of the line, Chapter V pursues an inverse methodological approach to analyze linear-musical renderings in the visual arts. Focusing on artistic visualizations of musical compositions by artists at the Bauhaus—notably Wassily Kandinsky, Paul Klee, and Henrik

19 “In die Kontrapunktik von der Linie als Einheit und Urgebilde aus einzudringen.” Ernst Kurth, Grundlagen des Linearen Kontrapunkts: Einführung in Stil und Technik von Bach’s melodischer Polyphonie (Bern: Max Drechsel, 1917), ix. The emphasis is original.

Neugeboren—I appraise the visual theories explored in Chapter I in artistic practice. My analysis uncovers how the artists inscribed profoundly performative and analytical interpretations of the music in question within their visual renderings. Indeed, I read these artistic displays as material manifestations of the performance practice of their day, proposing thus an additional interpretive layer to Kandinsky’s example (which I also analyze in Chapter I). Moreover, I show how these two-dimensional graphs and the related sculpture mirror the music-theoretical ideas and the underlying cognitive concepts that I discussed in the previous chapters. In particular, I demonstrate how Klee’s and Neugeboren’s visual translations of Bach’s music resonate with

Kurth’s theory of linear polyphony. My analyses of these depictions are informed by the recent scholarship of Sybille Krämer, who has theorized the epistemic potential of diagrammatic visualizations.20 Against this backdrop, I investigate the allure of hand-drawn, linear annotations in contrast to mechanical, discrete representations of music, and of the line in comparison to a row of dots. This approach solidifies the convergence of cognitive, artistic, and musical principles in the melodic line that I portray.

While this dissertation excavates the convergence of interdisciplinary strains of thought in a historically defined moment, the readings that I present have a bearing on developments over the entire twentieth century and up to today. Put simply, the music-theoretical concepts at the center of my investigation were nothing short of foundational for the academic discipline of music theory. They continue to shape the way that we think about music today. Indeed, notions of musical linearity persist in common musical parlance. Musicians speak of lines to be brought

20 Sybille Krämer, “Punkt, Strich, Fläche: Von der Schriftbildlichkeit zur Diagrammatik,” in Schriftbildlichkeit: Wahrnehmbarkeit, Materialität und Operativität von Notationen, ed. Sybille Krämer, Eva Cancik-Kirschbaum, and Rainer Totzke (Berlin: Akademie Verlag, 2012), 79–100; Krämer, Figuration, Anschauung, Erkenntnis: Grundlinien einer Diagrammatologie (Berlin: Suhrkamp, 2016); and Krämer, “Friedrich Kittler - Kulturtechniken der Zeitachsenmanipulation,” in Medientheorien: Eine philosophische Einführung , ed. Alice Lagaay and David Lauer (Frankfurt/Main: Campus, 2004), 201–24.

out in performance, as much as music teachers instruct their students to listen for particular lines of the musical texture, perhaps even encouraging them to visualize these lines in a sort of proto- notation. The aesthetic connotations tacitly attributed to the line in such instances—such as continuity, coherence, immediacy, dynamism, motion, and expressivity—are firmly rooted in the historical context that I develop in this dissertation.

I. SOUNDING LINES

Es ist bekannt, was eine musikalische Linie ist (siehe Fig. 11).* [Footnote: ] Die Linie wächst organisch aus Punkten heraus. 1 What a musical line is, is well known (see Fig. 11).* [Footnote: ] The line grows organically out of points.

In an essay on “Farbe und Linie” (“Color and Line”) published in the Viennese cultural journal Wiener Rundschau in 1900, art and literature critic Anton Lindner talked of the graphical line metaphorically as a sonic phenomenon (“eine wundersam klingende Linie”).2 Extending the allegory, he also observed the tendency of lines to intertwine sonically (“klingend ineinander zu greifen”). Such allusions to the sounds that a line might represent or elicit have been perpetuated almost as a matter of course to the present day. At the end of this chapter, an artwork from 2014 by French painter Fabienne Verdier illustrates how lines continue to evoke sound—most commonly in the form of melody—in the visual arts of today. But how exactly does a line sound? I mean this question in its dual sense to ask both “What might a line sound like?” and

“How does a line come to evoke sound in the first place?”

These questions take us back to the time of Lindner and urge us to inquire into the conditions in which he propositioned his poetic invocation of sounding lines. Already around the turn of the twentieth century, Lindner was far from alone in such ruminations. In spite of the

1 Wassily Kandinsky, Punkt und Linie zu Fläche: Beitrag zur Analyse der malerischen Elemente , vol. 9, Bauhausbücher (Munich: Albert Langen, 1926), 92. English translation Point and Line to Plane: Contribution to the Analysis of the Pictorial Elements , trans. Hilla Rebay and Howard Dearstyne (New York: Solomon R. Guggenheim Foundation, 1947), 98. 2 Anton Lindner, “Farbe und Linie. Ein Versuch,” Wiener Rundschau 4 (1900): 2–6 and 31–6, esp. 3 (“eine wundersam klingende Linie,”) and 4 (“die Tendenz der Linien, klingend ineinander zu greifen”). Lindner served as editor of that journal. For a reading of Lindner’s text that highlights the physiological and psychological theories it invokes, see Régine Bonnefoit, Die Linientheorien von Paul Klee (Petersberg: Michael Imhof, 2009), 25.

epoch-making political and social disruptions, which significantly transformed cultural and intellectual life especially in Germany and Austria in the subsequent decades, the musical line continued to preoccupy thinkers across Europe. In the 1920s, many composers, performers, listeners, music theorists, artists, and art critics similarly proffered their ideas about the musical line. In this context, the statement by artist Wassily Kandinsky that “what a musical line is, is well known”—as quoted in the epigraph—was certainly topical. But while this proclamation suggests a uniformly accepted notion of the musical line at that time, a coherent understanding of even just some common characteristics that would define the musical line was explicated neither in Kandinsky’s treatise nor in any other single source of the era. Rather, each author contributed their own perspectives, with surprisingly little explicit cross-reference or acknowledgment of pertinent influences and ideas.

A holistic image of the discourse around the musical line can only emerge from drawing together these diverse accounts. As we shall see, the complementary perspectives stemming from the visual arts, music, and cognitive research are vital in examining not only the nature of the diverse conceptions of the musical line in their own right, but also their interrelations and dependencies. Rather than seeking a single, ultimate definition of “the musical line”—even within the specific context of the 1920s—I am interested in distilling commonalities and differences, and in assembling an array of aesthetic connotations that the musical line assumed in its various applications. These explorations will moreover illuminate possible reasons for the popularity of this imagery and metaphor at that particular moment in history.

Setting the trend for the dissertation overall, this chapter traces creative and theoretical trajectories within the visual arts, science, psychology, composition, and music theory and examines their confluences. It attends to fluctuating definitions of the line in the histories of

geometry and the visual arts, and to the question of which particular musical phenomena they mapped onto, a predilection that was similarly a function of history. I investigate circumstances outside these disciplines that aided their cross-fertilization, in order to provide a theoretical foundation for translating between a musical and a primarily graphical idea, or indeed an aural and visual sensation. This last issue, framed within debates in the visual arts as the line’s natural habitat, will be the starting point to my explorations.

Between the Arts, Physics, and Psychology

The period from 1850 to 1920 witnessed some significant re-alignments in the arts and sciences that had a direct bearing on thinking about lines. We can pick up the thread with our

Viennese critic Lindner. Lindner’s essay was an art-philosophical position paper, framed as a critique of the then current exhibition of the Viennese Secession. In it, the sounding line constitutes a recurrent idea, but not the crux of the argument. Rather, Lindner sought to explain effects induced by visual artworks, such as the illusion of a spatial perspective

(“Raumwirkung”), through subjective, psychological processes. In musical terms, this approach was reminiscent of the way in which Eduard Hanslick assigned the creation of meaning in music to the individual listener’s mind in Vom Musikalisch-Schönen (1854). As their common source of reference, both authors appealed to the work of Hermann Lotze, who had established associative relationships between psychic phenomena and the physical world.3 With this backdrop, Lindner

3 On page 6 of his essay, Lindner quoted from Hermann Lotze, Über den Begriff der Schönheit (Göttingen: Vandenhoeck and Ruprecht, 1845). Eduard Hanslick, Vom Musikalisch-Schönen: Ein Beitrag zur Revision der Aesthetik der Tonkunst (Leipzig: R. Weigel, 1854). Hanslick, too, took inspiration from Lotze’s theories. On the relationship between Lotze and Hanslick, see for example Franz Michael Maier, “Lotze und Zimmermann als Rezensenten von Hanslicks ‘Vom Musikalisch-Schönen,’” Archiv für Musikwissenschaft 70, no. 3 (2013): 209–26.

mapped his perceptions from one domain to those of another. Besides the allusion to sounding lines quoted earlier, he asserted,

Man kann dieses Tendieren der Linie, das vielleicht gleichfalls nur eine optische Täuschung ist, beispielsweise … an Schienensträngen beobachten, die in unendlicher Curve durch die Felder gleiten und in endloser Melodie sich krümmen und zu wachsen scheinen. 4 One can observe this tendency of the line, which might similarly be only an optical illusion, … for instance in train tracks, which glide through the fields in an infinite curve and wind and seem to grow in an endless melody.

In passages like this, Lindner intimated many ideas that we shall encounter again throughout this chapter, where they arise as central premises to formulations of the musical or sounding line. The above quotation, for instance, casually implies the sensation of movement and growth in the line, which might be perceived both visually (in the gliding of the line through the fields) or aurally (in the winding and growing of melody). While Lindner still hesitantly considered these sensations as potential “illusions,” both the capturing of motion in the line and the psychological orientation of his approach heralded trends that were constitutive for the reframing of the line as a pictorial element in the early twentieth century. Lindner indeed envisioned the impact of emerging theories of perception and cognition in radical and comprehensive ways. He posited no less than the cultural and historical variability of perception, making subjective impressions the foundation to art-analytical studies:

Dass diese Vorgänge sich zum großen Theile in unseren Nerven abspielen und objectiv nicht bestehen, kann gleichgiltig sein; wir haben eben anders sehen gelernt als die Laokooniden—und andere Empfindungen verlangen andere Begriffsbildungen, wenn auch der Empfindungs-Erreger derselbe geblieben ist seit vielen Jahrhunderten. 5 That these processes occur, for the majority, in our nerves and are not objectively existent can be irrelevant. We have simply learned to see differently than the Laocoonists. And

4 Lindner, “Farbe und Linie,” 3. 5 Lindner, “Farbe und Linie,” 3.

different sensations require different terminology, even if the stimuli triggering the sensations have remained the same for many centuries.

Lindner emphasized the need for new vocabulary to properly account for these new, culturally situated impressions. This call for lexical expansion was seemingly answered in the variety of terms through which physiologists, psychologists and visual artists of the early 1900s interpreted the same physically manifest linear shapes (I return to some of these below). Under the auspices of evolving scientific paradigms, these thinkers probed the different ways in which a line could be created and perceived. In turn, they shaped new terminological distinctions between linear concepts, alongside a wealth of aesthetic connotations attached to the line. As

Lindner suggested, the theoretical framework through which the line was viewed determined its potential to embody musical qualities. And on a meta-level, the frameworks of the early twentieth century situate the flourishing discourse on musical lines firmly within a specific cultural and intellectual context.

In the above quotation, Lindner’s maneuver to dissociate himself from the perceptions of the “Laocoonists” (“Laokooniden”) hints at the monumental debate in the philosophy of the arts that had grown over the centuries around the famous sculpture of Laocoon and His sons, now housed in the Vatican Museums. A landmark reference, Gotthold Ephraim Lessing’s Laocoön:

An Essay on the Limits of Painting and Poetry from 1766 foregrounded a proposed separation of the arts into purely spatial and purely temporal forms of expression.6 According to Lessing, in the sculpture, Laocoon’s suffering as he battled the snakes, seeking to defend his two sons, could not be fully depicted. Not only was sculpture required to fulfill criteria of beauty that thwarted realistic expressions of pain, but moreover it was constrained to rendering a single moment, in

6 Gotthold Ephraim Lessing, Laocoön: An Essay on the Limits of Painting and Poetry , ed. and trans. Edward Allen McCormick (Indianapolis: Bobbs-Merrill, 1962), original Laokoon, oder über die Grenzen der Mahlerey und Poesie (Berlin: C.F. Voss, 1766).

contrast to poetry’s temporal unfolding. Accordingly, while Virgil recounted Laocoon’s screams in the Aeneid , the Trojan priest’s mouth had to be closed in the sculpture, following the pictorial laws of Antiquity. In more general terms, sonic and visual art forms were theorized as catering to different sensual experiences. 7

With his free associations across senses and perceptions, Lindner, by contrast, targeted a much more unified conception of the arts. Already the very idea of a musical line unites forms of expression and sensation (temporal and spatial, aural and visual) that according to Lessing would be strictly dichotomous. Through his cursory reference to the “Laocoonists,” Lindner acknowledged that a mapping across these domains was neither an obvious nor an uncontested operation, while suggesting that his age strove to transcend these limitations.

The issues at the heart of these debates have continued to provoke illustrious thinkers to ruminate on the essence and relation of the arts. In recent scholarship, Daniel Albright has explored art’s unity and plurality in several monographs.8 While reviewing the history of debates on comparing the different arts, much of Albright’s work focuses on early twentieth-century

Modernism as the golden age of “Panaesthetics,” during which traditional distinctions between the arts were forced to collapse under manifold pressures arising both within and outside the arts, including such realms as the physical sciences.9 As Albright asserts,

7 For a review of the Laocoon problem, various positions arising from it, and contributions made towards the debates see for example Daniel Albright’s introduction to Untwisting the Serpent: Modernism in Music, Literature, and Other Arts (Chicago: University of Chicago Press, 2000), 5–33. Based on their contributions, Albright lists Horace, Lessing, Theodor W. Adorno and Clement Greenberg as the designated “patron saints to the study of comparative arts” on p. 8. 8 Among Albright’s many books on the subject, two are particularly pertinent to the question of what separates and unites the arts: Panaesthetics: On the Unity and Diversity of the Arts (New Haven: Yale University Press, 2014) and Untwisting the Serpent . 9 The term “Panaesthetics” refers to Albright’s eponymous monograph (2014), a collation of his Anthony Hecht Lectures in the Humanities that he held at Bard College.

The twentieth century is a particularly fruitful field for this search for figures of consonance [between different art forms ], perhaps in part because the physicists of this period refused to separate time from space, but instead regarded time and space as a multi-dimensional whole. 10

Two of the physicists to whom Albright must be referring are Albert Einstein and

Hermann Minkowski. Einstein’s special theory of relativity of 1905 famously turned the paradigms of physics upside down and paved the way for a significantly altered conception of time and space. In 1908, Minkowski formalized the model of the space-time continuum on the basis of Einstein’s theory and in turn provided the grounds for Einstein’s later general theory of relativity. In combining the three dimensions of space with one dimension of time, the space- time continuum superseded the norms of Euclidian geometry (which did not include time as a dimension) and Isaac Newton’s laws of motion in an absolute framework of time and space.

These epistemic shifts in physics merged with parallel developments in philosophy that similarly targeted theories of time and space. Most pivotal in that regard might have been the theories of time by Edmund Husserl—notably his phenomenology of time-consciousness—and

Henri Bergson, including the latter’s influential debate with Einstein in 1922, which is also reflected in his Duration and Simultaneity .11 Indeed, Bergson and Husserl alike famously employed melody as their favored test case to explore and demonstrate their theories of a

10 Albright, Untwisting the Serpent , 6. 11 Husserl’s lectures on time-consciousness from 1905 were published as Edmund Husserls Vorlesungen zur Phänomenologie des inneren Zeitbewusstseins , ed. Martin Heidegger (Halle/Saale: M. Niemeyer, 1928). The English translation is On the Phenomenology of the Consciousness of Internal Time (1893- 1917) , transl. John Barnett Brough (Dordrecht: Kluwer Academic Publishers, 1991); Henri Bergson, Duration and Simultaneity: Bergson and the Einsteinian Universe , ed. and trans. Robin Durie (Manchester, UK: Clinamen Press, 1999), originally Durée et simultanéité. À propos de la théorie d'Einstein (Paris: Alcan, 1922). A recent interpretation of the debate between Bergson and Einstein is offered in Jimena Canales, The Physicist and the Philosopher: Einstein, Bergson, and the Debate That Changed Our Understanding of Time (Princeton: Princeton University Press, 2015).

phenomenology of time, inquiring at once how melody could be appreciated as a unified whole from the succession of perceived events.

In this “Culture of Time and Space,” as Stephen Kern has dubbed the decades around the turn of the twentieth century, these scientific and philosophical debates informed approaches to time and space in literary and artistic practice.12 As theories of time and space were in flux and increasingly co-dependent, the distinction between temporal and spatial art forms—formally, the essence of the Laocoon problem—was blurred, as Albright suggests. Traditionally spatial art forms such as painting and sculpting could now be conceived as also embracing a temporal dimension, just as the spatial dimension of music and other inherently temporal forms of expression received increased attention. Or, more generally, an art form was no longer confined to being either of time or of space, but could now be both.

A famous incubator where such panaesthetic ambitions were promoted was the Bauhaus school, Germany’s highly influential educational institution for aspiring artists between 1919 and

1933. Featuring such eminent artists as Walter Gropius, Johannes Itten, Wassily Kandinsky, Paul

Klee, Ludwig Mies van der Rohe, László Moholy-Nagy, and Oskar Schlemmer among its teachers, the Bauhaus was formative in establishing a modernist aesthetic across Europe. The school advocated an integrated conception of the arts, in which a general aesthetic was to transcend all art forms. Not only did the training at the school foster a holistic artistic approach to craftsmanship, creativity, and design in different media, but it also promoted the aesthetic ideal that any idea should be equally expressible in different art forms, media, and materials.

An example of this approach is documented in Kandinsky’s treatise Point and Line to

Plane: Contribution to the Analysis of the Pictorial Elements (1926)—the source of the epigraph

12 Stephen Kern, The Culture of Time and Space, 1880–1918 (Cambridge, MA: Harvard University Press, 1983).

to this chapter—which was published in the Bauhaus’s own book series four years after

Kandinsky joined that institution’s roster of teachers in 1922. As Kandinsky observed at the outset of the treatise, the visual arts were lacking thorough methods of analysis and theory compared to the other arts. To rectify this shortcoming, he focused on the three basic graphical elements of his title—point, line, and plane—and he explored their functionality in a variety of artistic practices, not only in drawing and painting, but also in music and dance. Kandinsky observed the expressive and iconic potential of the graphical elements in these different contexts and studied their crafted arrangement in composition. Ultimately, this meticulous inquiry allowed Kandinsky to enrich both his own and his students’ artistic practice.

By intertwining applied experiments and analysis, Kandinsky’s approach illustrates the integration of theory and practice that engendered the Modernist reconfiguration of the arts. As I mentioned in the discussion of Lindner’s text above, changing paradigms governing artistic inquiry affected both the practical and theoretical domains of the arts. An excellent example for such a (panaesthetic) network of correlated ideas lies in early twentieth-century theories of the line. Within the evolving integrated spatial-temporal model, the line became conceptualized as an inherently dynamic entity. The temporal quality concomitantly ascribed to the line, I argue, was vital for drawing analogies with musical phenomena and their intrinsic evanescence.

Kandinsky’s footnote in the epigraph, in which he asserted that “the line grows organically out of points,” already implied a dynamic conception of the line, as did Lindner’s intimation of the movements that a line might capture. A more full-fledged definition of a dynamic line appears in the Bauhaus-treatise of Kandinsky’s colleague Paul Klee.

The Genetic Line

In contrast to Kandinsky’s deductive approach in Point and Line to Plane , which prioritized analytical observation over decisive definitions, Klee opened his Pedagogical

Sketchbook (1925) with a postulate. Presenting one of his most influential artistic concepts, Klee asserted:

Eine aktive Linie, die sich frei ergeht, ein Spaziergang um seiner selbst willen, ohne Ziel. Das agens ist ein Punkt, der sich verschiebt. 13 An active line on a walk, moving freely, without goal. A walk for a walk’s sake. The mobility agent is a point, shifting its position forward.

Figure I.1 : Paul Klee, “active line,” Pedagogical Sketchbook , Figure 1 14

In much detail, art historian Régine Bonnefoit has traced the formation of such an organic, self-generating line in what she terms “genetic” (“genetische”) geometry in the intertwined histories of geometry, philosophy, and the visual arts. Through a historical survey of earlier theories of the line, she demarcates the specificity of this line in distinction from the traditional model of Euclidian geometry.15 As Bonnefoit chronicles, the line was described as the connection or addition of multiple, immobile points at least up to the mid-fifteenth century and

13 Paul Klee, Pädagogisches Skizzenbuch , Bauhausbücher 2 (Munich: Albert Langen, 1925), 6; English translation from Pedagogical Sketchbook , trans. Sibyl Moholy-Nagy (London: Faber and Faber, 1968), 16. Klee also talked about the line as a “trace of motion” (“Die Linie ist die Spur einer Bewegung.”). See Bonnefoit, Die Linientheorien von Paul Klee , 43. 14 Paul Klee, Pädagogisches Skizzenbuch (1925), 6. 15 See in particular Bonnefoit, Die Linientheorien von Paul Klee , Ch. 2 “Die Definition der Linie,” 23–50.

Leon Battista Alberti’s treatise Della Pittura . While the order of Euclidian geometry remained a potent frame of reference for many centuries to come, Bonnefoit observes intimations of a more dynamic conception for generating geometrical entities out of one another starting in the early sixteenth century with Albrecht Dürer ( Unterweysung der Messung mit dem Zirckel und

Richtscheyt in Linien, Ebenen unnd gantzen Corponen, 1525), who drew attention to the movement of the painter’s hand, and Leonardo da Vinci (“Codex Arundel,” ca. 1505–08), who proposed the relation between increasing geometrical dimensions through the application of motion.16 While especially the latter anticipates Klee’s idea of generating the “active line” through a moving point, Bonnefoit argues that the genetic line became fully established in artistic discourse only around 1900 under the auspices of the above-mentioned physical and philosophical theories of time and space.

In that historical moment, genetic theories of the line were additionally shaped and reinforced by a variety of nineteenth-century schools of thought, including organicism as expressed in Johann Wolfgang Goethe’s Spiraltendenzen der Vegetation (ca. 1830) and Carl

Gustav Carus’s Natur und Idee oder das Werdende und sein Gesetz from 1861, the latter of which experienced a “renaissance” in the 1920s.17 Bonnefoit moreover refers to the theosophical movement around Russian occult scientist Helena Petrovna Blavatsky, who propagated the idea of the creation of the universe from a single point by adapting ideas from Emanuel

Swedenborg’s Principia rerum naturalium (1734) through sexually charged metaphors, as found in Cosmogenesis (1888), which first appeared in German translation in 1907.18 Bonnefoit traces the influence of these theories on ideas propagated at the Bauhaus through a citation in

16 Bonnefoit, Die Linientheorien von Paul Klee , 24. 17 Bonnefoit, Die Linientheorien von Paul Klee , 26 and 28. Bonnefoit refers to a statement by Hans Kern, a student of philosopher and graphologist Ludwig Klages, who observed a “Carus-Renaissance” in 1927. 18 Bonnefoit, Die Linientheorien von Paul Klee , 26.

Kandinsky’s earlier treatise On the Spiritual in Art (1912). Especially in light of these latter theories that associated linear propagation with growth processes in nature, most conceptions of the line in early twentieth-century thought addressed a curved or curly line—like in Klee’s emblematic depiction in Figure I.1—rather than a straight one. Through the collection of sources and the lineage of ideas that Bonnefoit gathers in her monograph, she illuminates a vivid and rich discourse on the line in early twentieth-century culture. Klee’s writings and creative oeuvre not only sit at the center of her investigations, but he also personifies the tight connection between theory and practice in the visual arts that the line forged at that time.

Media theorist and philosopher Sybille Krämer also appeals to Klee’s theories (as well as

Kandinsky’s) in her recent scholarship on the line in diagrammatic reasoning.19 Krämer captures the distinction made above between energetic and static lines through the terms

“Verbindungslinie” and “Bewegungslinie” (or “connective line” and “motive line”). 20 The former arises as the connection between two fixed points in a plane, yielding thus a straight line whose length and orientation is predefined. The latter, by contrast, is equivalent to Klee’s “active line,” which grows out of a single point in motion, and whose trajectory is thus entirely free and unpredictable. For artists, and especially those exploring new Modernist forms of expression around the turn of the twentieth century, the second kind was obviously of much greater interest.

In the history of artistic practice, indeed, the prominence of the line in the early twentieth century is hard to overlook. Already in the various local and national manifestations that the Arts and Crafts movement initiated across Europe around the turn of the century—be it as Jugendstil,

Stile Liberty, or Art Nouveau—lines abounded in elaborate ornaments and framed elongated

19 Sybille Krämer, Figuration, Anschauung, Erkenntnis: Grundlinien einer Diagrammatologie (Berlin: Suhrkamp, 2016), esp. Ch. 5, “Aisthesis und Erkenntnispotenzial der Linie,” 95–144. 20 Krämer, Figuration, Anschauung, Erkenntnis , 102–3. Krämer notes that a similar theory can be found in Tim Ingold, Lines: A Brief History (London: Routledge, 2007), esp. 72–3.

proportions. Gurminder Bhogal has illustrated such ornamental figures, including the arabesque, as intertwining musical and visual artistic concerns in fin-de-siècle French culture. 21 She examines how ornamental lines infused artistic practice and compositional idioms of the time as well as their critical reception. While many of Bhogal’s analyses and observations illuminate visions of melody and the line in a distinctly French, or more specifically Parisian, cultural constellation and musical repertoire, the popularity of these ideas transcended cultural and political boundaries. Indeed, also across the subsequent stylistic breaks induced by modernist ambitions, the line remained an underlying constant. Especially with the tendencies towards abstraction in the early decades of the new century, artists emancipated the line from even these functional ties. From its traditional objective of delineating contour in the service of pictorial representation, the line emerged as an expressive entity in its own right.

At the same time, artists like Kandinsky and Klee felt the need to support this newly found fascination with the line through theoretical leverage. After all, in 1902 Belgian architect

Henry van de Velde had observed in his influential essay on “The Line” that this graphical element had been drastically neglected in theoretical accounts of the arts (often in favor of color).22 His essay is one of the many contributions to follow in the early decades of the twentieth century that examined various theoretical aspects of the line. Van de Velde himself stressed the expressive potential that he perceived in the line, describing it as a primitive, intuitive form of expression:

Linien—übertragene Gebärden—offenkundige psychische Äußerungen, deren Primitivität die Nuancen beschränkte. … [Linien ] zeugen von latenten Kräften, die in uns

21 Gurminder Kaur Bhogal, Details of Consequence: Ornament, Music, and Art in Paris (New York: Oxford University Press, 2013). For a brief discussion of ornamental lines and the arabesque, see also Bonnefoit, Die Linientheorien von Paul Klee , 54. 22 The essay is printed in Henry van de Velde, “Die Linie,” in Essays (Leipzig: Insel-Verlag, 1910), 41– 74; see Bonnefoit, Die Linientheorien von Paul Klee , 9.

sind, durch plötzliches Verlangen gereizt und entfesselt, von Kräften, die ungeduldig sind, sich in Taten umzusetzen. 23 Lines, transferred gestures, evident psychic expressions, whose primitivism delimited their nuance. … [Lines ] are evidence of latent forces that are in us, excited and unleashed through sudden urges, of forces that impatiently await being transferred into actions.

Van de Velde’s description of the inner forces that engender the outburst of lines draws attention to the expressive subjectivity of the painter. The hand-drawn line became associated with the uninhibited manifestation of the painter’s psyche and emotional state. While French psychologist Pierre Janet employed hand-writing and line-drawing as a therapeutic means that allowed patients (in trance) to unload their unconscious onto the paper, this psychological charging of the line conversely leveled the way for the emergence of the research field of graphology, marked, for instance, by the foundation of the “Institut für wissenschaftliche

Graphologie” in Munich in 1895, followed by the “Deutsche Graphologische Gesellschaft” in

1896. 24 Graphologists read the linear scribbles of their subjects as keys into their psychological constituency. Unlike other painterly forms of expression, abstractly drawn lines and the continuous strokes of handwriting lent themselves well to such investigations since they encapsulate both the expressive representation of the drawer’s psychic state and a clear, unidirectional trace of its progress. As we shall see in Chapter II, Ernst Toch described the composition of melodies in similar terms as van de Velde, as an intuitive drawing of lines, thus

23 Van de Velde, “Die Linie,” 42–3. 24 Pierre Janet, L’automatisme psychologique: essai de psychologie expérimentale sur les formes inférieures de l’activité humaine (1889), ed. Serge Nicolas (Paris: l’Harmattan, 2005). Janet’s method of “écriture automatique” focused on linguistic writing, the free association and concatenation of words. In 1924, André Breton popularized the method in his Surrealist manifesto. André Breton, Manifeste du surréalisme; Poisson soluble. (Paris: Éditions du Sagittaire, 1924). A prominent figure in the graphological movement was Ludwig Klages (1872-1956), whose writings such as Probleme der Graphologie (1910), Ausdrucksbewegung und Gestaltungskraft (1913), and Handschrift und Charakter (1917) have been read by Bonnefoit as a source of inspiration to the artists at the Bauhaus. Bonnefoit, Die Linientheorien von Paul Klee , esp. 90–93.

emphasizing one of the aesthetic ascriptions shared between melody and the line in early twentieth-century thought.

In France, philosopher Paul Souriau solidified the close connection between the line and its drawing hand, describing the appearance of a graphical line in physiological terms, as “a graph of the hand in which one reads the exact gesture of the hand that produced it,” as Cécile

Guédon has highlighted.25 Guédon further examines Souriau’s concept of “rémanence” through which he sought to capture the tension between the ephemeral process of the line’s creation and the graphical imprint it leaves on the page: the visual manifestation—“une image présente”— relays the essential parameters of the creative motion-process, such as its speed and trajectory.26

Already in this concept, Souriau showed concern for the perceptibility of certain attributes of the line, allowing Guédon to envision “Klee’s ‘walking line’ as a specifically graph-like image, enabling effects of intersection between motion-transmission from the draughtsman

(‘rémanence’) and motion-enactment by the viewer (‘résonance’).”27

Since the early twentieth century, then, the line has been theorized as a trace of motion— not only of a point moving across the page, as Klee’s definition of the “active line” suggested, but also as a manifestation of the embodied movement of the draughtsman’s hand. 28 As Guédon intimates, the inherent temporality of these processes has furthermore raised questions about the

25 Cécile Guédon, “Abstraction in Motion: A Choreographic Approach to Modernism” (Ph.D. dissertation, Birkbeck, University of London, 2014), 190, citing Paul Souriau, La suggestion dans l’art (Paris: F. Alcan, 1893), 140: “Chaque ligne est comme un graphique de la main où nous lisons exactement le geste de la main qui l’a tracée.” I adapted Guédon’s translation. For a broader discussion of Souriau’s theory and context, see also Bhogal, Details of Consequence , 185–86. 26 See Guédon, “Abstraction in Motion,” 190. 27 Guédon, “Abstraction in Motion,” 190. The “walking line” is a different designation for the “active line” discussed above (and reproduced in Fig. I.1). 28 See also Bonnefoit, Die Linientheorien von Paul Klee , 43–7 on the various ways in which Klee conceived of the line as a “trace [and representation ] of motion” (Klee’s motto: “Die Linie ist die Spur einer Bewegung”). Bonnefoit also reviews earlier theories and applications of the line as a means of representing motion.

necessary passing of time in their re-enactment through the viewer. This interpretation elegantly interlocks two big shifts in the history of artistic theory. The first concerned the reading of the line as a mark of the artist’s movement. From there, the line became reattached, away from the artist’s hand, to the viewer’s eye movement. This turn towards the spectator and her perceptual strategies heralded the impact of a broader methodological re-orientation across the arts and sciences in the early twentieth century. Indeed, extensive studies on human perception accompanied the reconfiguration of the line in the visual arts. As we shall see, the artistic inquiries into the line’s creation and cognition were an essential foundation for theorizing perception and cognition as temporal processes. Moreover, many of these psychological investigations leaned on music to explore the ways in which cognition might be bound by time.

Tracing Perception: From Eye Paths to the Gestalt Quality of Melody

In re-tracing the steps in this interdisciplinary cognitive inquiry, I first turn again to

Bonnefoit, who provides a convincing survey and narrative with respect to visual concerns.

Bonnefoit considers a range of sources from Adolf von Hildebrand’s 1893 treatise Das Problem der Form in der bildenden Kunst and Friedrich Schumann’s 1900 article “Zusammenfassung von

Gesichtseindrücken zu Einheiten,” to Max Wertheimer’s “Experimentelle Studien über das

Sehen von Bewegung” (“Experimental Studies on the Perception of Motion”) from 1912.29

29 See Bonnefoit, Die Linientheorien von Paul Klee , chap. 5, “Die Wahrnehmung der Linie und ‘lineare Wahrnehmung,’” as well as Bonnefoit “ Der ‘Spaziergang des Auges’ im Bilde – Reflexionen zur Wahrnehmung von Kunstwerken bei William Hogarth, Adolf von Hildebrand und Paul Klee, ” kritische berichte - Zeitschrift für Kunst- und Kulturwissenschaften 32, no. 4 (January 14, 2013): 6–18. Focusing on motion (rather than the line), Romana Schuler observes the trend towards kinetic art at the turn of the twentieth century, not least with the emergence of film as a “moving” art form. Romana Karla Schuler, Seeing Motion: A History of Visual Perception in Art and Science (Berlin; Boston: De Gruyter, 2016). See also Adolf von Hildebrand, Das Problem der Form in der bildenden Kunst (Strassburg: Heitz, 1893),

Especially the earlier authors likened eyes scanning the page to the sense of touch (“tastendes

Auge”), describing how the eye collected a series of sensory inputs (“Einzelwahrnehmungen”) that were then assembled into a holistic image in the mind. These theories, in turn, led to the conception of the imaginary lines that traced this scanning process (rendered again in German through the tactile metaphor of “abtasten”), as Klee captured in the term “eye paths” (or “scan paths,” in German “Augenwege”). Robert Vischer promoted a corresponding theory through the distinction between “sehen” and “schauen” (roughly equivalent to the distinction between

“seeing” and “viewing” in English), the latter of which he described as the drawing of a line

(“Linienziehen”). 30 In Klee’s “active line,” the “point [that ] shifts its position forward” on the page thus embodies at once the tip of the pen as moved by the painter’s hand and the mobile focus point of the viewer’s eye. Kandinsky’s footnote in this chapter’s epigraph, in which he clarified that “the line grows organically out of points,” allows for a similar interpretation.

However, the trajectory of an “eye path” did not necessarily match that of the graphical line on the paper. Rather, the viewer might first be drawn to a holistic perception of the entire graphical shape and then scan bits and pieces of it for a more detailed impression. While research showed that that process was still largely predictable, and could even be guided or manipulated, the “eye path” ultimately depended on the haphazard movement of the viewer’s eyes across the page.

Friedrich Schumann, “Beiträge zur Analyse der Gesichtswahrnehmungen. Erste Abhandlung: Einige Beobachtungen über die Zusammenfassung von Gesichtseindrücken zu Einheiten,” Zeitschrift für Psychologie und Physiologie der Sinnesorgane 23 (1900): 1–32, Max Wertheimer, “Experimentelle Studien über das Sehen von Bewegung,” Zeitschrift für Psychologie und Physiologie der Sinnesorgane 61, no. 1 (1912): 161–265. 30 See Bonnefoit, Die Linientheorien von Paul Klee , 78–82, referring to Robert Vischer, Über das optische Formgefühl. Ein Beitrag zur Ästhetik (Leipzig: Hermann Credner, 1873). Klee produced various sketches in which he explored possible forms of “Augenwege,” as Bonnefoit discusses in particular in her article “Der ‘Spaziergang des Auges’ im Bilde.” Today, these investigations are carried out in psychological research on “eye-tracking,” which examines precisely such processes.

Notably, apart from the sense of touch, music and aural perception served as an important model for studies in visual cognition. As an inherently temporal form of expression, music constituted an obvious test case for psychologists to explore processes of perception and cognition. A seminal study in this respect was Christian von Ehrenfels’s essay “On ‘Gestalt

Qualities’” from 1890, a founding document for the school of Gestalt theory in German academia.31 While both Guédon and Bonnefoit allude to the impact of that school of thought on theories of the line and linear perception, I propose that Ehrenfels’s text in particular can illuminate crucial connections between the line, music, and processes of cognition.

Ehrenfels’s study took as its starting point the question of how listeners apprehend melodies as coherent and holistic entities even though they only ever perceive them as individual tones in temporal succession—a question, which, as mentioned, also preoccupied the leading phenomenologists of the time. He proposed that mnemonic and cognitive processes of imagination (“Vorstellung,” translated by Smith as “presentation”) tie across these separate impulses and the temporal lag between them and ultimately merge them into a single cognitive image. While Ehrenfels coined such holistic units of cognition “Gestalt qualities,” later theorists referred to them simply as “Gestalten.” As I explore more extensively in Chapter III, Ehrenfels not only took into account the temporality inherent in aural phenomena, but he also argued that the cognitive realization of the sounding phenomenon required additional time, even when all

31 The essay was first published as Christian von Ehrenfels, “Über ‘Gestaltqualitäten’,” Vierteljahrsschrift für wissenschaftliche Philosophie , 14 (1890): 249-92. Here and below, I refer to the version of the essay published as “Über ‘Gestaltqualitäten,’” in Das Primzahlengesetz, entwickelt und dargestellt auf Grund der Gestalttheorie (Leipzig: O.R. Reisland, 1922), 7–29, 77–95, and to the translation “On ‘Gestalt Qualities,’” in Foundations of Gestalt Theory , ed. and trans. Barry Smith (Munich: Philosophia Verlag, 1988), 82–116. On the history of Gestalt theory see in particular Mitchell G. Ash, Gestalt Psychology in German Culture, 1890–1967: Holism and the Quest for Objectivity (Cambridge: Cambridge University Press, 1995).

component stimuli were perceived at once. 32 Moreover, he suggested that this was true equally of aural and visual perception.

Ehrenfels’s theory thus modeled those processes of visual cognition on the sense of hearing that Hildebrand and Schumann sought to explain through the sense of touch (“abtasten”) a couple of years later.33 Common to all these accounts was the acknowledgement that the perception of complex entities was based on the mental re-composition of a multiplicity of stimuli and that this cognitive process evolved over time, regardless of the sense involved. By explaining that the eye did not perceive a picture as a single holistic impression, but as discrete elements in time, these theories further negated long-established distinctions between the temporal and spatial arts.

These accounts of visual and aural perception were epitomized in the line and in melody, respectively. In the visual domain, the line assumed a temporal quality, either in its definition as a point in motion or as an organic growth process, as Kandinsky described in the footnote of this chapter’s epigraph. In the explorations discussed above, the line was once as an exemplary object of investigation, through which artists and psychologists could examine the parallel temporalities of creating and viewing the line. Moreover, the line became the principal metaphor to describe the resulting insights about the processes involved in visual cognition, such as in Klee’s “eye paths.”

The dual interpretation parallels processes in music. Just as the line manifests a physical process of creation, which it prompts its viewer to recreate, the sounding formation of melody

32 Earlier notions of the time lag in aural perception between the physical event, the physiological stimulus, and the psychological image are intimated in the work of Hermann von Helmholtz, as Benjamin Steege has analyzed. Benjamin Steege, Helmholtz and the Modern Listener (Cambridge, UK: Cambridge University Press, 2012). 33 I am referring here to Hildebrand, Das Problem der Form in der bildenden Kunst and Friedrich Schumann, “Beiträge zur Analyse der Gesichtswahrnehmungen.”

over time demands the continuous sensory and cognitive engagement of the listener. As

Ehrenfels theorized, the result is the perception of a larger coherent whole, the Gestalt quality of melody. If the line served artists and psychologists as an image to track the movements of the eyes across the surface of a paper, did it also lend itself to capturing the experience of listening, of connecting a melody’s component sounds and sensory impressions into a single, holistic entity? In other words, how apt is the line as an image to depict a melody’s Gestalt quality?

This question implicates the three different manifestations of the line that can be distilled from our explorations thus far. In a first step, we saw how the line transgressed the dimensions of time and space and became defined as a dynamic graphical element. Its genetic process of creation came to denote the movement of the artist’s hand. This motive capacity, in turn, stimulated the employment of the line as a trace of the viewer’s eye movements as they scanned visual information, such as a graphical line. Through this dynamic engagement, the viewer could reinscribe the genetic process of the line’s creation into the static appearance that it left on the paper. The interrelation between these three stages of the line could be captured by the terms

“rémanence” and “resonance,” as Guédon proposed, following Paul Souriau.

Let us now appraise these interpretative layers and their representational value for processes in the aural domain in a concrete example, which takes us back to Kandinsky’s treatise

Point and Line to Plane and to his enigmatic proclamation of the “musical line” quoted in the epigraph. On that occasion, Kandinsky referred to his Figure 11 to support his assertion about

“musical line.” That figure constitutes the musical showcase of the entire treatise. It comprises four parts, each of which translates a short excerpt from the first movement of Ludwig van

Beethoven’s Fifth Symphony, Op. 67 into a form of graphical notation that Kandinsky explored as an alternative to staff notation. The most obvious implementation of what we might expect

from Kandinsky’s hint at the “musical line” appears in the figure’s last part (reproduced in

Figure I.2), which pertains to the entrance of the symphony’s second theme (mm. 58–65).

Figure I.2 : Wassily Kandinsky, visualization of Beethoven, Symphony No. 5, 1 st movement, mm. 58–65, from Point and Line to Plane , Figure 11, part 4 34

The graphical rendition depicts the symphonic melody as a line, which floats on the page above the points of the fading opening motto. It thus lends itself to exploring a Gestalt-theoretical reading through the lens of Ehrenfels’s propositions.

34 The somewhat misleading annotation that the second theme, too, is “translated into points,” (“dasselbe in Punkte übersetzt”), is due to the position of this figure in Kandinsky’s treatise, where it appears in the section on the point rather than the line. All other parts of the figure are rendered exclusively through points.

In Ehrenfels’s theory, Gestalt qualities are defined by two central principles, which ensure our capacity to recognize Gestalten as distinct entities. The first is that of “supra- summativity” (“Übersummenhaftigkeit”), meaning that the whole is more than the sum of its parts—or, when expressed in terms of melody, the whole is more than the sum of its constituent tones. In Kandinsky’s figure, the line ties together the melody’s constituent tones into a single graphical entity. As an idiosyncratic holistic shape the line thus enacts Ehrenfels’s principle of

“supra-summativity.” Moreover, as I describe in Chapter V, as a graphical figure, the line also affords different expressive means compared to a series of points. Kandinsky could, for instance, signal expressive swells between the tones through variations in thickness of the line, or alter its acuity.

The second principle that Ehrenfels codified is that of transposability

(“Transponierbarkeit”), indicating that an entity like a melody maintains its essential characteristics even when transposed to a different context, such as a different key or register. 35

Kandinsky’s figures appear on a plain white background, with no reference to absolute pitch or register. In Figure I.2, the black dots, which represent the fading opening motto, only provide a relative indication of pitch and temporal organization. In this relative tonal space, the line still captures the contour of Beethoven’s melody and remains recognizable independently of its placement in absolute pitch or register.

With the fulfillment of both of Ehrenfels’s essential principles, the line represents not merely melody itself, but also the Gestalt quality of melody. Suitably, the excerpt that Kandinsky chose encompasses the span of a musical phrase, which we usually apprehend as a perceptual

35 While Ehrenfels conceived of “transposability” to refer literally to the transposition in pitch, Wilhelm Jerusalem explored the applicability of this principle to variations in timbre and performing forces. See Luitgard Schader, Ernst Kurths “Grundlagen des linearen Kontrapunkts”: Ursprung und Wirkung eines musikpsychologischen Standardwerkes (Stuttgart: J.B. Metzler, 2001), 58–59.

unit. The line thus expresses at once the emergence of melody over time as well as the process of the listener’s perception and cognition of it. Borrowing Klee’s notion of the eye path

(“Augenweg”), the line in Kandinsky’s Figure I.2 can thus also be more metaphorically construed as a “ear path” or “ear track,” as it traces the ear’s attention from tone to tone and from one sensory impulse to the next. In the case of Figure I.2, this trace overlaps with that of the melodic contour, which we might associate with the manifestation of melody as a sounding phenomenon.

In other instances, however, a melody’s contour might not be rendered through a graphical line, such as in the case of the famous motto that opens Beethoven’s symphony. This musical excerpt constitutes the first part of Kandinsky’s illustration (see Figure I.3).

Figure I.3 : Wassily Kandinsky, visualization of Beethoven, Symphony No. 5, 1 st movement, mm. 1–5, from Point and Line to Plane , Figure 11, part 1

In Figure I.3, Kandinsky translated this motto exclusively through dots—even the triangular shapes that extend from the larger dots are made out of a series of dots. (The shapes express the diminuendo and extension of the longer fermata tones, as I analyze in more detail in Chapter V.)

The graphical options for depicting this theme are limited by an essential musical feature. The repeated notes of the motto defy a representation through a line, which would obscure their attacks as discrete sonic events. Repetition in pitch thus constrains linear graphical renderings of melody. In fact, also in Kandinsky’s representation of the symphony’s second theme, the line is slightly interrupted at the repeated c’’ between the last two measures of the excerpt (see Figure

I.2). The same reasoning applies to the legato slur in conventional staff notation as it is printed above Kandinsky’s illustration. This interruption is a small disturbance to the coherence of the musical phrase that the line depicts, which obviously continues until the b-flat’, the final note of the excerpt.

Our perception of the line sees across this graphical incision, just as we hear the musical phrase as a coherent expression. Similarly, we still perceive the symphony’s opening motto as a unit rather than a collection of disjointed tones, both when listening and when looking at

Kandinsky’s visual representation of it. As I review in Chapter IV, further studies in Gestalt psychology have codified theoretical principles that explicate how we group the tones and dots of the motto into patterns, always gathering together those elements that appear closest to one another.

To capture these groupings, we could draw lines—“ear tracks”—that tie across and connect the dots. Like the “eye path” discussed above, the “ear track” mediates between the physical and physiological appearance of music as a sounding phenomenon, and its psychological, cognitive essence. Through the predefined temporal order of tones in which

melody evolves, the “ear track” might at once appear more predictable than the haphazard movements of a viewer’s eyes. But already when confronted with a slightly more complex musical constellation, for instance a melody with accompaniment, or a polyphonic texture, the exact “path” that our aural perception and cognition takes, becomes just as contingent on external factors and internal propensities. In that sense, we could imagine many more musical lines in Kandinsky’s Figure 11 than the one that meets the eye in Figure I.2 above. In this dissertation, I will address both kinds of lines, some readily visible and others merely conceptual and visible only to the inner eye. What they share is a reliance on psychological theories of the early twentieth century to provide a conceptual bridge between music as an audible phenomenon and the line as its visual imagery. How exactly music theorists explained and employed this mapping will be the subject of Chapters III and IV, where I examine the music theories of Ernst

Toch and Ernst Kurth.

Bach and Beethoven as Linear Icons

As we have seen, the Modernist re-definition of the line in the arts and sciences occurred under the auspices of a psychological paradigm. These tendencies transcended political and national boundaries, just as Modernism claimed its international influence. More specifically, across Europe, artists and scientists explored a conceptual mapping between melody and line, the linear qualities of melody, and the melodic nature of the line. Noticeably, across these contributions, two German composers recurrently featured as exemplars of linear-melodic composition: Johann Sebastian Bach and Ludwig van Beethoven. They were handled as competitors over the prize of modeling a particularly linear coherence in their melodies, depending on the respective ideological leanings of their advocates.

When Beethoven and Bach emerge as two musical cornerstones in this dissertation, this prominence is highly representative of the significance ascribed to them in musical discourse of the early twentieth century. Indeed, the popularity of both composers was certainly not limited to their mastery of linear composition. Rather, both were lively celebrated as creative icons in artistic communities well beyond merely musical circles in the early twentieth century. 36 Yet, the reception of both Bach and Beethoven was far from unanimous, within the German cultural realm, as well as across national hostilities. Already in Germany, diverse ideological camps contended for claiming the two composers, or variably one of them, as paragons of a specific cultural heritage—whether in a conservative, nationalist agenda, or a more Modernist, international one. As I review in Chapters II and V, these contentions were particularly oppositional with respect to the cultural-political appropriation of Bach. This was due in part to the appeal that Modernist composers of the time made to Bach’s polyphonic style as their authoritative model. 37 At the same time, their music was increasingly described for its “linear” qualities, as I discuss in Chapter II. In the wake of dissolving tonal hierarchies and its vertical- harmonic ties, the ascription of linearity appeared particularly apt for capturing the linear- horizontal stratification of the new style. These debates prompted a close association between

Bach and linear composition. This connection was further reinforced as the debates over

36 From the comprehensive literature on the reception of these two composers, see for instance Alessandra Comini, The Changing Image of Beethoven: A Study in Mythmaking (Santa Fe: Sunstone Press, 2008) and Leo Schrade, Beethoven in France: The Growth of an Idea (1942) (New York: Da Capo Press, 1978). Michael Heinemann and Joachim Lüdtke, eds., Bach und die Nachwelt, vol. 3, 1900–1950 (Laaber: Laaber, 2000) provides a good overview of the widespread manifestations of the Bach reception during this time. On Bach and Beethoven, see in particular Hans-Joachim Hinrichsen, “Motorik, Organik, Linearität: Bach im Diskurs der Musiktheoretiker,” in the same, 337–78, esp. 348–53. See also Walter Frisch, German Modernism: Music and the Arts (Berkeley: University of California Press, 2005), 144–49. 37 For an overview over these positions, see Werner Krützfeld, “Polyphonie in der Musik des 20. Jahrhunderts: Die Logik der Linie,” in Musiktheorie , ed. Helga De la Motte-Haber and Oliver Schwab- Felisch, vol. 2, Handbuch der Systematischen Musikwissenschaft (Laaber: Laaber, 2005), 311–34.

contemporary composition were intertwined with the reception of Ernst Kurth’s treatise

Foundations of Linear Counterpoint: Bach’s Melodic Polyphony (1917).

The association of Bach’s polyphonic music with an emblematic “music of lines” was also propagated in the UK, for instance, where music educator Percy A. Scholes captured this repertoire in precisely these terms in a series of lectures he held for children in 1925. 38 When

Scholes described Bach’s compositions as a “music of ‘line’” in his second lecture, he echoed a comment made by his chairman John Borland (himself the musical advisor to the London

County Council). Borland had captured the music of the era of Bach and Handel as depending

“chiefly upon line and form,” and distinguished it from music of the Romantic period, “which is largely atmospheric and depends upon colour.” 39

Kurth’s broader oeuvre exemplifies how theories of music history served their authors as a stage for developing a political program. Across his monographs, Kurth devised an idiosyncratic narrative of music history that clearly exposed his ideological bent for linear- melodic developments in music. 40 He divided common practice tonality—already a deliberate restriction—into three phases: “polyphonic harmony” of the Baroque, “homophonic harmony” of the Classical, and “polyphonic homophony” of the Romantic era. In this scheme, Bach embodied not only the style of “polyphonic harmony,” but indeed its equilibrium of forces, in which melody co-created both harmonic and formal coherence. This relation was forcefully inverted in

38 Percy A. Scholes, The Appreciation of Music by Means of the “Pianola” and “Duo-Art”: A Course of Lectures Delivered at Aeolian Hall, London (London; New York: H. Milford, Oxford University Press, 1925), 39–40. The book is a transcription of a lecture series that Scholes held in 1925 in Aeolian Hall, London, to promote the use of player pianos for music education. 39 Scholes, The Appreciation of Music by Means of the ʻPianola’ and ʻDuo-Art’ , 31. 40 See Lee Allen Rothfarb, “Kurth’s Historical View of Harmony,” chap. 5 in Ernst Kurth as Theorist and Analyst (Philadelphia: University of Pennsylvania Press, 1988). On the “energetics” movement in music see for instance Lee Allen Rothfarb, “Energetics,” in The Cambridge History of Western Music Theory , ed. Thomas Christensen (Cambridge: Cambridge University Press, 2002), 927–55.

the “homophonic harmony” of Viennese Classicism, Kurth lamented, in which harmonic periodicity subordinated melody and dictated thematic development. Within the strictly symmetrical divisions of these Classical forms, melody could not develop freely, which was reason enough for Kurth to erase the entire era from further consideration. After he had dedicated a monograph to Bach’s “linear polyphony,” Kurth’s attention was refocused on the era of

“polyphonic homophony” of the nineteenth century, where Richard Wagner could recuperate melody as a driving force, even if he was preoccupied as well with the creation of sensuous

(“klangsinnlich”) components that did not contribute to the music’s linear-horizontal trajectory. 41

A last predilection was reserved for the symphonies of Bruckner, which Kurth explored in a two- volume monograph of 1925. 42 In this music-historical narrative, Beethoven received only negative valence, due to the lack of independent melodic development that his association with the style of “homophonic harmony” implied.

While Kurth blatantly dismissed Beethoven’s music as a worthy object of study, August

Halm—his colleague at the Free School in Wickersdorf and often grouped together with Kurth in the “energetics” school of music theory—presented a more nuanced reading. Halm’s Two

Cultures of Music (Von zwei Kulturen der Musik , 1913) offers an emblematic example both of the staged dichotomy between Bach and Beethoven, and of the diverse music-theoretical readings that Beethoven’s oeuvre received.43 In Halm’s two cultures, Beethoven personified the

Sonata, and Halm’s approach explicitly opposed hermeneutic readings of some favored objects of discussion (such as the “Tempest”-Sonata) with a distinctively formalist approach, albeit one

41 Ernst Kurth, Romantische Harmonik und ihre Krise in Wagners “Tristan” (Berlin: M. Hesse, 1923). 42 Ernst Kurth, Bruckner (Berlin: M. Hesse, 1925). 43 August Halm, Von zwei Kulturen der Musik (Munich: Georg Müller, 1913). For translation and commentary, see Laura Lynn Kelly, “August Halm’s ‘Von Zwei Kulturen der Musik’: A Translation and Introductory Essay” (Ph.D. dissertation, Austin: University of Texas, 2008).

presented in notably metaphorical language. 44 Alexander Rehding notes how Halm competed against a clan of “hermeneutic Beethoven scholars of the turn of the century, such as Hermann

Kretzschmar, Arnold Schering and Paul Bekker.” 45 Halm juxtaposed the idiom of Beethoven’s

Sonata to that of Bach’s Fugue in a dialectical reading, for which he envisioned a synthesis in the symphonies of Anton Bruckner, as delineated in his next monograph ( Die Symphonie Anton

Bruckners , 1914). While Laura Lynn Kelly suggests that Halm’s dialectics targeted an opposition between melody and harmony, Rehding proposes a more subtle reading that illuminates how Halm conceived of the different interplay between these two fundamental musical elements (nuanced by Rehding to scale and chord) within the construction of a fugal subject and a sonata theme.46 In turn, Halm propounded a taxonomical distinction regarding how he understood the relation of these two elements to feature in the evolution of musical form.

As Rehding discusses, Halm’s analysis of the subject of Bach’s Fugue in Bb minor from the second volume of The Well-Tempered Clavier (BWV 891) exposes a quasi-Schenkerian reading that unveils a structure of two interlocking tetrachords of “linear motion” (reproduced below as Figure I.4). 47

44 See Alexander Rehding, “August Halm’s Two Cultures as Nature,” in Music Theory and Natural Order from the Renaissance to the Early Twentieth Century, ed. Suzannah Clark and Alexander Rehding (Cambridge: Cambridge University Press, 2001), 143. 45 Rehding, “August Halm’s Two Cultures as Nature,” 153. For a discussion of the different music- analytical approaches competing over Beethoven’s music in the 1910s and 20s see also Lee Allen Rothfarb, “Music Analysis, Cultural Morality, and Sociology in the Writings of August Halm,” Indiana Theory Review 16 (1995): 171–96. 46 See for example Kelly, “August Halm’s ‘Von Zwei Kulturen der Musik,’” 1: “Halm’s first culture of music, melody, is exemplified by Bach’s fugues for keyboard. His second culture, harmony, is exemplified by Beethoven’s works in sonata form, such as his piano sonatas and symphonies.” 47 See Rehding, “August Halm’s Two Cultures as Nature,” 144–46, incl. his Ex. 6.1 (here reproduced as Figure I.4), which collates figures from Halm’s text into a single graphical display. See Halm, Von zwei Kulturen der Musik , 207–22.

Figure I.4 : August Halm, analysis of J. S. Bach, B-flat minor Fugue (BWV 891), as collated by Rehding

These two contrapuntally combined scalar progressions (one descending, the other ascending) supersede the initial, more conventional demarcation of a formative motive in the Fugue subject

(a six-note figure circling around the tonic pitch B-flat). Moreover, the bisection of the subject into two interlocking scalar motions illustrates its harmonic underpinning. This “interpenetration of harmony and melody is for Halm a sign of its organic nature,” as Rehding explains. Halm opposed it to the sonata, which “builds on the fundamental opposition between the [two ] principles—chord and scale.” 48 Indeed, instead of their amalgamation in organic synthesis like in

Bach’s fugal subject, harmony and melody (represented through the chord and scale, respectively, in Halm’s analysis) are separated and systematically opposed in the “themes” of

Beethoven’s “Tempest”-Sonata, which Halm used as his demonstrative example. Moreover, the

48 Rehding, “August Halm’s Two Cultures as Nature,” 146 and 149. As Rehding relates, Halm justified his focus on the two principles of chord and scale in a sonata theme by Beethoven through a quotation by the composer himself.

themes of Beethoven’s sonatas are subjugated to the overall form. As Rehding concludes, “fugal form is engendered by its theme, while sonata in turn engenders its themes in the service of the form.” 49

As Rehding shows, Halm further associated the compositional principles that he isolated in his analyses with socio-political models of the individual (Bach’s Fugue) and the State

(Beethoven’s Sonata). In this analogy, and on the basis of Hegel’s theory of the State,

Beethoven’s Sonata introduced a more profound notion of freedom than what might superficially be ascribed to the organically growing subject in a Bach Fugue. While Bach’s writing might continuously spin out of an initial nucleus, to Halm, the constrained reiteration of the same idea in Beethoven’s music served a larger objective of a communal State. Halm’s framing of the two composers Bach and Beethoven as dichotomous ideal types will continue to illuminate discussions in the following chapters, in particular since his ideas of their work are representative of thinking about melody in 1920s Germany.

For the present context, Halm’s reading of Bach and Beethoven counterbalanced the tendency to promote Bach as the paradigm of linear composition. As we saw, Kandinsky, for one, chose Beethoven’s music to illustrate the linear quality of melody. In Chapters II and III, we will encounter other prominent advocates of Beethoven’s music. In addition to the fascist ideology of Hans Pfitzner, who idolized Beethoven above any other composer, Ernst Toch chose as his paragon of good melodic composition an excerpt from a Beethovenian symphony.50

Moreover, Toch displayed his theoretical idea by means of a graphical line to illustrate its aesthetic success.

49 Rehding, “August Halm’s Two Cultures as Nature,” 150. 50 Another example that demonstrates melodic linearity through the music of Beethoven is Georg Göhler, “Die Führung der melodischen Linie in Beethovens c-Moll-Sinfonie,” Neue Zeitschrift für Musik 91, no. 2 (February 1924): 60–66.

In France, Jean Cocteau investigated the very same constructive principles underlying

Bach’s and Beethoven’s music as Halm, albeit in more poetic terms. He captured the notion that

Beethoven develops the form and Bach the idea in a literary allegory:

Beethoven est fastidieux lorsqu’il développe, Bach pas, parce que Beethoven fait du développement de forme, et Bach du développement d’idée. Beethoven dit: « Ce porte-plume a une plume neuve — il y a une plume neuve à ce porte- plume — neuve est la plume de ce porte-plume » ou « Marquise, vos beaux yeux… » Bach dit: « Ce porte-plume a une plume neuve pour que je la trempe dans l’encre et que j’écrive, etc… » ou « Marquise, vos beaux yeux me font mourir d’amour, et cet amour, etc… » Voilà toute la différence. Beethoven is tedious in his developments, but not Bach, because Beethoven develops the form and Bach the idea. Beethoven says: “This penholder contains a new pen; there is a new pen in this penholder; the pen in this penholder is new”—or “Marquise, vos beaux yeux, etc.” Bach says: “This penholder contains a new pen in order that I may dip it in the ink and write,” etc., or “Marquise, vos beaux yeux me font mourir d’amour, et cet amour … etc.” There lies the difference. 51

In that passage, the opposition between Beethoven and Bach exemplifies the dualistic antagonism that pervades Cocteau’s text. While Beethoven’s repetitive formalism opposes

Cocteau’s objective of concision and simplicity, Bach is portrayed as spinning forward an initial idea in a continuous, logical stream of thought. 52 From this description, Bach arises as the obvious embodiment of linear-melodic composition, in autonomous development. Cocteau’s

51 Jean Cocteau, Le Coq et l'arlequin: notes autour de la musique (Paris : Éditions de la Sirène, 1918), 10. Translation amended from Cock and Harlequin: Notes Concerning Music , trans. Rollo H. Myers (London: Egoist Press, 1921), 20 . 52 Interestingly, this juxtaposition between a cyclical form of thinking in Beethoven and a linear development in Bach is almost turned on its head in Karol Berger, “Time’s Arrow and the Advent of Musical Modernity,” in Music and the Aesthetics of Modernity: Essays, ed. Karol Berger and Anthony Newcomb (Cambridge, MA: Harvard University Press, 2005), 3–22, an idea that he later develops in his book Bach’s Cycle, Mozart’s Arrow: An Essay on the Origins of Musical Modernity (Berkeley: University of California Press, 2007). As the images of the book title suggest, Berger argues that only in the later eighteenth century, with the advent of theories of linear time, music started to express—and was perceived as—a unidirectional trajectory from past to future. The music of Bach’s era, by contrast, developed in a more circular understanding of time, in which the ordering of events was not as central to the musical logic as in later periods.

denigration of Beethoven, meanwhile, has to be read within the cultural-political climate of the postwar era. Indeed, in his pamphlet Cock and Harlequin (1918) the duality between French and

German culture is captured already in the title’s juxtaposition between the French national symbol of the cock and the harlequin, who personified the “other,” predominantly German approach to art. 53

Within the aesthetic ideals that Cocteau promoted throughout his pamphlet, he conjured a

“return to melody” to typify a distinctively French culture. This “return to melody”—and by implication to the line—promised to achieve the aspired realness and simplicity of art that

Cocteau envisioned.

En musique la ligne c’est la mélodie. Le retour au dessin entraînera nécessairement un retour à la mélodie. La profonde originalité d’un Satie donne aux jeunes musiciens un enseignement qui n’implique pas l’abandon de leur originalité propre. Wagner, Stravinsky et même Debussy, sont de belles pieuvres. Qui s’approche d’eux a du mal pour se dépêtrer de leurs tentacules; Satie montre une route blanche où chacun marque librement ses empreintes. In music, line is melody. The return to drawing will necessarily involve a return to melody. The profound originality of a Satie provides young musicians with a teaching that does not entail the desertion of their own originality. Wagner, Stravinsky, and even Debussy are first-rate octopuses. Whoever goes near them has difficulty escaping from their tentacles; Satie leaves a clear road open upon which everyone is free to leave their own imprint. 54

Cocteau not only equated the line with melody in the paragraph quoted above, but also associated the focus on this parameter in the work of the composers he named with evidence of their “originality.” Just a couple of sentences below the quoted passage, Cocteau affirmed Erik

53 See Jane Fulcher, “Music Theories,” in The Columbia History of Twentieth-Century French Thought , ed. Lawrence D. Kritzman (New York: Columbia University Press, 2006), 299. Fulcher also situates Cocteau’s denigration of Beethoven on a continued lineage in French musical thought following Debussy’s aesthetic positioning. For a detailed discussion of French discourses on melody and line through mappings onto the arabesque, see Bhogal, Details of Consequence , esp. chap. 2, “Ornament and the Arabesque from Line to Melody.” 54 Cocteau, Le Coq et l'Arlequin , 20. The translation has been amended, with kind help from Russ Manitt, from Myers’s translation, 20.

Satie as the paragon of this ideal: “Satie teaches what, in our age, is the greatest audacity, simplicity.” 55 This advocacy followed Cocteau’s intensive collaboration with that composer on their truly inter-artistic ballet “Parade” (1916–17), which also involved choreography by Léonide

Massine and stage and costume designs by Pablo Picasso. Picasso also demonstrated, in two monograms that he provided for Cocteau’s treatise, how a “return to the line” could be realized in the visual arts. The two figures, which depict respectively the cock (not reproduced here) and harlequin (Figure I.5), are drawn of a single line each, constituting examples of Picasso’s idiosyncratic line drawings. In these drawings, Picasso rendered entire figures exclusively through a black, uninterrupted line on a white background.

Figure I.5: Pablo Picasso, harlequin, from Cocteau’s treatise Cock and Harlequin 56

55 Cocteau, Cock and Harlequin , 20. 56 The harlequin appears on p. 33 of Cocteau, Cock and Harlequin , the cock on p. 17.

The qualities of “originality” and genuine expression of artistic truth that Cocteau ascribed to melody and the line in music and the visual arts respectively ties back to my earlier discussion of early twentieth-century artistic theories of the line. The extent to which shared aesthetic connotations between melody and line have persisted into artistic practice today will be the focus in the final section of this chapter.

Musical Lines Today

In this chapter, I have illustrated how musicians, music theorists, psychologists, and visual artists of the early twentieth century shared a preoccupation not merely with line and melody as artistic parameters, but also with their perception and cognition. The respective theories merged in parallel accounts, in which line and melody were featured as metaphors to explore reciprocally auditive and visual principles in musical, artistic, aesthetic, psychological, and physiological studies. This mapping has become so ingrained in Western thought that it has persisted to the present day. It crops up in common parlance about music and visual art. An artwork from 2014 will illustrate the extent of the continued allure of the melodic line, and help to draw together many of the shared aesthetic connotations that have been attached to melody and line during and since the 1920s.

“Mélodie du réel,” a series of paintings by French artist Fabienne Verdier (born in 1962), features a continuous brush stroke across seven large panels (see Figure I.6).57

57 Verdier’s panels are held at the Pinakothek der Moderne, Munich and were on exhibit in 2017. See “Talking Lines,” on Fabienne Verdier’s website, accessed December 4, 2017, http://fabienneverdier.com/db/talking-lines/ .

Figure I.6 : Fabienne Verdier, “Mélodie du réel” (2014), mounted at the Pinakothek der Moderne in Munich in Fall 2017 (my photograph)

When hung in a row on the museum wall, Verdier’s line presents a single horizontally oriented gesture, which moves up and down in carefully planned, organically proportioned waves. The evocation of melody, evolving “in the real,” as the title suggests, taps many of the epistemic conditions for such a mapping that originated about a century ago, as I discussed above. To start, the horizontal trajectory of Verdier’s line implies an underlying axis that denotes the passing of time. Given that the sounding line was conceptualized as the trace of a temporal process, such a horizontal orientation is a commonality across all examples of musical lines that I discuss in this dissertation and that I have found so far. The temporal axis dictates a unidirectional shape of the

musical line that progresses from left to right in a waveform, which cannot “return” towards the left since this move would denote a return into the past. This also means that the shape of Klee’s

“active line” as reproduced in Fig. I.1 above is unlikely to depict a specific “sounding line” since it curls back both at its start and end. Notably, however, the hand-drawn line in Klee’s manuscript takes a slightly different shape (see Figure I.7), which is more adept to representing melody (except for its curling back at the end towards the letter b).

Figure I.7 : Paul Klee, “freie Linie,” from the manuscript Bildnerische Formlehre 58

The temporal frame that is invoked through this alignment coheres with the majority of two-dimensional graphs that map a temporal evolution on the horizontal axis, as well as with

Western systems of writing and not least with music notation. All these systems have conditioned our eyes to trace the passing of time from left to right. But for painters to use this dimension creatively, Lindner observed in the same article from which I quoted at the beginning, a new tendency in the artistic practice of his day, the turn of the twentieth century:

Das künstlerisch decorative Bild hat nun die merklich-unmerkliche Tendenz, sich aus seiner verticalen Lage gleichsam um die Querachse des Rahmens, der in Ruhe bleibt, wandwärts ins Horizontale zu schieben. Von der Schwere des Materials befreit, das sich eine ihm immanente Technik erzwungen hat, lösen sich nun Linien und Farben—dies mag nur physiologisch zu erklären sein—vom Untergrunde los und kommen in

58 Paul Klee, “Bildnerische Form- und Gestaltungslehre” (Zentrum Paul Klee, Bern, 1921–1931), https://www.zpk.org/de/sammlung-forschung/sammlung-archiv/paul-klee-bildnerische-form-und- gestaltungslehre-389.html , “Bildnerische Formlehre,” 8 (BF/10), http://www.kleegestaltungslehre.zpk.org/ee/ZPK/BF/2012/01/01/010/ (accessed April 29, 2018).

schaffende Bewegung, indes das Papier oder Linnen fast transparent wird oder schwindet. 59 The artistic decorative image has the noticeable yet hardly imperceptible tendency to shift from its vertical to its horizontal position around the transversal axis of its frame, which stays still. Freed from the material weight that an immanent technique has enforced on it, lines and colors are released—this may only have a physiological explanation—from the background and are set into creative motion, while the paper or canvas becomes almost transparent or disappears.

According to Lindner, the shift of focus from the vertical to the horizontal orientation of painting liberated lines and colors from their material weight and enabled in turn their “creative motion” across the surface of the canvas. Music critic Friedrich Stichtenoth articulated a strikingly similar view in an essay that advanced metaphors from chemistry to characterize the musical textures of homophony and polyphony.60 Besides chemistry, Stichtenoth pointed to the historical juxtaposition between the horizontal and vertical dimensions in music and likened them to the techniques of drawing and painting in the visual arts. In art history, this duality traces back to the famous rivalry between “disegno” and “colorito” in Renaissance Italy. Projecting some of the central issues of that debate into the twentieth century, Stichtenoth further ascribed individualistic expression to the drawing of lines—and, analogously, to melody and other horizontally oriented formations in music—while he considered color and verticality “decorative material,” and associated this mode of expression with the masses rather than the individual.61

These analogies resonate in many ways with early twentieth-century discourse in the visual arts, as van de Velde’s text earlier illustrated.

59 Lindner, “Farbe und Linie,” 3. 60 Friedrich Stichtenoth, “Richtungs- und Quantentheorie in der Musik,” Die Musik 17, no. 12 (September 1925): 902–4, esp. 903. Stichtenoth’s essay is a response to an article by Paul Bekker in the same journal. Paul Bekker, “Einstimmige und mehrstimmige Musik,” Die Musik 17, no. 9 (June 1925): 648–57. 61 Stichtenoth, “Richtungs- und Quantentheorie in der Musik,” 903.

The artists Klee and Kandinsky described vertical and horizontal lines in similar terms in their treatises. Drawing on physical principles and positions of the human body, both connoted verticality with gravity, and horizontality with motive freedom, stirred by individualistic expression.62 For painters, these references not only identified the representational functions that lines might assume on the page, but they also determined physical, embodied actions in artistic practice. Indeed, the physical interplay between material gravity and the horizontal surface was also essential in the creation of Verdier’s “Mélodie du réel.” Having been trained in Japanese calligraphy, in which the pen is regarded as a direct, perpendicular connection between heaven and earth, Verdier exploited gravity to maximal efficiency by laying the canvases flat on the floor, aligning them thus with horizontality in the most primal way. 63 Across these surfaces, which had been covered in black, Verdier applied the white paint with a giant custom-made brush (made out of 36 horsetails). The perpendicular mounting of the brush exposed the canvases directly to the gravity of the paint and moreover carried the brush’s weight, thus freeing the artist to stir it in an expansive movement. The physical arrangement of materials thus allowed her to tap the expressive potential of the line, as a gesture growing out of an initial impetus.

Just as Verdier could thus paint the line of “Mélodie du réel” as a single coherent gesture, the viewer can follow the line not only with her eyes, but also her ears, to create—or recreate—a melody that rises and falls with the shape of the line. This engagement of the viewer accounts for the “realness” that the artist evoked in the artwork’s title.64 As we have observed above, the theoretical frame for such an interpretation goes back to early twentieth-century theories of

62 See Bonnefoit, Die Linientheorien von Paul Klee , 51–53. 63 This orientation is different from that of the paintings when they are affixed to the museum wall. 64 See Corinna Thierolf, curator of the exhibit “Talking Lines: Sigmar Polke meets Fabienne Verdier” at the Pinakothek der Moderne, Munich, booklet for the exhibit (trans. Lance Anderson): “‘Mélodie du réel’ is the realization of an event in the present time.… The viewer follows the white material in its natural and monumental movement.”

embodiment and cognition that were developed around the graphical line. “Realness,” moreover, summons up the aesthetic qualities of immediate and intuitive expression ascribed to the line in that cultural-historical context, such as in the writings of Henry van de Velde, as quoted earlier.

Throughout the twentieth century to today, scholars have continued to investigate the cognitive processes that facilitate metaphorical analogies between imagery related to different senses—such as in the “musical line.” Building on the groundbreaking research of George

Lakoff and Mark Johnson on conceptual metaphors, Lawrence Zbikowski has examined many common metaphors of musical parlance, attending in particular to issues of cross-domain mapping.65 For instance, in comparing different systems of organizing musical space, Zbikowski has analyzed the conceptual backdrop to denoting pitch along a vertical axis in the Western tradition (entailing as well the metaphor of “height”).66 This approach to structuring the vertical axis in two-dimensional depictions of music complements the temporality ascribed to the horizontal axis as noted above. This frame, which also determines conventional music notation, applies to all the musical lines discussed throughout this dissertation. It is through this cognitive map that viewers hear Verdier’s line as melody, or Kandinsky’s, or any of the examples to follow in the subsequent chapters.

65 George Lakoff and Mark Johnson, Metaphors We Live By (Chicago: University of Chicago Press, 1980), Lawrence Zbikowski, Conceptualizing Music: Cognitive Structure, Theory, and Analysis (Oxford: Oxford University Press, 2002). 66 See in particular Lawrence Zbikowski, “Metaphor and Music Theory: Reflections from Cognitive Science,” Music Theory Online 4 (1998): np, esp. § 3.4., and “Conceptual Models and Cross-Domain Mapping: New Perspectives on Theories of Music and Hierarchy,” Journal of Music Theory 41, no. 2 (October 1997): 193–225, esp. 200–4.

II. THE STATUS OF MELODY IN THE EARLY TWENTIETH CENTURY :

AESTHETICS , COMPOSITION , NOTATION , THEORY

Zur Zeit existiert ein Kursus “Melodielehre,” der die Materie vom Prinzip aus schematisch entwickelte, an den Musikschulen und in Lehrbüchern nicht, sondern die Elemente der Melodielehre werden notdürftig in der Harmonielehre abgehandelt und die höhern Stufen in der Kompositionslehre. 1 At present there does not exist a course teaching the theory of melody [”Melodielehre” ], which would develop the matter systematically from the fundamental principles, neither at the music schools nor in text books; instead the elements of a theory of melody are provisionally taught in the context of harmonic theory and the more advanced levels in composition studies.

From Nineteenth-Century Melodik to Twentieth-Century Melodielehre

As the doyen of the German tradition of nineteenth-century harmonic theory, Hugo

Riemann was himself complicit in the imbalance that he observed in the entry on “Melodie” quoted above from his Musik-Lexikon . Taking stock of this era, Riemann concluded that around

1900, there was neither an established pedagogical tradition nor a collection of theoretically substantial materials dedicated to melody. Even though by the turn of the century the topic attracted increasing attention, it is true that the hegemony of harmony had virtually eclipsed any theoretical endeavors focusing on melody throughout the nineteenth century. In the early twentieth century, in turn, melody moved center stage—not only in music theory, but also in compositional trends of the time, as well as in accompanying aesthetic and journalistic debates.

This chapter chronicles these parallel developments.

A central figure to my narrative unifies these trends in a single person. As one of the leading composers of his day, Ernst Toch (1887, Vienna – 1964, Santa Monica, CA) expanded his influence through his teaching. He took up his first position in Mannheim upon returning

1 Hugo Riemann, “Melodie,” in Musik-Lexikon , 5 th rev. ed. (Leipzig: M. Hesse, 1900), 714. 57

from World War I in 1919, and stayed there until 1929 when he moved to Berlin. Also after his

emigration to the United States in 1933, Toch dedicated much of his time—and increasingly also

his enthusiasm—to teaching, building a reputation as one of California’s preeminent teachers in

music. Dorothy Crawford surmises that by hiring Toch in 1940, the University of Southern

California attempted to rival the appointment of Arnold Schoenberg at UCLA. 2 After losing the

job in Southern California in 1948, Toch continued to teach privately at his home and attracted

many prominent students. Like so many esteemed teachers in music at the time, Toch also wrote

a treatise based on the preparations for his teaching: The Shaping Forces in Music: An Inquiry

into the Nature of Harmony, Melody, Counterpoint, and Form (1948). 3 Despite Crawford

describing The Shaping Forces in Music as “a book … still highly respected today,” few scholars have critically engaged with Toch’s ideas. 4

Even less known is Toch’s Melodielehre , which grew out of his doctoral dissertation, completed in 1921.5 I will discuss this treatise as an emblematic example of music-theoretical

2 Dorothy L. Crawford, “Ernst Toch,” chap. 7 in A Windfall of Musicians: Hitler’s Émigrés and Exiles in Southern California (New Haven: Yale University Press, 2009), 143. 3 Ernst Toch, The Shaping Forces in Music: An Inquiry into the Nature of Harmony, Melody, Counterpoint, and Form (New York: Dover, 1948). Another impetus for the publication of The Shaping Forces in Music came from Toch’s Harvard lectures in 1944, which were arranged by Elizabeth Sprague Coolidge, a close friend and avid supporter of Toch’s work. Incidentally and infelicitously, it was the publication of the treatise that ultimately cost Toch the job at the University of Southern California after the then acting dean of the university sought to interfere with the publication and enrich himself with it. Crawford, A Windfall of Musicians , 148. 4 Crawford, A Windfall of Musicians , 144. The shortcoming in scholarly acknowledgement of Toch as a music theorist is evinced by his absence from such standard encyclopedias of music theory as David Damschroder and David Russell Williams, Music Theory from Zarlino to Schenker: A Bibliography and Guide (Stuyvesant, NY: Pendragon Press, 1990). 5 Ernst Toch, Melodielehre: ein Beitrag zur Musiktheorie (Berlin: M. Hesse, 1923), Ernst Toch, “Beiträge zur Stilkunde der Melodie,” (Ph.D. dissertation, University of Heidelberg, 1921). Notable contributions to research on Toch as a music theorist come in particular from German scholars, including Michael Polth, “Zwischen Gestaltpsychologie und Funktionalität: Anmerkungen zur Melodielehre von Ernst Toch,” in Spurensicherung: der Komponist Ernst Toch (1887–1964)—Mannheimer Emigrantenschicksale , ed. Hermann Jung (Frankfurt/Main: Peter Lang, 2007), 101–19; Luitgard Schader, “Das Verhältnis von Ernst Tochs ‘Melodielehre’ zu Ernst Kurths ‘Grundlagen des linearen Kontrapunkts,’” Musiktheorie 18, no. 1 (2003): 51–64; and Heiko Schneider, Wahrhaftigkeit und Fortschritt: Ernst Toch in Deutschland 1919– 58

thought on melody of the early 1920s, both in the contextualization of theories on melody below and in more detail in Chapter III. As we shall see, Toch forged his own position within the aesthetic debates that accompanied the enthusiasm for melody in the 1920s. His compositions challenged performers, listeners, music publishers, and critics to adjust their expectations, notational possibilities, and vocabulary to account for musical trends of their time. It is in this context and out of these demands, I will argue, that lines emerged as a particularly effective imagery for melodic processes in music.

To understand the disruption that these tendencies meant at Toch’s time, I begin with a review of the stakes attached to discussions of melody in the nineteenth century, which induced

Riemann’s observation about the absence of melodic theories around 1900.

The Nineteenth Century

For the nineteenth century, and more specifically for German culture at the time of

Richard Wagner, David Trippett diagnoses a “neurosis surrounding melodic expression” in musical identity, which he ascribes to the idealist conception of melodic invention as a “gift of nature,” reserved serendipitously for the intuition of a few genius composers. 6 To frame these stakes arround discourses on melody, Trippett evokes the words of Johann Wolfgang Goethe, who likened the inspiration behind Ludwig van Beethoven’s music to a stroke of lightning. 7

Trippett analyzes the ways in which nineteenth-century aesthetics of creative genius directed such assumptions of effortless and unconscious musical composition primarily at the invention

1933 (Mainz: Schott, 2007), esp. chap. 3 “Die Akzentuierung des Melos—Tochs theoretische Arbeit,” 58–77. 6 David Trippett, Wagner’s Melodies: Aesthetics and Materialism in German Musical Identity (New York: Cambridge University Press, 2013), 70. “The gift of nature” is an expression of Hector Berlioz (1837). 7 Trippett, Wagner’s Melodies , 69. 59

of melody—an association that he traces back to eighteenth-century Scottish physician John

Gregory. 8 Couched as such in Romantic discourses on genius in the wake of the Kantian-

Hegelian tradition, melody was variously theorized as the locus of emotional expression, individuality, and originality—values that overloaded melodic composition “with expectations of expressive truth, emotional intensity, natural form.” 9

This precious status was also reflected in German copyright law, which in the 1830s

“recognized … [melody ] as the main protectable ‘object’ of a musical work”—a legacy that continues to the present day, as Michael Polth reminds us. 10 While conceived at first to defend the commercial property of publishers, Trippett narrates how the concern with fending off the creative property of their works increasingly agitated composers as well, including Wagner, whose “fear of copyright infringement” conflicted with “his desire to learn from Bellini by imitation.” 11 Much as with Wagner’s desire to learn by imitating his contemporaries, Trippett discusses how legal concerns resurfaced in music pedagogy, where the common method of learning through imitation and modeling had to be weighed against accusations of infringing on someone else’s original work. Also Toch addressed preoccupations with issues of plagiarism in melodic composition, though through the back door and with an apparently more lenient attitude.

Observing the prevalence of certain quasi-formulaic melodic and rhythmic gestures especially in the music of the Classical era, Toch cited various musical examples to demonstrate their similarities. Toch’s Examples 255 and 256, for instance, comprise themes from Beethoven’s

8 Trippett, Wagner’s Melodies , 70, referring to John Gregory, A Comparative View of the State and Faculties of Man with those of the Animal World (London: R. Griffiths, 1765, 364): “musical genius consists in the invention of melody suited to produce a desired effect on the mind.” 9 Trippett, Wagner’s Melodies , 72. 10 Trippett, Wagner’s Melodies , 137; Polth, “Zwischen Gestaltpsychologie und Funktionalität,” 104 fn. 7. 11 Trippett, Wagner’s Melodies , 11. 60

Symphony No. 7 and a similar melody from a symphony by Christian Cannabich. 12 Toch presented these two excerpts, which differ primarily in their metrical organization, as a

“curiosity” and as fodder for “plagiarism hunters.”13 However, the nonchalance with which Toch treated such cases belied his deep-rooted beliefs in the originality of melodic composition, which mirrored his nineteenth-century predecessors, as we shall see later.

Aggravating the resistance to a pedagogical approach towards the construction of melody in the nineteenth century, meanwhile, was what Trippett refers to as the “idealist mantra that melody could not truly be invented through conscious awareness.” 14 Trippett reconstructs how the vision for overcoming such skepticism relied on an epistemological shift towards a materialist aesthetic, which would objectify melody and isolate it from the subject of the genius composer. 15 Only as such could melody become the issue—or, indeed, the matter—of theoretical scrutiny and pedagogical scaffolding. Melodic invention had thus to be dissociated not only from the pedestal of the predestined genius composers, but also from the specter of unconscious and effortless intuition. Concomitantly, theorists had to redefine the meaning of talent and genius and their relation to one another, to acknowledge that the fruition of genius relied on talent paired with assiduous work and practice. Only in this realm could music theorists offer didactic

12 Toch, Melodielehre , 147–8. 13 Toch commented on the two examples under a section entitled “‘Plagiat’-Jäger heraus!” in Melodielehre , 148. An early review of Toch’s treatise by Eugen Tetzel testifies to the fact that Toch’s contemporaries reacted promptly to such calls. Tetzel took issue with another group of musical examples in Toch’s treatise, dedicated to an excerpt of Mozart’s Die Zauberflöte (referring to Melodielehre , 174 and 179–80, Examples 313 and 325–7). In the respective examples, Toch experimented with the rhythmic organization of Mozart’s theme, recomposing it in two alternative variants, to demonstrate the effect of different structural orders. Though he suggested that the theme was not originally composed by Mozart, Toch was primarily concerned with the rhythmic versatility of any given melodic motive. Tetzel, however, reacted with a vehement defense of Mozart against the—alleged—insinuation of plagiarism of a melody by Muzio Clementi. Tetzel, review of Toch’s Melodielehre , Archiv für Musikwissenschaft 6, no. 2 (July 1924): 250. 14 Trippett, Wagner’s Melodies , 76. 15 Trippett, Wagner’s Melodies , 79. Trippett discusses the “epistemological shift between thought as disembodied imagination and quantifiable, material substance.” 61

guidance. In full self-awareness of the aesthetic ideals that they intervened against, theorists like

Gottfried Weber modestly propounded not the teaching of “melody” itself, but merely the construction of a “succession of tones” (“Tonfolgen”).16 Trippett summarizes these efforts of offering didactic guidance under the heading of Melodik , a term that Weber coined to demarcate his endeavors as a self-consciously theoretical approach to teaching the unteachable

(“melody”).17

Melodik continued to determine the common theoretical approach towards melody in the final decades of the nineteenth century, beyond the timeframe that Trippett considers in his monograph. 18 My list of treatises in Table II.1 picks up from where Trippett’s study leaves off and shows that up to the turn of the century, most treatises on melody pursued the pedagogical effort of Melodik , occasionally also under the alternative title of Melodiebildungslehre .19 Ludwig

Bussler’s Elementarmelodik zur Weckung und Förderung des musikalischen Talentes und

Vorstellungsvermögens (1879), for instance, is a representative Melodik in this sense, which corroborates its agenda further in the subtitle, sechsunddreissig Aufgaben in rein anschaulicher

Darstellung (thirty-six exercises in clear demonstrative presentation). In accordance with the ambitions of Melodik , the book is structured around these practical exercises and promises to foster and nurture musical talent on an individual basis: “to awake the slumbering talent, to nurture it once awake, as well as to establish the existence and degree of talent in the first

16 Trippett refers to a term used by both A.B. Marx (1837) and Johann Christian Lobe (1854). He also cites a passage from F.A. Kanne’s “Der Zauber der Tonkunst” (1821), in which Kanne juxtaposes aesthetic ascriptions of “melody” against the purely theoretical conception of Melodik. Trippett, Wagner’s Melodies , 72–74. 17 Trippett locates the definition in Weber’s Versuch einer geordneten Theorie der Tonsetzkunst , vol. 1 (Mainz: Schott, 1824). Trippett, Wagner’s Melodies , 71. 18 See the list of approaches to Melodik that Trippett provides in Wagner’s Melodies , 75. 19 This term appears for instance in the title of Franz Joseph Kunkel, Theoretisch-praktische Vorschule der Melodiebildungslehre ( Leipzig: C. Merseburger, 1874), or Emil Breslauer’s Melodiebildungslehre auf Grundlage des harmonischen und rhythmischen Elements (Stuttgart: C. Grüninger, 1895). 62

place.” 20 In the list of Table II.1, Bussler’s contribution marks the tail end of nineteenth-century

Melodik . While his text served later theorists as a reference point—as I discuss below—their endeavors soon took different directions.

Table II.1 : Treatises on Melody, 1874–1937 21 Author Publication Title

Kunkel, Franz Leipzig, 1874 Theoretisch-praktische Vorschule der Joseph Melodiebildungslehre Bussler, Ludwig Leipzig, 1879 Elementarmelodik zur Weckung und Förderung des musikalischen Talentes und Vorstellungsvermögens: sechsunddreissig Aufgaben in rein anschaulicher Darstellung 22 Riemann, Hugo Hamburg, 1883 Neue Schule der Melodik: Entwurf einer Lehre des Contrapunkts nach einer gänzlich neuen Methode Michaelis, Alfred Leipzig, 1887 Melodielehre nebst einleitenden praktischen Akkordstudien Breslauer, Emil Stuttgart, 1895 Melodiebildungslehre auf Grundlage des harmonischen und rhythmischen Elements Kuhlo, Franz Charlottenburg, Über melodische Verzierungen in der Tonkunst 1896 Cremers, E. Paris et.al., 1898 L'analyse et la composition mélodiques 23 Jadassohn, Leipzig, 1899 Das Wesen der Melodie in der Tonkunst 24 Salomon Goetschius, Percy New York, 1900 Exercises in Melody-Writing: A Systematic Course of Melodic Composition, Designed for the Use of Young Music Students, Chiefly as a Course of Exercise Collateral with the Study of Harmony

20 “Das schlummernde Talent zu wecken, und das geweckte zu fördern, sowie auch über das Vorhandensein des Talentes überhaupt und den Grad desselben rechtzeitige Aufschlüsse zu geben.” Ludwig Bussler, Elementarmelodik zur Weckung und Förderung des musikalischen Talentes und Vorstellungsvermögens: sechsunddreissig Aufgaben in rein anschaulicher Darstellung (Leipzig: Breitkopf und Härtel, 1879), iv. 21 This table collects pertinent treatises from Europe and North America in the indicated time frame and thus continues a survey of studies on melody that David Trippett has provided for the nineteenth century. See Wagner’s Melodies , 75. Trippett cites F. Geyer’s Musikalische Compositionslehre (1862) as the last entry to his list. The table also includes the contributions listed by Polth, “Zwischen Gestaltpsychologie und Funktionalität,” n. 3. The focus is on German language sources and those cross-referenced in them. 22 Cited as a reference both by Riemann, Musik-Lexikon (Leipzig: M. Hesse, 1900), 714, and Toch, Melodielehre , iii. 23 Referenced by Riemann, Musik-Lexikon, 714. 24 Referenced by Toch, Melodielehre , iii. 63

Table II.1 (Continued)

Pembaur, Josef Leipzig, 1901 Harmonie- und Melodielehre: praktisches Lehrbuch mit vielen Beispielen der hervorragendsten Komponisten (+ Beispiele und Aufgaben zur Harmonie- und Melodielehre , 1903) Mey, Curt Leipzig, 1901 Die metaphysischen Urgesetze der Melodik (Die Musik als tönende Weltidee, Versuch einer Metaphysik der Musik , vol. 1) Meyer, Max Columbia, Mo., Contributions to a Psychological Theory of Music 1901 Lipps, Theodor Leipzig, 1902 “Zur Theorie der Melodie” (in Zeitschrift für Psychologie und Physiologie der Sinnesorgane) 25 Abert, Hermann Halle a S., 1902 Die ästhetischen Grundsätze der mittelalterlichen Melodiebildung: Eine Studie zur Musikästhetik des Mittelalters Weinmann, Fritz Leipzig, 1904 Zur Struktur der Melodie 26 Capellen, Georg Leipzig, 1908 Fortschrittliche Harmonie- und Melodielehre Bingham, Walter Baltimore, MD, Studies in Melody (in Psychological Review ) Van Dyke 1910 Leichtentritt, Leipzig, 1911 Musikalische Formenlehre 27 Hugo Lach, Robert Leipzig, 1913 Studien zur Entwickelungsgeschichte der ornamentalen Melopöie: Beiträge zur Geschichte der Melodie Kurth, Ernst Bern, 1917 Grundlagen des Linearen Kontrapunkts: Einführung in Stil und Technik von Bach’s melodischer Polyphonie Scheffler, Karl Berlin, 1919 Die Melodie: Versuch einer Synthese nebst einer Kritik der Zeit Schenker, Vienna, since Der Tonwille. Flugblätter (Vierteljahrschrift) zum Heinrich 1921 Zeugnis unwandelbarer Gesetze der Tonkunst einer neuen Jugend dargebracht (early ideas on Urlinie ) Mersmann, Hans Berlin, 1922 Beethoven: die Synthese der Stile Toch, Ernst Berlin, 1923 Melodielehre: ein Beitrag zur Musiktheorie Hauer, Josef Leipzig, 1923 Deutung des Melos: Eine Frage an die Künstler und Matthias Denker unserer Zeit Hoffmann, Ernst Berlin, 1924 Das Wesen der Melodie , vol. 1 Roeseling, Oberkassel, Beiträge zur Untersuchung der Grundhaltung Kaspar 1928 romantischer Melodik

25 Lipp’s essay is a reaction to Max Meyer’s Contributions to a Psychological Theory of Music (1901). 26 Weinmann’s monograph grew out his doctoral dissertation that he completed under Theodor Lipps in Munich. 27 Referenced by Toch, Melodielehre , iii. 64

Table II.1 (Continued)

Woehl, Leipzig, 1929 Melodielehre Waldemar Nestele, Albert Leipzig, 1930 Die musikalische Produktion im Kindesalter: eine experimentalpsychologische Untersuchung der kindlichen Melodik Blessinger, Karl Stuttgart, 1930 Melodielehre als Einführung in die Musiktheorie Kind ī; Mahmoud Leipzig, 1931 Ris āla f ī ḫubr t āʼlīf al-al ḥān (Über die Komposition El Hefny, Robert der Melodien) 28 Lachmann (ed., transl.) Danckert, Werner Kassel, 1932 Ursymbole melodischer Gestaltung: Beiträge zur Typologie der Personalstyle aus sechs Jahrhunderten der abendländischen Musikgeschichte Kauder, Hugo Vienna, 1932 Entwurf einer neuen Melodie- und Harmonielehre Scheffler, Berlin, 1933 Melodie der Welle (Rundfunkschriften für Rufer und Siegfried Hörer , vol. 4) Schenker, Vienna, 1935 Der freie Satz: das erste Lehrbuch der Musik (Neue Heinrich musikalische Theorien und Phantasien , vol. 3) Hindemith, Paul Mainz, 1937 Unterweisung im Tonsatz , esp. vol. 1 “Theoretischer Teil” Szabolcsi, Bence Budapest, 1950 A melódia története (Bausteine zu einer Geschichte der Melodie, 1959) 29

Into the Twentieth Century

Melodik (griech.), die Lehre von der Melodie. 30 Melodik (Greek), the theory of melody.

According to his preface, Ernst Toch wrote his Melodielehre to overcome the dearth of treatises on melody that he perceived as the inevitable consequence of the dominion of harmony treatises throughout the nineteenth century. 31 Toch illustrated the exigency of his undertaking

(and the inequality of attention that the two musical parameters had attained) by observing the

28 A copy with annotations of this volume is preserved in Arnold Schoenberg’s Nachlass. 29 By his own indication, the author started to compile materials in 1930, and had accumulated the bulk of materials for the book by 1940. 30 Hugo Riemann, Musik-Lexikon , 715. 31 Ernst Toch, Melodielehre , iii. 65

inexistence of even a single professorship for melody, let alone a textbook. To underscore his point, Toch invoked the authority of Hugo Riemann, indicating that that author had lamented the lack of a systematic theory of melody in his Musik-Lexikon .32 Toch must have been referring to the passage cited in the opening epigraph of this chapter, which is taken from Riemann’s lexicon entry on “melody.” Also the following entry that Riemann offered in his Lexikon , on “Melodik,” is—in its lack of content besides an etymological definition of the term—suggestive of the scarcity he perceived in the field: “ Melodik , the theory of melody.”

In calling upon Riemann’s authority for the assessment of the situation, Toch did not seem to mind that it was this theorist, who, at the same time, personified the very tradition that he sought to overcome, namely the predominance of harmony treatises in German music theory of the nineteenth century. Indeed, he even included Riemann in the desultory list of a handful of other theorists who had made tentative advances towards a rigorous study of melody—despite the fact that Riemann classified his Neue Schule der Melodik in its sub-title as a “sketch of a wholly new approach to counterpoint” (“Entwurf einer Lehre des Contrapunkts nach einer gänzlich neuen Methode”) rather than a real “Melodielehre.” Nonetheless, as Toch put it,

“Riemann, Bußler, Jadassohn, Leichtentritt and others have more or less skated over the question of melodic formation and have thus granted it a modest place within the all-encompassing theory of forms ( Formenlehre ).” 33 This statement also echoes Riemann’s hesitant acknowledgement of a list of eighteenth- and nineteenth-century theorists (including himself) whom he considered to

32 See Toch, Melodielehre , iv, referring to Riemann’s Musik-Lexikon . 33 “Riemann, Bußler, Jadassohn, Leichtentritt und andere haben die Frage der Melodiebildung mehr oder weniger gestreift, wobei sie ihr ein bescheidenes Plätzchen in der allumfassenden Formenlehre einräumten.” Toch, Melodielehre , iii-iv. The subsumption of these approaches under the title of “Formenlehre” most likely stems from Leichtentritt, Musikalische Formenlehre . Based on the reference to Riemann’s lexicon entry, the citation of that author must be geared more specifically at Riemann, Neue Schule der Melodik . 66

have proposed, as he put it with an excess of caution, “attempts at an initial approach to an actual theory of melody.”34

According to Michael Polth, taking stock of contemporary approaches in this vein—as merely modest advances towards a “real” theory of melody—was a practice extending much beyond Riemann and Toch. 35 In his survey of treatises on melody from around 1900, Polth observes that many authors of the period indicated their lack of awareness of any other robust study dedicated to melody, leading to what Carl Dahlhaus described as “Beziehungslosigkeit verstreuter Ansätze” between the emergent Melodielehren of the time. 36 In spite of this perception at the time (as conveyed in the dire picture of the field that Toch painted in his preface, alongside Riemann and other authors) and an apparent lack of coordination between the various contributions, Polth has discerned a historically unprecedented (and unrepeated) surge in treatises on melody around the turn of the twentieth century. Toch’s Melodielehre falls about mid-way in the time period that Polth considers for this intensified attention on melody, which he frames with Hugo Riemann’s Neue Schule der Melodik (1883) and Hugo Kauder’s Entwurf einer neuen Melodie- und Harmonielehre (1932) respectively. I propose a slightly extended time frame for this phenomenon, which encompasses both Ludwig Bussler’s Elementarmelodik

(1879)—an earlier contribution that both Riemann and Toch mention as a source of reference, as seen above—and Paul Hindemith’s Unterweisung im Tonsatz (1937). Hindemith’s treatise not

34 “Als Versuche der Anbahnung einer eigentlichen Melodielehre sind zu nennen...” Riemann, “Melodie,” 714. The theories that Riemann lists in this category include Joseph Riepel’s volumes on Tonordnung (1755 and later), Christoph Nichelmann’s Die Melodie (1755), Anton Reicha’s Traité de mélodie (1814), Ludwig Bussler’s Elementar-Melodik zur Weckung und Förderung des musikalischen Talentes und Vorstellungsvermögens (1879), Riemann’s own Neue Schule der Melodik (1883) as well as a chapter from his Katechismus der Kompositionslehre (1897), and E. Cremers’ L’analyse et la composition mélodiques (1898). 35 Polth, “Zwischen Gestaltpsychologie und Funktionalität.“ 36 Quoted from Polth, “Zwischen Gestaltpsychologie und Funktionalität,“ 102, referring to Lars Ulrich Abraham and Carl Dahlhaus, Melodielehre (Colone: Gerig, 1972), 16. Dahlhaus’s assessment refers to the history of melody treatises holistically. 67

only contains influential thoughts regarding the formation of melody, especially in its first volume, “Theoretischer Teil,” but also constitutes a pertinent source given that evaluations of

Toch’s oeuvre have repeatedly staged him in comparison Hindemith. Table II.1 provides a list of treatises within this extended time frame (1874–1937).

The diversity in orientation between these various contributions justifies the contemporaneous perspective expressed by many authors that an “actual” theory of melody had yet to be written. From the historically removed vantage point of today, this plurality can be delineated historiographically as the progression from nineteenth-century Melodik to the “new”

Melodielehren of the early twentieth century. In my discussion below, I elucidate how this trajectory was linked with the two designations Melodik and Melodielehre . Since their distinction does not translate well into English, I henceforth use the two terms in the German original.

I argue that the change in orientation of treatises on melody was conditioned by the flux in epistemic and aesthetic paradigms that underlay musical discourse. While Polth’s study contextualizes the treatises on melody within purely music-theoretical concerns—suggesting that, whether consciously or not, the various authors engaged with the shared heritage of

Riemann’s theory of tonal functions ( Funktionstheorie )—I propose to consider a more diverse scope of ideas as the intellectual background to theories of melody. 37 My analysis examines how the emergence of research in cognition around 1900 impacted discourses on melody, arguing that this new scientific paradigm facilitated an enriched interpretation of melody as a line. Moreover,

I position the music-theoretical attention devoted to melody in the broader musical life, with compositional trends and aesthetic debates equally shaping theoretical approaches.

37 “Daher treffen sich die Melodielehren der Jahrzehnte nach 1900 darin, dass sie in irgendeiner Weise auf die Funktionstheorie Hugo Riemanns rekurrieren.” Polth, “Zwischen Gestaltpsychologie und Funktionalität,” 103. 68

In terms of situating Toch’s contribution within the legacy of music-theoretical thought, I

propose that, rather than reflecting specifically on Riemann’s function theory, Toch took

guidance from the ambitions of (German) harmony treatises of the nineteenth century. In

particular, he picked up their agenda of chronicling principles of “musical logic,” a catchword

that, according to Adolf Nowak, had accompanied music-theoretical endeavors since the Middle

Ages. “Musical logic” became a prominent umbrella particularly for music theorists of the

nineteenth and early twentieth centuries. 38 Considering that Riemann had successfully

instantiated himself as the epitome of this tradition, his early essay on the topic and his vision of

music theory in general likely served Toch as reference when he declared his aspiration to

unravel the “musical logic” of melodic composition.39 For Toch, this task consisted in exploring

the “eternal iron laws” (“ewig eherne Gesetze”) of melodic construction that had persisted

through centuries of constant stylistic change:

eine Art Leitfaden der musikalischen Logik …, der sich freilich wird ändern, erneuern und anpassen müssen, wie der Strom der Musik selbst sich stets erneuert, jedoch in jeder Wandlung und Erneuerung “ewig eherne” Gesetze bergen wird, wie alle Wandlung und Erneuerung nur verschiedener Ausdruck einer ewigen Wahrheit ist. 40

38 For a broad history of definitions of “musical logic” in music theoretical thought from Augustinus to John Cage see Adolf Nowak, Musikalische Logik: Prinzipien und Modelle musikalischen Denkens in ihren geschichtlichen Kontexten (Hildesheim: Georg Olms Verlag, 2015). For discussions of specific discourses in the nineteenth and early twentieth centuries—especially by German theorists—see Patrick Boenke and Birger Petersen-Mikkelsen, eds., Musikalische Logik und musikalischer Zusammenhang: vierzehn Beiträge zur Musiktheorie und Ästhetik im 19. Jahrhundert (Hildesheim: Georg Olms Verlag, 2014). 39 On Riemann’s early article on “Musikalische Logik” (originally published in 1872 under the pseudonym Hugibert Ries), see Kevin Mooney, “‘Musical Logic: A Contribution to the Theory of Music’ by Hugibert Ries,” Journal of Music Theory. 44, no. 1 (2000): 100–126, Kevin Mooney, “Hugo Riemann’s Debut as a Music Theorist,” Journal of Music Theory 44, no. 1 (2000): 81–99, and Helga De la Motte-Haber, “Musikalische Logik: Über das System von Hugo Riemann,” in Musiktheorie , ed. Helga De la Motte-Haber and Oliver Schwab-Felisch (Laaber: Laaber, 2005), 203–23. With regards to Riemann’s influence on German music theory, see in particular Alexander Rehding, Hugo Riemann and the Birth of Modern Musical Thought (Cambridge: Cambridge University Press, 2003), and David W. Bernstein, “Nineteenth-Century Harmonic Theory: The Austro-German Legacy,” in The Cambridge History of Western Music Theory , ed. Thomas Christensen (Cambridge: Cambridge University Press, 2002), 778–811. 40 Toch, Melodielehre , Preface, iii. 69

a kind of guidance of musical logic …, which obviously will change, will have to renew and adapt, like the stream of music which constantly regenerates itself; but will bear in every change and renewal “eternal iron” laws, as all change and renewal is only varied expression of eternal truth.

History—the constant “stream” of change in compositional styles, as Toch portrayed it— thus served as the epistemological cornerstone of Toch’s approach. The broad historical and stylistic range of musical examples that Toch provided throughout the treatise—spanning over four centuries and including also folk song melodies and hymn tunes—not only offers plenty of illustrations, but also constitutes the very essence of Toch’s argument.41 For only from this vast survey of musical styles could he derive those melodic features that history carved out as persistently successful. In evaluating these principles and deducing analytical categories from them, Toch’s endeavors parallel those of nineteenth-century harmony treatises. Toch aspired to do for melody what Riemann had achieved for harmony: to discuss the musical parameter on an aesthetic and scientific level and to develop apposite theoretical taxonomies for it.

Lifting melody to the level of aesthetic investigation, Toch in turn dismissed any pedagogical ambitions for his work. Here as well, he invoked the tradition of Harmonielehren as his model, to declare that melodic composition, “just like harmonic invention, could not be taught.” 42 Toch articulated this casting off of a pedagogical responsibility yet more explicitly in his preface, as I cite below, distancing himself thus from the air of pedagogical systematization that had become both historically and etymologically ingrained in the tradition of Melodik.

Through this approach, which targeted the aesthetics and history of melody in lieu of its pedagogy, Toch’s treatise exemplifies the new era of Melodielehren . Polth has labeled it “im neuen Geiste” and characterized these treatises as theoretical rather than practical, and as

41 Polth has described the rich amount of musical examples in Melodielehre as one of its most convincing features, without however acknowledging the rational weight that they have to carry in Toch’s approach. Polth, “Zwischen Gestaltpsychologie und Funktionalität,” 101. 42 “Aber ebensowenig kann das Erfinden von Harmonien gelehrt werden.” Toch, Melodielehre , iii. 70

redirecting their focus from the pedagogical construction of melody to its scientific and aesthetic exploration.43 In that vein, the Melodielehren of the early twentieth century are clearly set apart from the Melodik of their nineteenth-century precursors. The treatises listed in Table II.1 clarify this trajectory. In the decades after 1900, pedagogically oriented treatises on melody became increasingly rare. And even though the terminological distinction between “Melodielehre” and

“Melodik” did not consistently reflect a treatise’s methodological orientation—a vagueness manifest as well in the entry on “Melodik” in Riemann’s Musik-Lexikon , as quoted in the epigraph to this section —the denomination “Melodik” gradually disappeared from titles. Any further publications appearing under the heading of “Melodik” referred not to pedagogical endeavors but only to studies of stylistically contained repertoires, such as Kaspar Roeseling’s

Beiträge zur Untersuchung der Grundhaltung romantischer Melodik (1928), or Albert Nestele’s examination of children’s expression in melodic composition (1930). Overall, treatises on melody from the 1900s to the 30s were dedicated predominantly to aesthetic discussions of melody in various forms, rather than to didactical concerns. Or, as Polth describes it, they were no longer invested in “the aesthetic quality of the still-to-be-composed melody, but rather in the scientific quality of explanation of the already-composed melody.” 44

Under these altered conditions, then, melody transcended its status as an idea and was now discussed as an a priori formation. It became the very substance of Melodielehre , whereas

Melodik positioned itself in self-conscious distance from the idealist notion of “melody” to focus

43 Polth delineates this trend from practical to theoretical Melodielehren (his terms: “praktische und theoretische Melodielehren”) in a cursory survey. Polth, “Zwischen Gestaltpsychologie und Funktionalität,” 104–5. Even though Polth hints at the necessary pragmatism of the superseded practical approach, his narrative does not consider the rich aesthetic debates underlying such decisions. 44 “Der Anspruch hatte sich verlagert: Es ging nicht mehr um die ästhetische Qualität der (zu komponierenden) Melodie, sondern um die wissenschaftliche Qualität der Erklärung einer (bereits komponierten) Melodie.” Polth, “Zwischen Gestaltpsychologie und Funktionalität,” 105. 71

instead on “Tonfolgen.” This epistemological shift followed through to their fullest effect the materialist conditions that Trippett has outlined for a project of Melodielehre from its inception.

The historical trajectory in discourse on melody as delineated above—from nineteenth- century Melodik to twentieth-century Melodielehre —paralleled two other general developments in the history of music theory. The first pertains to the shift from harmony to melody as the main musical parameter of investigation. As his reflection on “musical logic” and its guidance for nineteenth-century harmony treatises indicates, Toch perceived himself to be a pioneer on the front of melody. Secondly, I propose that these developments correlate with the changing paradigms of scientific collaboration that underlie music-theoretical endeavors. In this narrative, the emergence of experimental psychology in German academia provided the epistemic basis for the endeavors of the new Melodielehre . I thus read the “new spirit” (Polth’s ascription of

“Melodielehren ‘im neuen Geiste’”) of twentieth-century Melodielehre in terms of its engagement with a cognitive perspective on music. While nineteenth-century theorists drew on physics, and later physiology, to explain the consistency of diatonic harmony, twentieth-century theorists preferred to invoke the emergent framework of psychology and cognitive research to underpin their elucidations of melody scientifically.45 And like the acoustic research in nineteenth-century laboratories, the music-cognitive investigations of the early twentieth century were a truly interdisciplinary endeavor. 46 Not only did music theorists lean on psychological

45 Alexander Rehding has described this shift in the history of music theory as the evolution from an “age of acoustics” to an “age of psychology.” Rehding describes this paradigm shift by the example of changes in Hugo Riemann’s thought, summarizing the period as, “the age of psychology was about to supersede the age of acoustics.” Rehding, Hugo Riemann and the Birth of Modern Musical Thought , 34. 46 On the interdisciplinary exchange between nineteenth-century scientists, instrument makers, and music theorists, see for example Myles W. Jackson, Harmonious Triads: Physicists, Musicians, and Instrument Makers in Nineteenth-Century Germany (Cambridge, MA: MIT Press, 2006), David Pantalony, Altered Sensations: Rudolph Koenig’s Acoustical Workshop in Nineteenth-Century Paris (Dordrecht: Springer, 2009), Alexandra Hui, The Psychophysical Ear: Musical Experiments, Experimental Sounds, 1840–1910 (Cambridge, MA: MIT Press, 2013), and Alexandra Hui, Julia Kursell, and Myles W. Jackson, “Music, 72

advances, but many pioneering studies in different streams of psychological research also drew on melody as the phenomenon of choice to examine and demonstrate cognitive mechanisms. As we shall see in the next chapter, this pertained to such seminal studies as Christian von

Ehrenfels’s article “On ‘Gestalt Qualities’” (1890), or to the contributions on melody by Theodor

Lipps (1901) and his student Fritz Weinmann (1904), listed in Table II.1. 47 Appearing shortly after the turn of the century, Lipps’s and Weinmann’s texts also corroborate the transition in focus from Melodik to Melodielehre , as outlined above. While Ehrenfels, Lipps, and Weinmann approached melody from the professional perspective of philosophy and psychology, Toch’s treatise offers a complementary angle, through the lens of a musically trained listener. How the changing paradigms from physics and acoustics to psychology and cognition impacted theories of melody will be at the center of my discussion in Chapter III.

Ernst Toch and Aesthetic Debates ca. 1920

It was not music theorists and psychologists who turned their attention to melody in the early twentieth century. The new Melodielehre was accompanied as well by aesthetic debates that negotiated the stakes of theorizing melody within the cultural and ideological conditions of the time. Some of the primary concerns in these discussions were inherited from the prejudice melody faced under the auspices of the nineteenth-century veneration of the genius composer as

Sound, and the Laboratory from 1750–1980,” Osiris 28, no. 1 (2013): 1-11. Other authors who have traced the changing alliances and research interests of music theorists and scientists during the nineteenth century and the emergence of a psychological orientation in music theory include Youn Kim, “Theories of Musical Hearing, 1863–1931: Helmholtz, Stumpf, Riemann and Kurth in Historical Context” (Ph.D. dissertation, Columbia University, 2003) and Benjamin Steege, Helmholtz and the Modern Listener (Cambridge: Cambridge University Press, 2012). 47 This narrative also holds true in scientific discourses in the United States. Walter van Dyke Bingham dedicated his doctoral dissertation in psychology (at the University of Chicago) to examinations of melody, citing both Lipps and Weinmann as authorities of reference. Walter Van Dyke Bingham, Studies in Melody , The Psychological Review: Monograph Supplements 12, no. 3 (1910): 3. 73

outlined above, while others arose from the changed dynamics of compositional styles and music-theoretical agendas after the turn of the century. The main issues of the debate that I examine below encompass the nature of music’s “material” and the compositional origins of melody, the role and relevance of pedagogical efforts and systematized music analysis, the pertinence of harmonic considerations in theories of melody, as well as the reliance on history as a carving stone for aesthetic ideals. The arguments featured some of the most prominent and vocal musical thinkers of the day, including Hans Pfitzner, Arnold Schoenberg, Alban Berg, and

Ferruccio Busoni. 48 Their propositions shaped musical ideas of melody at the time, meaning that authors of Melodielehren had to engage with the arguments in one way or another. In the following, I trace and contextualize this idiosyncratic position within the poles of the field.

Defining History to Shape the Present

Like Toch, Ferruccio Busoni, Arnold Schoenberg, and Hans Pfitzner called upon music history to legitimize their arguments—though their conceptions of music history ranged from determinedly utopian to radically dystopian. Verging towards one extreme on this scale,

Busoni’s Sketch of a New Esthetic of Music (1907) is often cited as sparking debates about the state of music in the 1910s and 20s. 49 Busoni’s vision targeted the future of music, which he envisioned as constantly striving to free itself from various material constraints. Pfitzner

48 For succinct discussions of these debates see for example Josef-Horst Lederer, “Pfitzner - Schönberg: Theorie der Gegensätze,” Archiv für Musikwissenschaft 35, no. 4 (1978): 297–309, and Ullrich Scheideler, “Einfall –Material – Geschichte: zur Bedeutung dieser Kategorien im Musikdenken Pfitzners und Schönbergs um 1910,” in Autorschaft als historische Konstruktion: Arnold Schönberg : Vorgänger, Zeitgenossen, Nachfolger und Interpreten , ed. Andreas Meyer and Ullrich Scheideler (Stuttgart: Metzler, 2001), 159–88. 49 Busoni’s manifesto was first published in German in 1907. Ferruccio Busoni, Entwurf einer neuen Ästhetik der Tonkunst , 2nd rev. ed. (1916), with annotations by Arnold Schoenberg and an afterword by H.H. Stuckenschmidt (Leipzig: Insel-Verl., 1974). As Scheideler writes, the vehement debates about its ideas started mostly in reaction to the second and slightly revised edition from 1916. Scheideler, “Einfall –Material – Geschichte,” 161. 74

forcefully contested this forward-looking aesthetic in his provocative essay Futuristengefahr

(1917), contending that music history had already passed its prime. 50 In Pfitzner’s nostalgia, a pedestal was reserved for Ludwig van Beethoven whose work instantiated an insurmountable pinnacle, which in turn entailed an inevitable downward trajectory in subsequent developments.

Also Schoenberg reacted to Busoni’s and, more strongly, to Pfitzner’s positions, though his comments remained unpublished as a draft essay under the title “Falscher Alarm,” an unperformed musical parody, and as various marginalia in his copies of Busoni’s and Pfitzner’s publications. 51 As Ullrich Scheideler analyzes, both Schoenberg and Pfitzner legitimized their respective compositional styles by claiming their obligation towards music history. As a result of their progressively diverging stylistic ideals, however, they construed increasingly oppositional narratives of music history and the attendant responsibilities of the composer. 52

Toch’s historical purview, in which he equitably quoted musical works from past and present, mediated between these positions—at least superficially. He quoted not only from

Pfitzner’s opera Palestrina (first performed in 1917), but also from several of Schoenberg’s compositions, including Verklärte Nacht, Op. 4 (Toch’s Example 24), Gurrelieder (Toch’s

Examples 111–12), and Kammersymphonie , Op. 9 (Toch’s Example 199). In Melodielehre , these excerpts coexist and might even illustrate the same observations as works by Anton Bruckner,

Richard Wagner, and indeed Beethoven. Among these composers, however, Beethoven received

50 Futuristengefahr was first published in 1917. For summaries and discussions of the issues of contention and the various positions of its protagonists, see Scheideler, “Einfall – Material – Geschichte” and Lederer, “Pfitzner – Schönberg.” While Lederer emphasizes the differences between Schoenberg’s and Pfitzner’s positions (as the title of the essay indicates), Scheideler sheds light more on common points between Schoenberg, Pfitzner, and Busoni. 51 On these various sources see especially Lederer, “Pfitzner – Schönberg,” and Joseph Auner, “Composing on Stage: Schoenberg and the Creative Process as Public Performance,” 19th-Century Music 29, no. 1 (2005): 64–93, as well as Scheideler, “Einfall – Material – Geschichte”, Josef Rufer, Das Werk Arnold Schönbergs (Kassel: Bärenreiter, 1959), and Hans Heinz Stuckenschmidt, Arnold Schönberg (Zurich: Atlantis, 1957). 52 See Scheideler, “Einfall – Material – Geschichte,” 169. 75

special attention from Toch as I will illustrate at the end of Chapter III, resulting in a partiality that parallels Pfitzner’s.

Despite some fundamental deviations from Pfitzner’s aesthetic—such as the span of musical repertoires that he considered in Melodielehre , which well exceeded the limited historical styles that Pfitzner deemed accessible—Toch’s viewpoints in general align most comprehensively with that composer-theorist’s ideas. 53 But again, Toch did not confine himself to a single position. As if ignorant of the overt opposition between the various parties—or, perhaps, overly confident in bridging these polar divides—he sent review copies of Melodielehre to all three protagonists mentioned above—Busoni, Pfitzner, and Schoenberg. From the former two, he elicited positive feedback, as Heiko Schneider has chronicled. 54 The few comments that

Schoenberg added to his copy of the treatise, by contrast, are mostly skeptical if not cynical, calling Toch a “dilettante,” and a “jackass.” 55 Possible reasons for Schoenberg’s judgment follow below.

Invention (“Einfall”)

Aside from shaping narratives of history, the notion of musical inspiration (“Einfall”) was a central issue in the debates. Schoenberg, Pfitzner, and Busoni all agreed on the utmost

53 Heiko Schneider has also commented on traces of Pfitzner’s ideology in Toch’s writings. See Heiko Schneider, Wahrhaftigkeit und Fortschritt: Ernst Toch in Deutschland 1919–1933 (Mainz: Schott, 2007), 67. In some respects, Toch aligned more with Schoenberg’s or Busoni’s perspectives rather than with Pfitzner’s, such as with regard to his view on musical performance. Toch’s meticulous annotations in the parts of his String Quartet Op. 26, for instance—as discussed below—would probably have raised a laugh from Pfitzner. As Lederer recounts, Pfitzner ridiculed Schoenberg’s detailed annotations of his scores, such as the “Hauptstimme-” and “Nebenstimme”-symbols. 54 Schneider, Wahrhaftigkeit und Fortschritt , 67–8. 55 Regarding Schoenberg’s reaction, see transcriptions of his comments in Julia Bungardt, “Die Bibliothek Arnold Schönbergs mit einem kommentierten Katalog des nachgelassenen Bestandes sowie einer Edition seiner Glossen in den Büchern” (Ph.D. dissertation, University of Music and Performing Arts Vienna, 2014), esp. Erläuterungen 30–40. Schoenberg’s exclamations read “Dilletant!, ” (sic) and “Natürlich, dieser Esel! ” 76

importance of inspiration in the compositional process. And as in the nineteenth century, they saw inspiration most distinctly manifest itself in melody, as representative of the motivic essence of a musical work. But while Schoenberg acknowledged the necessity of conscious reflection and the training of compositional craft (“Handwerk”) as preconditions to forming larger works,

Pfitzner confined his aesthetic to the unconscious invention of the musical “Einfall,” which by itself determined the quality of a composition. This distinction is also expressed in linguistic terms. While “Einfall” can simply denote an idea (as the result equally of conscious rumination or effortless intuition), Pfitzner employed the term as a near synonym to “Eingebung,” which carries connotations of a divine afflatus. In other words, while Schoenberg sought to objectify the “Einfall” as “idea” and as material that could—and had to—be manipulated in the compositional process, Pfitzner idolized melodic inspiration as subjective expression (and

“intuition”)—preferably of the genius composer—which should not be tampered with. 56

Pfitzner’s ideology thus mirrors melody’s idealist aura of unconscious and genius invention that had been so painstakingly contested about a century before, as Trippett’s study highlights.

The main issues of this debate reverberate in the following statement from Melodielehre , in which Toch weighed aspects of both positions in a careful terminological distinction. He differentiated between a theme—a constructed “product” of “labor”—on the one hand and a melody—the outgrowth of a composer’s “invention”—on the other:

56 This juxtaposition follows Lederer’s discussion of the debate. Lederer, “Pfitzner – Schönberg,” esp. 299. In reality, the situation might have been not quite as straightforward as this narrative suggests. The debate assumed a new dimension when Alban Berg got involved, offering a detailed analysis of Robert Schumann’s “Träumerei” from Kinderszenen in Alban Berg, “Die musikalische Impotenz der ‘neuen Ästhetik’ Hans Pfitzners,” Musikblätter des Anbruch 2, nos. 11–12 (1920): 399–408. While Berg sought to expose how the “simply beautiful” relied on motivic and formal constructive features of the composition and in doing so endorse Schoenberg’s position, Schoenberg himself was less enthusiastic about the escalation of the debate that Berg’s article caused. Another prominent voice at the time for the veneration of the genius composer was, of course, Heinrich Schenker. For a discussion of Schenker’s pertinent ideology see for example Suzannah Clark, “The Politics of the Urlinie in Schenker’s ‘Der Tonwille’ and ‘Der Freie Satz,’” Journal of the Royal Musical Association 132, no. 1 (2007): 141–64. 77

Das Thema ist vielmehr bereits ein Produkt, ein Geschöpf der Melodie. … Man wird niemals von einer “melodischen,” sondern immer nur von einer “thematischen” Arbeit , niemals aber von der “thematischen,” sondern nur von der “melodischen” Erfindung eines Tondichters sprechen. 57 The theme is rather already a product, born out of melody. … One would never speak of “melodic” working , but only ever of “thematic” working , and never of a “thematic” but only ever of “melodic” invention of a composer.

Reminiscent as well of August Halm’s dialectic juxtaposition between Two Cultures of

Music (Von zwei Kulturen der Musik , 1913), Toch further elaborated on the different stylistic contexts of theme and melody. 58 Just as Halm had hypostatized the two cultures as Bach’s Fugue and Beethoven’s Sonata respectively (as we saw in Chapter I), and opposed the free horizontal development of the one to the symmetrical punctuation of the other, Toch continued:

[Das Thema ] ist schon scharf umrissen und vor allem räumlich begrenzt (man denke an das klassische “achttaktige” Thema). Es ist der mit symmetrischen Flächen (“Zweitakt”) begabte Krystall, der sich aus dem lockeren, unbegrenzten Urstoff “Melodie” gebildet hat. Auch haftet dem Begriff “Thema” bereits der Gedanke der Wiederholung und Verarbeitung, ja der Polyphonie an, während die Melodie etwas durchaus frei bewegliches, homophones ist. … Die Melodie ist das Unendliche, das Thema das Endliche; die Melodie das Begriffliche, das Thema das Stoffliche. 59 [The theme ] is already clearly demarcated and particularly delimited in spatial terms (just think of the classical eight-measured theme). Like a crystal, it is enclosed in symmetrical facets, which formed from the loose, unbound Urstoff of “Melody.” Moreover, the term “Theme” already entails notions of repetition and reworking, of polyphony really, whereas melody is something quite freely moving, homophone. … Melody is infinite, theme finite; melody is conceptual, theme material.

In particular the differentiation between melody as an unbound mobile concept on the one hand, and a classical theme as symmetrically bound and materially delimited on the other follows the template of binaries in Halm’s theory. Only Toch’s association of these principles with homophonic and polyphonic textures inverts their relative attribution to Bach’s Fugue and

57 Toch, Melodielehre , 7. On that page, Toch also denoted melody the “Urstoff.” 58 For an incisive reading of Halm’s text Von zwei Kulturen der Musik (Munich: Georg Müller, 1913), see Alexander Rehding, “August Halm’s Two Cultures as Nature,” in Music Theory and Natural Order from the Renaissance to the Early Twentieth Century , ed. Suzannah Clark and Alexander Rehding (Cambridge: Cambridge University Press, 2001), 142–60. 59 Toch, Melodielehre , 7. 78

Beethoven’s Sonata in Halm’s universe. Toch’s study sheds light indeed on the melodies of

Beethoven’s compositions rather than on the themes —or so, at least, he conceived of it. Toch concluded not to deliberate over the labor of composition (a process associated with the musical theme)—even though he would certainly have had insights to share on this topic from his perspective as a working composer—but to study instead the creative outbursts of other composers in the form of melodies.

Theory vs. Pedagogy

This angle of aesthetic inquiry set the course for Toch’s pursuits in Melodielehre and diverted him away from any pedagogical commitment with regards to the composition of melody. Toch was in fact quite outspoken about the lack of pedagogical intentions of his treatise.

He explained his stance through the belief that melodic composition could not actually be taught.

Already in the opening paragraph of his preface, he conceded, with clear Pfitznerian undertones:

Nun ist es zwar selbstverständlich, daß das Erfinden von Melodien nicht gelehrt werden kann, sondern Sache der Eingebung ist. Aber ebensowenig kann das Erfinden von Harmonien gelehrt werden. 60 Now it is of course obvious that the invention of melodies cannot be taught, but that it is the outcome of inspiration. But the invention of harmonies can be taught to just as little an extent.

It was only consistent for Toch to clarify that he did not envision Melodielehre as a pedagogical treatise (“Lehrbuch”):

Wenngleich sie nicht gerade als Lehrbuch gedacht ist, so ist sie vielleicht doch imstande, einiges Licht auf ein Gebiet zu werfen, welches die sonst so regsame und geschäftige Musik“theorie” ziemlich im Dunkeln gelassen hat. 61

60 Toch, Melodielehre , iii. 61 Toch, Melodielehre , iii. 79

While not really conceived as a pedagogical treatise, [Melodielehre ] is perhaps still able to shed some light on an area that the otherwise so active and sedulous Music “Theory” has left mostly in the dark.

These declarations appear at odds with Toch’s lament in the same paragraph over the lack of textbooks and professorships pertaining to melody and his reference to Bussler’s Melodik as one of the tentative precursors to his endeavors. 62 By dismissing the possibility of didactic guidance for melodic composition, Toch’s treatise indeed emphasizes the rupture rather than the continuation in lineage of music theoretical discourse on melody from the time of Bussler’s

Melodik (1879).

Instead, Toch’s position finds prominent precedence in the ideological debates of his day, as outlined above. In particular, his premise regarding melody as a matter of “Eingebung”

(“inspiration”) parallels Pfitzner’s ideology. In full consistency with his propositions regarding the origins of melodic invention—which he considered a matter of effortless intuition—Pfitzner had maintained that melodic composition could not be taught. As mentioned earlier, Pfitzner revived the “idealist mantra,” which Trippett has chronicled for the early nineteenth century. In parallel to these debates, which had led to the materialist turn on melody in the 1830s, Pfitzner’s polemic instigated theorists in the 1910s and 1920s to tackle and redefine anew such fundamental categories as intuition, creativity, expression, and comprehensibility in music.

Pfitzner’s take on melody as un-teachable invention was paired not only with his dismissal of pedagogical efforts towards the composition of melody, but furthermore with a defensive stance against the intervention of systematized music analysis.

62 As noted above, both Riemann and Toch each mentioned Bussler in their respective lists of theorists whom they considered as having prepared a path towards a “real” Melodielehre . 80

Theory vs. “Entzauberung”

Pfitzner sought to protect music against explanatory attempts through analysis, an infringement that he considered to be disenchantment (“Entzauberung”). In its place, he asserted that the quality of a composition could be assessed solely through intuitive sensibility—a capacity that he himself claimed to possess. This conceit gave rise to derision in Schoenberg’s commentary in the margins of his copy of Futuristengefahr , as Josef-Horst Lederer recounts, and also inspired a rebuttal by Alban Berg in a review of Pfitzner’s essay Die neue Ästhetik der musikalischen Impotenz .63 Unlike these counters, the specter of Pfitzner’s mistrust of theory crops up in various places in Toch’s writings. In an essay from 1923 on “Musik-‘theorie,’” for instance, Toch criticized the discipline of music theory for its detachment from the practical concerns that inspired him as a composer. 64 Such skepticism towards the achievements of

“Music Theory,” with capital letters, also shined through in the passage from the preface to

Melodielehre quoted above, where Toch announced his intention to “shed some light on a topic which has been left mostly in the dark by the otherwise so active and sedulous Music ‘Theory.’”

While such assertions raise the expectation that Melodielehre—coincidentally published in the same year as his essay of discontent—would rectify such shortcomings, the remainder of the preface is rather modest in tone. By Toch’s own accounts, the treatise constitutes a

“collection of thoughts that I received as the manifestations of practical musical experience and

63 See Lederer, “Pfitzner - Schönberg,” 304n42. Berg’s review appeared under the title “Die musikalische Impotenz der neuen Ästhetik Hans Pfitzners” Musikblätter des Anbruch 2 (1920): 399–408. The first edition of Pfitzner’s text was printed in 1920 as well. For a discussion of Berg’s essay see Scheideler, “Einfall –Material – Geschichte,” 168n37. 64 The essay was published in Ernst Toch, “Musik-‘theorie,’” Rheinische Musik- und Theater-Zeitung 24 (1923): 94–8; see also Klaus Wolfgang Niemöller, “Ein ‘rheinisches Jungtalent’ : Ernst Toch im Rheinland der 1920er Jahre,” in Spurensicherung: der Komponist Ernst Toch (1887-1964)—Mannheimer Emigrantenschicksale , ed. Hermann Jung (Frankfurt/Main: Peter Lang, 2007), 67–82 at 71. 81

from teaching in music theory, and which I deemed worthy of writing down.” 65 Toch chose to remain quiet about the analytical scrutiny that served to derive and collate these “thoughts.”

Rather than admitting to any such “disenchanting” process of examination, he again adopted a distinctively Pfitznerian viewpoint and claimed to have “received” (“empfangen”) these insights, as a listener who (so the implication) did not interfere with the sacrosanct manifestations of melodic invention. 66

Still, within the aesthetic debates of his day, Toch’s contribution stands out as the only treatise devoted to melody, against the pamphlets and manifestos through which especially

Busoni and Pfitzner expressed their views. Toch’s decision to write a Melodielehre demonstrated his commitment to engage with the legacy of earlier contributions to the genre, to which Toch responded at least in demarcating his distance from the pedagogical orientation of his precursors.

For the rest, his appeal to Riemann’s assessment, which concluded in a lack of a pertinent body of literature—a survey in the negative—seemingly absolved Toch from the need of further reflection.

This evasion of dialogue is symptomatic of Toch’s presentation of his treatise more broadly, which similarly appears tinged by Pfitzner’s safeguarding of melodic invention from theoretical scrutiny and modeling. In Toch’s portrayal of his treatise, this also translated into his omitting to mention that Melodielehre arose from his doctoral dissertation Beiträge zu einer

Stilkunde der Melodie , which he had finished two years earlier (in 1921) under the supervision of

Theodor Kroyer at the University of Heidelberg. While the work on that manuscript had actually

65 “Sie enthält eine Sammlung von Gedanken, welche ich aus den Niederschlägen praktischen Musikerlebens und musik-theoretischer Unterrichtstätigkeit empfangen und der Aufzeichnung wert gehalten habe.” Toch, Melodielehre , iii. The emphasis is mine. 66 On the gender dynamics invoked in such conceptions see Claire Taylor-Jay, “‘I Am Blessed with Fruit’: Masculinity, Androgyny and Creativity in Early Twentieth-Century German Music,” in Masculinity and Western Musical Practice , ed. Ian Biddle and Kirsten Gibson (Farnham, UK: Ashgate, 2009), 183–207. 82

furnished the bulk of the published treatise, Toch chose to portray Melodielehre as more practically oriented instead, as emerging not from scholarly research but from “practical musical experience” and teaching. More gravely, Luitgard Schader has found fault with Toch’s veiling of the scholarly origins of his treatise by omitting various bibliographic references to his sources that he had originally included and cited in his dissertation. 67 Based on these observations,

Schader accuses Toch of deceiving the reader about the intellectual property of many of the ideas presented in the treatise, and in particular of suppressing the alleged influence of Ernst Kurth’s treatise Grundlagen des linearen Kontrapunkts: Bach’s melodische Polyphonie from 1917. 68

While Heiko Schneider has discounted Schader’s allegation of plagiarism of Kurth’s treatise as untenable—and in Chapter III I add additional aspects of divergence between Toch’s and

Kurth’s theories that call Schader’s allegation into question—the bibliographic laxity exposed in

Melodielehre undeniably distances Toch from the standards of scholarly discourse, perhaps even by the norms of the early twentieth century. 69 He evidently, and possibly opportunistically, chose to maintain references ad lib, while sweeping others under the carpet. While he peppered his argument with comments on contemporaneous aesthetic debates, for instance, on Schoenberg’s infamous stance on non-harmonic tones (as discussed below) and on Pfitzner’s equally polemical ideology on musical invention, Toch omitted possible relations to methodological models— including, notably, any indication of templates for his cognitive perspective and earlier mappings of melody onto the line.

67 Luitgard Schader, “Das Verhältnis von Ernst Tochs ‘Melodielehre’ zu Ernst Kurths ‘Grundlagen des linearen Kontrapunkts,’” Musiktheorie 18, no. 1 (2003): 51-64. Schader bases her accusations on a comparison of the dissertation with the published treatise. 68 Schader points out that Toch had quoted from Kurth’s treatise in his dissertation, but in his treatise he merely suggested that Kurth’s work had appeared in print during his own work on Melodielehre , without acknowledging its influence on his ideas. 69 Schneider, Wahrhaftigkeit und Fortschritt , esp. 67. 83

Harmony

Not surprisingly, harmony was a contested subject in aesthetic debates of the 1920s, including its pertinence for considerations of melody. Busoni had proposed to enrich the chromatic vocabulary by inserting quarter-tones and other smaller increments. Driven by a nostalgia for common-practice harmony, Pfitzner vehemently rejected this suggestion. He countered that even a single tone would suffice to compose a melody, aided perhaps by different shadings in harmony and rhythm. As an illustrious straw man, Pfitzner cited a melody from

Albert Lortzing’s Zar und Zimmermann (1837), which repeats the same tone eleven times, and provocatively lauded the excerpt as “one of the most popular melodies of German opera.”70 To

Schoenberg, this very example demonstrated Pfitzner’s poor judgment, and he derided his opponent for missing the irony of Lortzing’s melody as a representation of the respective character in the opera’s plot. 71 Toch, meanwhile, embraced Pfitzner’s stance unwaveringly. In one of his rare citations and bibliographical references, Toch quoted at length the pertinent passage from Futuristengefahr (of which a copy is extant in Toch’s Nachlass), including the musical excerpt from Lortzing’s opera.72 He concurred with Pfitzner not only on rebuffing

Busoni’s proposition of extending chromaticism, but also on advocating simplicity in melodic composition.

Toch’s outspoken alliance with Pfitzner could only have fostered Schoenberg’s scorn for

Melodielehre , as the latter expressed in such exclamations as “dilettante” and “jackass” in the

70 “Eine der allerpopulärsten Melodien der deutschen Opernmusik.” Hans Pfitzner, Gesammelte Schriften (Augsburg: Filser, 1926), 1:215–16. A similar musical example of such a pointed reduction in pitch is Peter Cornelius’s song “Ein Ton,” Op. 3/3 (1854). 71 On Schoenberg’s reaction, see Lederer, “Pfitzner - Schönberg,” 304n42. 72 Hans Pfitzner, “Futuristengefahr,” in Gesammelte Schriften , vol. 1 (Augsburg: Filser, 1926), 185–223. Toch’s Nachlass is hosted at the Library Special Collections, Performing Arts of, the University of California, Los Angeles. The copy of Futuristengefahr is listed in the catalog of the collection. Toch’s quote is in Melodielehre , 13–14. Toch references the original passage as page 40 of Futuristengefahr . 84

margins of his copy of the treatise. 73 The two composer-theorists also diverged with regards to their views on harmony, both in their creative and intellectual outputs. By the 1920s, as Toch was exploring the confines of tonality in his compositions—as I analyze below with regards to his String Quartet No. 9, Op. 26—Schoenberg had already claimed much more radical pathways.

Toch never adopted these compositional principles that Schoenberg pioneered, and in fact confined the works of Schoenberg’s that he cited in his treatise to compositions of an earlier, more conventionally tonal phase (from Verklärte Nacht of 1899 to the Gurrelieder of 1911).

Moreover, Toch defied Schoenberg’s propositions about harmony in theoretical terms. In

Melodielehre , Toch opened his own discussion on “Harmoniefremde Töne als

Melodiebildungsmittel” (his Ch. VII) by quoting at length from Schoenberg’s Harmonielehre

(1911). 74 The passage contains Schoenberg’s infamous dismissal of the very notion of

“harmoniefremde Töne.” Countering Schoenberg, Toch advocated for maintaining a distinction between “harmonic” and “non-harmonic” tones and argued that both were equally essential for the formation of melody. This defense of harmony as a valid factor in considerations of melody exposes—at least in theory—a conservative bent in Toch’s stance that his isolated study of melody might otherwise not suggest. In practice, however, instances in Toch’s analytical annotations of musical examples still evince carelessness with regards to the underlying harmonic organization of the respective excerpts, as Michael Polth in particular has criticized, and as I discuss in more detail in Chapter III.75 But rather than addressing melody’s functionality with regards to harmony, Toch envisioned his treatise as capturing principles of organization

73 See Julia Bungardt, “Die Bibliothek Arnold Schönbergs ,” 30–40. 74 Toch, Melodielehre , 108–111. 75 Polth, “Zwischen Gestaltpsychologie und Funktionalität.” Polth demonstrates what he perceives as a shortcoming of Toch’s theory through the example of Toch’s annotations of Frédéric Chopin’s Mazurka in B-flat major, Op. 7, No. 1. As I discuss in Chapter III, these examples illustrate the extent to which Toch isolated melody from its underlying harmonic framework. 85

internal to melody and to study their relation to music’s expressive effect. Indeed, the isolation of melody from harmony afforded Toch the possibility independently to explore principles of melodic construction in their own right and to analyze melody as a holistic musical entity. This ambition resonated with the cultural preoccupations of the time, as I illustrated earlier.

To Toch, the composer, moreover, this theoretical approach must have appeared highly relevant. Regardless of his stance on pedagogy, it must have seemed applicable to his compositional craft, not least at a time when traditional harmonic coherence was on the verge of dissolution. By the 1920s, chordal structure and cadential syntax had lost their structuring impact in musical composition. In lieu of these vertical ties, horizontally oriented structures determined the new compositional practice and aesthetics. One of Toch’s own compositions offers a model of these new compositional aspirations—as well as of the challenges they entailed for performers, music printers, listeners, and critics.

Composing, Notating, Performing, and Listening to Linear Music in the 1920s: Ernst Toch’s String Quartet No. 9 in C Major, Op. 26 (1919/20)

In 1919, upon returning from serving as a soldier in the war, Toch composed his ninth

String Quartet, Op. 26. It is his last work in this genre to bear a designated key: C major. While that key clearly comes to the fore at structural moments throughout the work, Toch also tested out its limits through high chromaticism and harmonic progressions beyond the vocabulary of functional tonality.76 Listeners then and now have remarked on this Quartet as a “key work of a new creative period,” referring both to Toch’s oeuvre, as well as to the compositional trends of

76 See Michael Kube, “Eckpunkte des Schaffens: zu den Streichquartetten Ernst Tochs,” in Spurensicherung: der Komponist Ernst Toch (1887–1964) – Mannheimer Emigrantenschicksale , ed. Hermann Jung (Frankfurt/Main: Peter Lang, 2007), 160. 86

the era more generally.77 While Alfred Rosenzweig noted in 1926 how “in this work the German musical style of the post-war-era emanates as organically grown,”78 Otto Steinhagen described this new style six years later with more specificity:

Im dritten [Satz ], einem Adagio , wird der melodische Zug der vier Horizontalen immer eigenmächtiger. Sie lösen sich scheinbar von jeder vertikalen Bindung. In the third [movement ], an Adagio , the melodic directionality of the four horizontal [lines ] becomes increasingly independent. They seemingly isolate themselves from any vertical ties. 79

Steinhagen’s commentary captures how the growing independence of each voice in the horizontal direction went hand-in-hand with the dissolution of “vertical ties.” This analysis of

Toch’s Quartet coheres with the general tendency in German composition of the 1920s as Hugo

Holle had summarized with stunning concision already ten years earlier. Remarking on the second Donaueschinger Kammermusikfest, Holle noted:

Da die zeitgenössische Musik klar erkennbar von der homophon-harmonischen Satzweise wegdrängt und (auch ein Zeichen der ewigen Wellenbewegung in allem künstlerischen Geschehen) wieder zu einer linear gerichteten Schreibart, zur polyphonen Kunst strebt…, erledigen sich naturgemäß Formen, die durch ihren komplizierten Apparat und ihre nur “füllenden” Stimmen das Eigenleben der einzelnen “Linien” im mehrstimmigen Satz beeinträchtigen. So kommt man wie von selbst auf die edelste, reinste und schönste allen Musizierens: die Kammermusik. 80 As contemporary music clearly shifts away from a homophonic-harmonic compositional practice and aims again towards a linearly oriented practice, a polyphonic art (a sign as well of the constant wave motion in all artistic creation)…, those forms that impede the independent life of the individual lines in a polyphonic texture through their complicated

77 “Schlüsselwerk der neuen Schaffensphase,” paraphrasing a judgment of Alfred Rosenzweig, see below. Schneider, Wahrhaftigkeit und Fortschritt , 83. 78 Quoted in Schneider, Wahrhaftigkeit und Fortschritt , 83–4, citing Alfred Rosenzweig, “Ernst Toch,” in Die Musik 18, no. 4 (January 1926): 250, “wie in diesem Werk der deutsche Musikstil der Nachkriegszeit organisch gewachsen aufsteigt.” 79 Quoted in Schneider, Wahrhaftigkeit und Fortschritt , 86, citing Otto Steinhagen, “Ernst Toch und die neue Musik,” Die Musik 25/2 (Nov. 1932): 90–1. 80 Hugo Holle, “Zum zweiten Kammermusikfest in Donaueschingen,” Neue Musik-Zeitung 43, no. 20 (August 1922): 318. The historical model that Holle alludes to as the “constant wave motion in all artistic creation” was developed by Alfred Lorenz. See Alfred Lorenz, Abendländische Musikgeschichte im Rhythmus der Generationen (Berlin: M. Hesse, 1928). 87

apparatus and their merely “filling” voices naturally become obsolete. Thus one arrives at the noblest, purest and most beautiful of all musicking: chamber music.

As Holle pointed out, the dissolution of harmonic ties rendered obsolete the function of “filling” voices. Instead, all voices were supposed to contribute to the linear-polyphonic texture. This shift meant not only a reduction of voices, but also their democratization: rather than serving as the accompaniment in a homophonic texture, all instruments participated equally in the horizontal interweaving of polyphonic voices. More so than in previous works, Toch explored the compositional consequences of such aspired equality among all voices in his Quartet Op. 26.

In yet other social terms, Schneider has described the focus on chamber music as the primary stage of compositional experimentation in the 1920s through the evocation of community (“Gemeinschaftsgedanke”) in music making.81 Small ensembles, Schneider reasons, were more adept at adapting to new demands—a fair assessment in principle, though Toch’s

Quartet Op. 26, among many other works of the era, tested the limits of this adaptability as we shall see below. Still, the focus on chamber music suited the economic conditions of the post-war era. Moreover, Schneider notes that the limitation to a few instrumental parts promoted the transparency of the musical texture, a quality soon to be captured as a trademark of “Neue

Sachlichkeit.” 82

While Holle defined chamber music at large as the locus for stylistic experiments,

Schneider and Michael Kube both zoom in more specifically on the string quartet as a genre in which composers such as Toch and Paul Hindemith, among many others, developed their

81 Schneider, Wahrhaftigkeit und Fortschritt , 80. 82 Schneider, Wahrhaftigkeit und Fortschritt , 78–82. While the string quartet was a favored genre of the early 1920s, composers increasingly experimented with the juxtaposition of sonically disparate timbres in less homogeneous and more unconventional combinations of instruments to further emphasize the linear independence of the various parts. This, however, applies less to Toch and more to other composers of his time, such as Paul Hindemith. 88

individual compositional voice.83 Both of these authors delineate Toch’s early stylistic evolution through a survey of his quartets. With a total of 13 finished compositions, Toch was indeed very prolific in this genre. As Kube chronicles, the clustering of many of these works in Toch’s early career is due to the pedagogical function that they assumed for the young composer. Toch, who preferably stylized himself as an autodidact, recounted that he learned most of his craft by studying and copying out scores of string quartets by Mozart and Brahms. 84 These studies transferred into Toch’s own compositional explorations, such that the first five works that he catalogued with opus-numbers are all string quartets (all of these are, however, lost). Three further early quartets (Nos. 6–8) appeared as opera 12, 15, and 18 respectively. After the hiatus of the first World War, three works followed during Toch’s “Mannheim period” of the 1920s:

After Op. 26, Quartets No. 10 (Op. 28, “On the Name ‘Bass’”) and No. 11 (Op. 34) were composed in 1921 and 1924 respectively. But then ensued a gap of over 20 years until Toch returned to the genre in 1946 and 1954 to add his opera 70 and 73. Kube additionally lists an unfinished quartet that Toch commenced in 1962, and the stand-alone piece “Dedication” for string quartet that Toch composed in 1948 for the wedding of his daughter.85

Another, yet more intimate kind of instrumentation that lent itself to the exploration of new tonal pathways were pieces scored for a single instrument, and here in particular, besides works for piano, those for solo string instruments. These compositions, which adapted the virtuosic études and studies of nineteenth-century composers and violinists to the “serious” style

83 Kube, “Eckpunkte des Schaffens.” Kube also published a parallel study on Hindemiths frühe Streichquartette (1915–1923): Studien zu Form, Faktur und Harmonik (Kassel; New York: Bärenreiter, 1997). A similar approach can also be applied to Arnold Schoenberg, whose four String Quartets famously delineate the composer’s stylistic periods. 84 Kube, “Eckpunkte des Schaffens,” 152–53. 85 The list of Toch’s quartets appears in Kube, “Eckpunkte des Schaffens,” 151. Another survey over Toch’s oeuvre, organized per genre and presented with incipits is provided in Charles Anthony Johnson, “The Unpublished Works of Ernst Toch” (Ph.D. dissertation, University of California Los Angeles, 1973); for the quartets see pp. 382–94. 89

of the early twentieth century, conjured the specter of Bach’s Sonatas and Partitas for Solo

Violin, as well as his Cello Suites. That allusion was important because of the lineage that

modernist composers claimed with Bach’s oeuvre, and the rejection of such a relation by

conservative critics, as I discuss later. 86

Toch’s Op. 26

Like critics of the 1920s, both Kube and Schneider discuss Toch’s Op. 26 as the crystallization of his compositional voice.87 Rather than granting agency to Toch, however—as

the earlier commentators did—recent authors have tended to subsume this style under trends

ascribed primarily to the efforts of Paul Hindemith, Toch’s fellow student at the Hoch

Conservatory in Frankfurt around 1910. Indeed, comparisons with Hindemith loom large in the

reception history of Toch’s work. Most commonly they credit Hindemith as the pioneer and

portray Toch unfavorably as a follower—despite Toch’s seniority and the chronological

precedence of some of his works compared to Hindemith’s. Kube, for instance, compares Toch’s

86 Examples include Max Reger’s works and work-cycles for solo violin between 1900–14, such as his Four Sonatas Op. 42 (1900), the Prelude and Fugue in A minor (without opus number) from 1920, Seven Sonatas Op. 91 (1905), Eight Preludes, Fugues and Chaconne Op. 117 (1909/12), and Six Preludes and Fugues Op. 131a (1914). Moreover, Reger scored the Three Suites Op. 131d (1916) for solo viola and the Three Suites Op. 131c for solo cello (1914). Hindemith’s compositions encompass three Sonatas for Solo Violin [Op. 11, No. 6 (1917), Op. 31, No. 1 and 2 (1924) ], four for solo viola [Op. 11 No. 5 (1919), Op. 25, No. 1 (1922), Op. 31, No. 4 (1923), and without number (1937) ], as well as one for solo cello [Op. 25, No. 3 (1923) ]. Other examples include Eugène Ysaÿe’s Six Sonatas for Solo Violin, Op. 27 (1923), Emil Bohnke, who composed his Three Sonatas Op. 13 respectively for solo violin, viola, and cello (1924), a Sonata for Violin Solo by Erwin Schulhoff (1927), and Ernst Krenek’s Sonata No. 1 for Solo Violin, Op. 33 (1925) (as well as a later one in 1949, his Op. 115). Also scored for solo cello are Zoltán Kodály’s Sonata Op. 8 (1915) and the Capriccio of the same year, as well as a Suite by Gaspar Cassadó (1926). Toch composed Two Études for Violoncello Solo (1930). Artur Schnabel’s Sonata for Solo Violin (1919) will be mentioned again later in the context of adopting a musical-analytical framework developed for Bach’s polyphony for compositions of the early twentieth century. 87 These two authors have also provided analytical commentary on the composition. While Kube has sketched the harmonic and formal layout of the whole work, Schneider’s more detailed analysis focuses on the last two movements. Schneider, Wahrhaftigkeit und Fortschritt , 86–90, Kube, “Eckpunkte des Schaffens,” 158–62. 90

Op. 26 (composed in 1919 and premièred in April 1920) with Hindemith’s String Quartet No. 3,

Op. 16, composed in 1920–21. 88 With both compositions marked in the key of C major, Kube notes that both composers used this traditional tonal frame to explore new harmonic pathways, with chromatic progressions and parallel chords, and a new emphasis on the linear dimension.

Other similarities that he observes include the energetic impetus of the respective opening movements, with similar motivic ideas and developmental strategies. Kube does not suggest an exchange of ideas between the two composers, even though the dates he cites do not preclude the possibility of Hindemith having seen sketches of Toch’s work—possibly even before starting work on his own composition—or of hearing Toch’s quartet in performance before starting work on parts of his own quartet. 89 Rather, the comparison is meant to point to general trends in composition of the time. But while Toch’s composition clearly preceded Hindemith’s in this instance, such cases do little to release the originality of Toch’s compositions from Hindemith’s shadow. As Schneider analyzes, this uneven reception was markedly boosted by the critiques of

Theodor W. Adorno, who continued to describe Toch’s compositions as imitations of

Hindemith’s style even when the musical languages of the two composers had noticeably grown apart again by the end of the 1920s. 90

88 Kube, “Eckpunkte des Schaffens,” 160–62. 89 “Hindemith datiert im Particellenentwurf seines Quartetts den 2. Satz auf den 30. Januar 1920, den Abschluss des Kopfsatzes auf den 21. Februar, das Finale aber erst auf den 24./25. Januar 1921. Die Uraufführung von Tochs Op. 26 erfolgte … bereits am 24. April 1920 in Mannheim.” See Kube, “Eckpunkte des Schaffens,” 162, esp. n28. As Kube establishes earlier, Toch’s score was completed in 1919. 90 Schneider points in particular to Theodor W. Adorno, “Ernst Toch: Drei Klavierstücke Op. 32; Quartett Op. 34,” Die Musik 19, no. 1 (October 1926): 60–61. Schneider, Wahrhaftigkeit und Fortschritt , 84. Also Toch’s friend Wilhelm Furtwängler insisted on hearing in Toch’s compositions the influence of a style that had first been developed with consistency by Hindemith, even when reassuring Toch of his individuality; see letter from Furtwängler to Toch, reprinted in Heiko Schneider, “‘Der wahrhaftige Künstler aber “experimentiert” nicht’: Ernst Toch in Mannheim 1919–1929,” in Spurensicherung: der Komponist Ernst Toch (1887–1964) – Mannheimer Emigrantenschicksale , ed. Hermann Jung (Frankfurt/Main: Peter Lang, 2007), 89. As Schneider observes, the assessment has survived in more recent reception history such as Giselher Schubert, “‘Kein Einfall ist, wo keine Erfindung ist!’ Briefe von 91

In the journalistic reception of Op. 26 following its première in Mannheim on April 24,

1920, Toch’s style also prompted the association with yet another stream of contemporary composition, namely the Second Viennese School around Arnold Schoenberg:

Auf dem Wege der letzten beiden Sätze kommt Herr Toch in das Lager Schönbergs und das wäre sehr zu bedauern. 91 Along the way of the last two movements Mr. Toch enters the camp around Schoenberg and that would really be a pity.

While Schneider rightly qualifies this association with Schoenberg as a common sweeping categorization applied by conservative critics at the time to any more dissonant avant-garde tendencies (we shall encounter another instantiation of this strategy later), I will explore a point of intersection in the work of the two composers below. The quoted passage again refers to the quartet’s last two movements, which Otto Steinhagen also highlighted as the sections in which he observed the dissolution of vertical harmonic ties to be the most striking. The earlier reviewer, however, described this much less favorably:

Der dritte, der langsame Satz ist ein quälendes Suchen und Grübeln, mehr improvisierend, und das Finale tut sich in harten Dissonanzen und zügellosem Sichgehenlassen viel zugute. 92 The third, slow movement is a tantalizing searching and pondering, rather more improvisational, and the Finale excels in hard dissonances and rampant liberty.

While the reduction and condensation of performing forces in the string quartet lent itself to such stylistic explorations, as discussed above, the concrete case went not quite so smoothly.

Relying on an intimation that Steinhagen added to his review, Schneider suggests that the performers initially appeared rather indisposed to the work’s new tendencies and challenges.

Ernst Toch an seinen Verleger.,” Neue Zeitschrift für Musik 148, no. 12 (1987): 4, see Schneider, “Der wahrhaftige Künstler,” 88. Compare also Niemöller, “Ein ‘rheinisches Jungtalent,’” 75. 91 K.E., “Ernst Toch-Abend des Birkigt-Quartetts,” Neue Badische Landeszeitung 65 (June 26, 1920): 3. Quoted in Schneider, Wahrhaftigkeit und Fortschritt , 86. 92 K.E., “Ernst Toch-Abend des Birkigt-Quartetts,” Neue Badische Landeszeitung 65 (June 26, 1920): 3. Quoted in Schneider, Wahrhaftigkeit und Fortschritt , 86. 92

This was a new turn in the working relationship between Toch and the Birkigt-Quartett, who had previously been avid supporters of Toch’s music. Toch had even made the quartet’s first violinist, Hugo Birkigt, the dedicatee of his Op. 26.

Expanding Notation

The performers’ reticence towards the composition might explain the invention of a further notable feature of this work. Presumably in response to the musicians’ frustrations, the composer resorted to inventive and laborious measures to aid their performance. In the printed instrumental parts, Toch added not only profuse verbal instructions—ranging from expressive indications and evocative descriptions of the music to playing techniques and alerting exclamations about musical events in other parts—but also cue notes and elaborate graphical annotations.93 The latter include in particular wave lines drawn horizontally over or under the staff to signal the thematic importance of the respective passage. Toch explained these annotations at the opening of each part:

N.B. Das Zeichen ’ bedeutet eine Luftpause (stets gut beachten)! Wo eine Stimme auf kürzere Strecken führend hervortreten soll, ist dies für die Dauer dieser Strecke durch eine darunter gesetzte Zickzacklinie ~~~~~~ angezeigt. (Den andern Spielern mitteilen!) N.B. The sign ’ is a breath mark (always attend carefully to this)! Where a part should stand out as leading over a shorter stretch this is indicated for the duration of the passage through a wave line ~~~~~~ under the part. (Communicate this to the other players!)

These wave lines not only invite the player to let her part emerge perceptibly over the others from the musical texture, but they also promote a horizontally oriented rendering. Indeed, by ascribing thematic prominence to the highlighted passage, the wave lines isolate stretches of

93 The comments include such descriptions as “Die Triolen förmlich einbohren” and “scharf!” in the final culmination of the last movement, or “Ein Hauch!” at the end of Movement III, or, describing the sounding effect of Movement IV, Nr. 4: “(ein Gemurmel)” (“a murmuring”). 93

music as horizontally coherent rather than tied by vertical structures. Toch himself captured this effect through the term “continuity,” in an essay published in 1926 on “Suggestions for

Simplifying Music Notation” (“Vorschläge zur Vereinfachung der Notenschrift”):

In meinen Quartetten ließ ich die Stellen, welche “hervortreten” sollten, durch Wellenlinien, die in die Stimmen gedruckt wurden, bezeichnen, weil ich glaubte, daß dieses Zeichen den Vorteil der Kontinuität hätte. 94 In my quartets I had passages that should “protrude” marked through wave lines that were printed into the [instrumental ] parts, because I believed that this symbol had the advantage of continuity.

This “continuity” that the line notates within the individual parts fosters their independence with respect to the other parts. Fittingly, the resulting sounding phenomenon has been described as a

“linear” idiom, such as in Steinhagen’s and Holle’s reviews cited above, or more recently in

Anja Oechsler’s observation of “an uncompromising emphasis on the linear dimension” in the quartet. 95 This metaphorical use of the line—pertaining to the aural experience—corresponds with the chosen graphical symbol that led to the apposite rendering of the music in the first place.

Or, put differently, the wave lines that Toch added to the printed music helped make audible the linear qualities of the composition as he envisioned them and evoke for the performer the imagery of the line.

Apart from graphical lines, Toch occasionally pursued a similar effect through verbal instructions such as “hervortreten” or “zurücktreten.” Examples include the Adagio-theme in the second violin at Nr. 1 in the third movement, where a wave line might have overpowered the fragile “flebile” character that Toch asked for. Similarly, in Movement II, when the viola briefly plays the theme in the four measures leading up to Nr. 5, it is marked only verbally with

94 Ernst Toch, “Vorschläge zur Vereinfachung der Notenschrift,” Musikblätter des Anbruch 7 (1926): 311. 95 Anja Oechsler, “Toch, Ernst,” Grove Music Online, accessed April 29, 2018, http://www.oxfordmusiconline.com/. Oechsler assesses the work as “more radical, employing an extended tonality and an uncompromising emphasis on the linear dimension.” 94

“hervortreten,” rather than by a wave-line—presumably because the theme has been heard often enough before this time, such that the players should be familiar with it by then. In some rare instances, Toch used the designation “Solo” to remind the musician of their leading role. In

Movement II, at Nr. 20, for example, for viola plays a reminiscence of the movement’s theme more softly than previously, and perhaps more freely, too, as “solo” might suggest.

Another prominent graphical feature of the parts are the cue notes. Most commonly in the quartet, these are unpitched notes in small print added above or below the staff to indicate an important rhythmic pattern occurring in a different voice. Sometimes, but far from always, the instrumental part to which they refer is specified. Occasionally, the cue notes might not reflect a single part, but distill a rhythmic structure from the intersection of multiple instrumentalists, such as in Movement III, in the excerpt shown in Figures II.1 and II.2. There, the rhythmic annotations in the cello part outline the shortest note values occurring in every beat from the other instruments combined (here specifically the second violin and viola parts).

Figure II.1 : Ernst Toch, String Quartet No. 9, Op. 26, 3 rd movement, No. 12, score

Figure II.2 : The same passage in the cello part, with added cue notes. At Nr. 12, the cue notes indicate the rhythmic pattern of the viola part, in the two previous measures the rhythmic pattern is extracted from the combination of the viola and second violin. Note that the measures are divided in the instrumental parts compared to the score (i.e. notated in 2/4 instead of 4/4).

More often, however, the rhythmic cue notes draw a connection to a single other instrument with which a sort of interlocking pattern should arise. At that movement’s climactic arrival of Nr. 12, for instance, the cello partakes more prominently in the thematic development, forming a counterpoint against the viola, who at this point takes the lead. The viola part is annotated with a wave-line throughout the first four measures of Nr. 12 (see Figure II.3). The cue notes in the cello part continue to show only the rhythmic values of the viola part (as can be seen in Figure II.2), without specifying which part they refer to—or, from the perspective of the cellist, who she is to interact with.

Figure II.3 : The same passage in the viola part, with the wave line to indicate thematic prominence.

At least two further aspects are interesting in this passage. First, the cue notes do not show the entire viola part, but drop out at the second half of the second and fourth measures respectively. This suggests that the figurations that the viola plays in these instances are not as

thematically essential as the rest—or, possibly, that they are meant to be continued through the cellist’s pattern, which imitates the viola’s gesture of the first two beats. This insight, however, is conveyed only in the cello part, and not the violist’s own part, where the wave line continues throughout the four measures without interruption. Moreover, in the third measure of Nr. 12 (as counted in the instrumental parts, see Figure II.2), Toch’s cue notes abstract the eight-note variations that the viola plays into the same rhythm in which the theme was enunciated two measures earlier. He thus made readily visible the thematic correlation between the two measures, and designated the semi-tonal neighbor tones unequivocally as embellishments. Yet, again this information—an analysis of the music, emphasizing its sequential construction—is contained not in the viola part to which it refers, but instead in that of the cello. This might constitute an example of the communication that Toch envisioned fostering among the musicians, as he alluded in the explanatory comment quoted earlier.

Second, the fact that Toch reproduced only the rhythm but not the pitch of the viola part in this passage (and many others) focuses the cellist’s attention on the rhythmic interlocking, without a concern for how her part might relate harmonically to the others. The harmonic organization of the passage arises from parallel falling chromatic lines that are articulated in all the parts through different gestures and rhythms. The result is a wavering, constantly shifting harmonic plane. Any sense of stability depends on the awareness of the linear-chromatic order that governs every part. In that regard, it makes sense to focus the musicians’ orientation on how their parts interlace rhythmically with the others—and to thus inscribe in the cue notes only rhythmic information, leaving them unpitched. More generally, in passages across the quartet,

Toch’s annotations target the precise and seamless interlocking of rhythms and trade-off of

rhythmic-melodic gestures among the four instrumentalists. They do not seek to build harmonic relations and instead suggest the linear independence of the parts.

Overall, these annotations are as much a guide to the performers as they are an analysis of the music, highlighting how Toch heard the interaction of the different instrumental parts. In some instances, Toch’s annotations are in fact more analytical of the music’s overall organization than perhaps relevant to the small-scale organization of individual instrumental voices. For instance, in Movement III at Nr. 2, the two violins trade off a thematic idea in close contrapuntal overlap (see Figure II.4), marked by “hervortreten” in the score. Meanwhile, the viola and cello similarly engage in an imitative exchange, with their fast figurations providing a murmuring background to the violins. However, the cue notes in both the viola and the cello parts show the thematic texture between the two violins, including their interlocking rhythms, rather than featuring the imitation between the violist and cellist—which would be more immediately pertinent to these two musicians. Unlike in other passages, these cue notes reflect the overall musical texture and its thematic hierarchies. In this instance, they appear perhaps even more helpful for the audience than for the performers.

Figure II.4 : Ernst Toch, String Quartet No. 9, Op. 26, 3rd movement, No. 2, score

Apart from facilitating the horizontally stratified rendering of his composition, Toch’s annotations also asserted his intentions in the rehearsal studio. To some extent, the visual preparation of the parts dictated the conversations and exchange that he hoped would occur between the musicians (as he noted in his opening remarks).

This additional level of intervention came at a cost, however, literally, of time and money. According to Schneider, the publishers—in this case Cologne music printers Tischer &

Jagenberg—insisted that Toch come up with the bulk of the expenses for the publication of the score and parts, as Schneider conjectures. 96 Yet, Tischer & Jagenberg still took pride and ownership in the complexity of the finished product, as their announcement of the print in 1921 shows:

96 “Vermutlich übernahm der Komponist auch einen Großteil der Herstellungskosten der Partitur.” Schneider, Wahrhaftigkeit und Fortschritt , 89–90. 99

Ein wertvolles Streichquartett in C-Dur von Ernst Toch …. Das Werk erscheint im Verlage Tischer und Jagenberg als Op. 26, und der Druck wird insofern ungewöhnlich sein, als an besonders komplizierten Stellen durch Stichnoten in den einzelnen Stimmen das Gesamtbild notiert wird, damit die Spieler das Wesentliche der betr. Stelle um so klarer herausarbeiten. 97 A valuable string quartet in C major by Ernst Toch …. The work will appear as Op. 26 from the publishers Tischer and Jagenberg and the print will be exceptional in that in particularly complex passages cue notes are printed in the individual parts to indicate the holistic image [of the musical texture ], so that the players bring out the essential [features ] of the respective passage with heightened clarity.

In collaboration with these publishers, this edition remained a unique manifestation of such efforts. Toch’s next quartet, Op. 28, “On the Name ‘Bass,’” appeared without any special features. Only for his Quartet No. 11, Op. 34, published in 1924, could the composer convince

Schott music publishing to apply similar annotations as those used in Op. 26.

Concerns with time and money in printing were the foremost factors that Toch listed as the motivation for his “Suggestions for the Simplification of Music Notation” (1926), alongside the ambition to enhance the ease and clarity of use for the performer and reader. That essay explicates how the dismay over the limitations of conventional notation expressed by so many composers in the early twentieth century grew out of the compositional trends of the time.

Fittingly, the two primary musical aspects that Toch addressed in his suggestions were heightened chromaticism and rhythmic complexity. With both parameters, he observed how rendering their gradations in the current compositional idiom, in which they constantly shifted and changed, all too often yielded a vexatious, convoluted visual appearance. To declutter the musical page and simplify the demands for both producers and readers, Toch proposed the adoption of more diverse shapes for note heads to denote different chromatic alterations and note

97 Tischer & Jagenberg, announcement in Rheinische Musik- und Theater-Zeitung 22 (1921): 202. Quoted in Niemöller, “Ein ‘rheinisches Jungtalent,’” 69. Interestingly, this text focuses on the cue notes and leaves unmentioned the wave lines that Toch had highlighted in his comment in “Vereinfachung der Notenschrift,” as quoted above. 100

values. Obvious drawbacks (such as the incompatibility between applying different shapes assigned to pitch and duration at once) might explain why Toch’s suggestions were never implemented, with the exception of the wave lines and cue notes analyzed above, which were geared at rendering more transparent the musical texture.

Toch’s essay and his efforts in curating the visual appearance of his compositions document concerns with the insufficiency of music notation that resonated with many composers and music theorists of the time. With the advent of player pianos and later electronic musical instruments, composers started to circumvent the limitations of notations step in the compositional process by engraving their works directly on an instrument. 98 Besides Busoni, whom I also discuss in Chapter V as a leading figure in this realm, Toch and Hindemith experimented with these technologies in their works for player piano, which were featured at the

Donaueschinger Musiktage in July 1926.99 This approach, however, was confined to works for that specific instrument. Any other performing forces—notably those that involved human musicians rather than a machine to (re)produce the musical work—still required written instructions. Thus, when composing for string quartet, for instance, notation remained the only feasible means of communication.

Here, Toch’s urge to aid—and, on the flipside, to control—the performance of his music through visual cues, was certainly not unique among early twentieth-century composers. One

98 See Thomas Patteson, Instruments for New Music: Sound, Technology, and Modernism (Oakland: University of California Press, 2016), esp. chap. 4, “‘Sonic Handwriting’: Media Instruments and Musical Inscription.” 99 Toch’s compositions were “Drei Originalstücke für das elektrische Welte-Mignon-Klavier.” Apart from contributions by Toch and Hindemith, the concert also featured a work by composer Gerhard Munch. On this event, see Schneider, Wahrhaftigkeit und Fortschritt , 92, Erica Jill Scheinberg, “Music and the Technological Imagination in the Weimar Republic: Media, Machines, and the New Objectivity,” (Ph.D. dissertation, University of California Los Angeles, 2007), esp. 45, and Andreas Maul, “Die Idee einer ‘mechanischen Musik’: Über Experimente von Hindemith und Toch mit dem Welte-Mignon-Klavier und der Welte-Philharmonie-Orgel.” Neue Zeitschrift für Musik 9 (1984): 4–7. 101

might think of Arnold Schoenberg and Alban Berg, for instance, who highlighted passages as

“Hauptstimme” and “Nebenstimme” in their compositions (denoted by “H” and “N” letters with square brackets attached), as Toch also mentioned in his essay. 100 The similarity between Toch’s and Schoenberg’s approaches lies in their highlighting the horizontal coherence of individual parts. Through their respective symbols they not only draw attention to the prominent melodic ideas of the musical texture, but moreover demarcated their durational extension: in Toch’s system through the length of the wave line, and in Schoenberg’s through the (open and closed) brackets. As Toch commented, his symbol featured the added advantage of underscoring the

“continuity” of the respective musical passage (as quoted earlier). Emphasizing this continuity must have seemed ever more decisive, given that the composition of each individual voice no longer followed predetermined structural and harmonic schemes. Without this traditional frame of reference and expectation, the performers needed additional guidance. Moreover, horizontal building blocks became ever more constitutive in the compositional practices of the early twentieth century. Schoenberg’s 12-tone row might be the most iconic example of this tendency, but Toch and other contemporary composers similarly organized their works increasingly around the primacy of horizontal melodic structures. Toch’s compositional style in his Quartets of the

1920s, which necessitated his elaborate annotations and were heard by contemporary listeners for promoting linear-horizontal experiences, are symptomatic of this ambition.

Notably, with the dissolution of harmonic and formal frameworks, melody became a free form of musical expression, in a similar way as the line in the visual arts. Toch expressed this idea in a lecture he gave in 1925:

100 “Man behilft sich hiefür entweder mit Worten …, oder mit Zeichen, wie sie etwa Schönberg in Form von Haken eingeführt hat …, denen er später noch Graduierungen durch Buchstaben, die sich auf Haupt- und Nebenstimmen bezogen, hinzufügte.” Toch, “Vorschläge zur Vereinfachung der Notenschrift,” 311. 102

Der wahrhaftige Künstler aber “experimentiert” nicht. Er setzt nicht einen Strich, der etwas anderes als wahrhaftigstes, innerstes Bekenntnis ist; nicht einen Strich, der “experimentiert” ist. 101 The true artist, however, does not “experiment.” He does not draw a line that is something other than the most genuine inner confession, not a single line that is “improvised.”

The notion of the composer’s idea manifesting itself in the form of a line rings reminiscent of the expressive immediacy that visual artists ascribed to the graphical line, as I discussed in Chapter

I. Recall, for instance, how Henry van de Velde described the line as an expressive unleashing of subconscious forces. 102 In the context of the ideological debates around melody reviewed above, in which Pfitzner summoned melody as the intuition of the genius composer, Toch’s “truthful, inner confession” likely assumed the form of melody. Like a visual artist sketching lines on the page as his inspiration urged him, the composer would jot down melodies to constitute the lines and essence of his musical composition.

“Linearity” in Music Criticism

Not only did the single melodic line become more constitutive of the compositional process and its eventual form, but also the interweaving of multiple lines. In lieu of accompanying chordal structures, the dissolution of common practice tonality and its functional hierarchies promoted the juxtaposition of horizontal trajectories. Interacting horizontally oriented parts not only granted more independence to the individual musical voices, but also resulted in an overall emphasis on the linear-horizontal dimension of composition.

In extension of the metaphorical mapping between individual melodies and the line, the resulting polyphonic textures soon attracted the designation “linear counterpoint.” Rehding has

101 Quoted in Schneider, “Der wahrhaftige Künstler aber ‘experimentiert’ nicht,” 97, referring to a lecture that Toch gave in 1925, which was printed in the Neue Mannheimer Zeitung 103 (March 3, 1925): 3. 102 Henry van de Velde, “Die Linie,” in Essays (Leipzig: Insel-Verlag, 1910), 41–74. 103

traced the origins of that catchword to Rudolf Louis, citing passages from his inaugural dissertation Der Widerspruch in der Musik of 1895 and later from his Die deutsche Musik der

Gegenwart of 1909.103 While Rehding stresses that in both instances the term appeared with a

“deliberate […] view to New Music,” he investigates how it had to be re-appropriated for avant- garde compositional practices after the publication of Kurth’s treatise Grundlagen des linearen

Kontrapunkts: Bach’s melodische Polyphonie in 1917. 104 That treatise not only instantly catapulted the designation of its title to unprecedented popularity, but also incited extended journalistic debates about its rightful application to music of the past (Bach) or the present.

As I discuss more extensively in Chapter IV, Kurth restricted the analytical framework he propounded in that monograph to the polyphonic style of Johann Sebastian Bach. Not only did he deduce his insights from that repertoire in the first place, but he also vigorously pursued an aesthetic agenda of recuperating Bach’s music from earlier analytical scrutiny, which to his eyes had disregarded the linear-horizontal dimension of Bach’s compositions in favor of studying its harmonic structure. However, the analytical framework that Kurth developed was adopted by a number of modernist composers and critics. 105 Ernst Krenek, for instance, “unabashedly” declared his enthusiasm for Kurth’s monograph in a letter to the theorist. 106 Critics and

103 Alexander Rehding, “(Mis)Interpreting Ernst Kurth” (M.A. thesis, Cambridge University, 1995), 64. 104 Rehding surmises that Kurth was unaware of the terminological coincidence with Louis’s sources. Rehding, “(Mis)Interpreting Ernst Kurth,” 64. 105 The most comprehensive accounts of the reception history of Kurth’s treatise are Rehding, “(Mis)Interpreting Ernst Kurth,” and Luitgard Schader, Ernst Kurths “Grundlagen des linearen Kontrapunkts”: Ursprung und Wirkung eines musikpsychologischen Standardwerkes (Stuttgart: J.B. Metzler, 2001), esp. 109–69. See also Lee Allen Rothfarb, Ernst Kurth as Theorist and Analyst (Philadelphia: University of Pennsylvania Press, 1988). 106 “Ernst Krenek is the only composer who unabashedly admitted to Kurth's formative influence.” Rehding, “(Mis)Interpreting Ernst Kurth,” 68.. The letter to Kurth dates from April 13, 1921 and is contained in Nora Schmid and Lea Hinden, eds., “Volltextbriefe zum Inventar Nachlass Ernst Kurth,” Vers. 4.0 (Bern: University, Institut für Musikwissenschaft, September 2007), http://www.musik.unibe.ch/dienstleistungen/nachlass_kurth/index_ger.html. In another letter, Heinrich Scherchen reported to Kurth about the enthusiastic absorption of his theory by “Wense, Erdmann, sowie jetzt auch Arthur [sic] Schnabel.” Schmid and Hinden, eds., “Volltextbriefe,” letter from Sept. 3, 1920. 104

proponents of new music like Paul Bekker and Hans Mersmann welcomed Kurth’s theory and terminology for the analysis of contemporary music. An example is Mersmann’s analytical essay on Artur Schnabel’s Sonata for Violin Solo published in the journal for new music, Melos .107

Also Hugo Holle and Otto Steinhagen, whose commentary on compositional trends of the time I quoted earlier, chimed in and endorsed the need for a new contrapuntal pedagogy as Kurth had asserted. 108 While they admitted that Kurth’s treatise itself was not suited as a textbook per se, they found its vocabulary pertinent. Adolf Weißmann, meanwhile, criticized the transfer of vocabulary from the circumscribed style of Bach to compositions of his early twentieth-century contemporaries. 109 In 1930, Hermann Grabner propagated Kurth’s theory and vocabulary in his more didactically structured treatise Der lineare Satz , and extended its analytical applications to a wide musical repertoire.110

In terms of its reception among composers and theorists of the day, the attraction of

Kurth’s Linear Counterpoint was due in part to the reference of Bach’s polyphonic music, which many composers claimed as the model to their stylistic explorations. Moreover, as Anton

Lindner intimated in his essay from which I quoted at the opening of Chapter I, the evolution of compositional idioms demanded a terminological extension to account for the sensations they entailed for the listeners. In this context, Kurth’s vocabulary—which featured not only the line

107 Hans Mersmann, “Die Sonate für Violine allein v. Artur Schnabel,” Melos 1, no. 18 (Nov. 1920): 406– 18. 108 Hugo Holle, “Dr. Ernst Kurth: Grundlagen des linearen Kontrapunkts,” Neue Musik Zeitung 42, no. 21 (1921): 340–42, Otto Steinhagen, “Dr. Ernst Kurth: Grundlagen des linearen Kontrapunkts,” Musikpädagogische Blätter 1, no. 9 (1919): 139. See Schader, Ernst Kurths “Grundlagen des linearen Kontrapunkts ,” 115. 109 Adolf Weißmann, “Tradition und Entwicklung,” in Von Neuer Musik. Beiträge zur Erkenntnis der neuzeitlichen Tonkunst , ed. Heinrich Grues, Eigel Kruttge, and Else Thalheimer (Cologne: F.J. Marcan, 1925), 1–4. See Schader, Ernst Kurths “Grundlagen des linearen Kontrapunkts ,” 165–66. 110 Hermann Grabner, Der lineare Satz: ein neues Lehrbuch des Kontrapunktes (Stuttgart: Ernst Klett, 1930). 105

but also a wealth of energeticist metaphors—must have appealed to much wider audiences than he had perhaps intended. 111

Indeed, the adoption of Kurth’s ideas by modernist thinkers derailed the reception of

Linear Counterpoint to become the issue of heated cultural-political debates. According to

Rehding’s assessment, Bekker’s review of the treatise, “launched the active reception of what became known as ‘linear counterpoint,’” and initiated an infusion of this new catchword into the volumes of many journals. 112 The volumes of the (Neue) Zeitschrift für Musik , particularly the issues between 1919 and 1926, are good examples, featuring scathing contributions from the likes of Alfred Heuß and Adolf Diesterweg.113 These two conservative critics not only decried the phenomenon of linearity “indiscriminately as just another catchphrase in the controversy about New Music,” but also sought to decouple it from the compositional technique of counterpoint, which they sought to defend as a high art form of true German heritage. 114

Diesterweg’s rant from 1926 compacted many of these issues of contention and singled out

Bekker and Kurth to be blamed for the problematic trend of misappropriating historical references for contemporary compositional tendencies:

Es ist unter gewissen Anhängern der extremsten musikalischen Moderne Mode geworden, ihren Bestrebungen dadurch einen musikgeschichtlich beglaubigten moralischen Kredit zu verleihen, daß sie behaupten, es handle sich um eine

111 Also in recent scholarship, Schader has proposed “transferrable analytical criteria [from Kurth’s framework ] for linear compositions [of the 1910s and 20s ].” Schader, Ernst Kurths “Grundlagen des linearen Kontrapunkts ,” 196–98. Schader examines these principles in analytical vignettes in the last part of her monograph. 112 Rehding, “(Mis)Interpreting Ernst Kurth,” 3 and 57, referring to Paul Bekker, “Kontrapunkt und Neuzeit,” Frankfurter Zeitung (March 27, 1918): 1. Also of relevance to the debate is Paul Bekker, “Neue Musik,” in Neue Musik (Gesammelte Schriften, Vol. 3, Stuttgart, Berlin: Deutsche Verlags-Anstalt, 1923), esp. 100–1, where Bekker “heard the ‘cry for melody,’ which nowadays sounds everywhere,” as Rehding comments (57). 113 Numerous other authors contributed to the dispute in articles more or less explicitly dedicated to Kurth’s treatise. An example, praised by the editors for endorsing their view, is Martin Friedland, “Die ‘Neue Musik’ und ihr Apologet: Gedanken eines fortschrittlichen Reaktionärs zum ‘Düsseldorfer Tonkünstlerfest,’” Neue Zeitschrift für Musik 89/15–16 (August 1922): 334–8. 114 Rehding, “(Mis)Interpreting Ernst Kurth,” 55. 106

Wiederanknüpfung an die vorbachische Musik. Nachdem Paul Bekker in seiner im Jahre 1919 erschienenen Broschüre „Neue Musik“, deren Gedanken bekanntlich an Ernst Kurths einseitige und verwirrende „Grundlagen des linearen Kontrapunkts“ anknüpfen, von dem „Problem des neuen melodischen Stils aus dem Geist der alten Polyphonie“ gesprochen hat, finden wir dieses Schlagwort bei allen Versuchen wieder, eine von jeder Rücksicht auf harmonisches Empfinden gewaltsam losgelöste Musik zu rechtfertigen. 115 It has become fashionable among certain adherents of the most extreme musical Modernism to elevate their aspirations through historically validated moral credit by asserting that they build on pre-Bachian music. Since Paul Bekker spoke in 1919 in his pamphlet “Neue Musik”—which famously built on Ernst Kurth’s one-sided and confusing Foundations of Linear Counterpoint —of the “problem of the new melodic style [growing out ] of the spirit of old polyphony,” since then we find this catchword in all attempts at justifying a music that has been forcefully disrupted from any consideration of harmonic sensitivity.

In his powerful position as editor in chief of the (Neue) Zeitschrift für Musik , meanwhile, Heuß lost hardly any opportunity to condemn Kurth’s theory and its contemporary application. The following is a particularly colorful display of Heuß’s provocative diatribes.

Als, auf Grund der melodischen Polyphonie Bachs, der Name “linearer Kontrapunkt” gefunden war, da gab es ein großes Hurrageschrei dieser niedrigen Lebewesen, sie erklärten in ihrer „Selbstständigkeit“ ohne weiteres Sebastian Bach für ihren Stammvater und gebärdeten sich nunmehr um so sicherer, selbstherrlicher und zukunftssicherer. 116 When, in reference to the melodic polyphony of Bach, the designation “linear counterpoint” was found, there was a big uproar of hoorays from these lowly creatures. Without further ado, they declared in their “independence” Sebastian Bach as their progenitor, and from then on carried themselves the more confident, self-possessed, and assured of a good future.

Rehding has analyzed a similar passage from 1926, in which the “lowly creatures” appear as

“linear musical adolescents,” as an expression of their immaturity (presumably both sexual and artistic) 117 :

115 Adolf Diesterweg, “Berliner Musik,” Zeitschrift für Musik 93, no. 4 (April 1926): 220. 116 Alfred Heuß, “Das 53. Tonkünstlerfest des Allgemeinen deutschen Musikvereins in Kassel vom 8. bis 13. Juni,” Neue Zeitschrift für Musik , 90/13–14 (July 1922): 278. 117 Sexualizing such metaphors was a common trope among certain authors of socio-cultural texts in the early decades of the twentieth century, among them notably Pfitzner and Heuß. See for example Taylor- Jay, “‘I Am Blessed with Fruit’.” 107

Wie, diese linearen Musikjünglinge, die um diese Zeit vor allem mit intellektuell verkrampften, ekstatisch sein wollenden oder grotesken Kammermusikwerken ans Licht traten, sind Urmusiker gewesen! 118 What—these linear musical adolescents, who stepped out into the light around this time with their intellectually convulsed, would-be ecstatic or grotesque chamber music, were primordial musicians! 119

The duality of Bach and Beethoven as the two lodestars in music-aesthetic discourse of the time featured also in these debates. The succinct commentary in a survey of the (inadequate) music- theoretical reception of Beethoven’s music at the centennial of his death appears mild in comparison to the earlier quotations: “Bach’s counterpoint has as little in common with the modern ‘linear’ one as Beethoven’s melody with the new ‘melos.’” 120

In order to fend off Bach’s polyphonic style from these modernist appropriations, the conservative critics willingly surrendered Kurth’s theoretical framework. Ironically, these debates thus weighed up against one another the value attached to Bach’s heritage on the one hand and the advantages of Kurth’s analytical framework on the other, and thus dissected what

Kurth had declared as a unitary foundation to his approach. In 1927, in the preface to the third edition of the treatise, he gave voice to his discomfort with the reception of his theory and limited the intended applicability of Linear Counterpoint to strictly tonal contexts.

This outcry was clearly motivated by the cultural-political debates surrounding his work—and even in a twofold sense. For one, Kurth had to reassert his profound veneration for the incomparability of Bach’s legacy, upholding it as the only true model of contrapuntal

118 Alfred Heuß, “Eine Kundgebung der neuen Musik” (Review of 25 Jahre Neue Musik, Jahrbuch der Universal Edition ), Neue Zeitschrift für Musik 93, no. 4 (April 1926): 200. 119 Translation quoted from Rehding, “(Mis)Interpreting Ernst Kurth,” 55. 120 “Bachscher Kontrapunkt hat mit dem modernen ‘linearen’ nicht mehr zu tun als Beethovensche Melodie mit neuem Melos.” Alfred Heuß, “Beethoven in der Gegenwart,” Neue Zeitschrift für Musik 94, no. 3 (March 1927): 136. 108

composition.121 Despite this attempt at shielding Bach from modernist, non-tonal appropriations, however, and his attendant alignment with a powerful camp of Bach-admirers, the reception from that constituent of critics remained tepid. 122 Moreover, by delimiting the applicability of his theory to a strictly diatonic framework, Kurth at once addressed another stream of criticism that his treatise had elicited. As Diesterweg alluded in the passage quoted above, critics held that

Kurth neglected music’s harmonic organization, or, as Diesterweg put it, disregarded any

“consideration of harmonic sensitivity.” This allegation was due in part to Kurth’s assertions in the treatise, in which he promoted the melodic line’s precedence over harmonic verticality in analytical approaches to Bach’s music. These declarations defined Kurth’s reactionary opposition to earlier harmonically centered analyses in the lineage of Johann Joseph Fux, as I review in Chapter IV. But he certainly did not mean to suggest that Bach’s music was anything but firmly grounded in functional harmony.123

Yet, the duality between harmony and melody remained a prominent issue of discussion, as I laid out earlier in this chapter with respect to the role of harmony in aesthetic debates on theories of melody. 124 In this climate, the advocacy for linear-horizontal approaches to music all too often elicited misreadings in the vein of Kurth’s case. The example of Busoni’s designation

121 See for instance the preface to Ernst Kurth, Grundlagen des linearen Kontrapunkts , 2 nd rev. ed (Berlin: Max Hesse, 1922), ix. 122 Luitgard Schader discusses the reception of Kurth’s treatise, including by leading Bach scholars of the day. She refers to an early review by Hermann Wetzel published in the Bach-Jahrbuch that set the tone for later critical appraisal. Hermann Wetzel, “Ernst Kurth: Grundlagen des Linearen Kontrapunkts. Einführung in Stil und Technik von Bachs melodischer Polyphonie, Bern 1917,” Bach-Jahrbuch 14 (1917): 173–75. See Schader, Ernst Kurths “Grundlagen des linearen Kontrapunkts ,” 112–13. 123 I revisit these appropriations of Bach’s polyphonic oeuvre in Chapter V, where I document the two opposing ideologies in visual-artistic renditions of select compositions by artists at the Bauhaus. 124 In the title of an essay he announced on the topic, Heuß spoke straight-out of a “battle” between the harmonic and melodic principles: “Der Kampf des harmonischen Prinzips gegen das melodische Urprinzip in der Tonkunst des 19. Jahrhundert.” Alfred Heuß, “Innerer Betrachtung gewidmet,” Neue Zeitschrift für Musik 88, no. 24 (December 1921): 634. It is, however, unclear whether that article actually materialized, since it does not appear in that or any succeeding issue of the journal. See also the earlier edition of that series of essays, Alfred Heuß, “Innerer Betrachtung gewidmet,” Neue Zeitschrift für Musik 88, no. 23 (December 1921): 605–7, esp. 607. 109

“rücksichtslose Polyphonie” (“reckless, uncompromising polyphony”), which I discuss in

Chapter V, similarly illustrates this heightened sensitivity. What Busoni had cast as an empowering perspective on contrapuntal principles in his own compositional practice, August

Halm decried indiscriminately as a shortcoming in harmonic consideration. 125

In addition to the historical, music-theoretically oriented contentions that informed the positions in these debates, the modernist compositional tendencies that could now be associated with them added cultural-political weight and fuel to the discussion. As Rehding has pointed out with respect to Kurth’s theory, the perceived independence of melody from harmony in any linear-horizontal theoretical system facilitated its adaptation by modernist composers. 126 Not surprisingly, Heuß found more scornful words to describe these circumstances. Continuing from the 1923 tirade quoted above about the “lowly creatures,” who boasted in “an uproar of hoorays,” he lambasted,

Der eigentliche Begründer dieser Infusorienmusik, Arnold Schönberg, hatte, wie schon seine Verfasserschaft einer Harmonielehre nahelegt, ihre Abkunft vom harmonischen Prinzip noch klar gezeigt nur war mit diesem in seiner jetzigen Beschaffenheit überhaupt kein Staat mehr zu machen. ... Die Harmonie war ein altes, verdorrtes Hutzelweibchen geworden, über dessen einstige Urnatur, die Tonalität, man atonal grinste und seine Witze riß. 127 The real originator of this music of infusoria, Arnold Schoenberg, had still shown clearly—as his authorship of a Harmonielehre already suggested—their descent from a harmonic principle. But in its current condition there was nothing to be made of this sorry sight. … Harmony had become an old, withered, wizened old hag, about whose primordial nature—tonality—one sneered atonally and cracked jokes.

125 Ferruccio Busoni, “Selbst-Rezension (1912),” Musikblätter des Anbruch 3 (January 1921): 22–24, esp. 23; August Halm, “Über Ferruccio Busoni’s Bachausgabe,” Melos 2, no. 10, 11–12 (1921): 207–13, 239– 44, esp. 241–42. 126 Rehding, “(Mis)Interpreting Ernst Kurth,” esp. 59. 127 Alfred Heuß, “Das 53. Tonkünstlerfest,” 278. The reference to infusoria, aquatic microorganisms, which in Heuß’s time formed their own biological order, might be intended as an invective that infers evolutionary logic. Alternatively, it might suggest an impure, turbid music, in allusion to murky water. I am grateful to Alex Rehding for these interpretive suggestions. 110

In this context of total decay, Heuß cynically portrayed the designation “linear counterpoint” as a salvation, a fictitious vision of theoretical stability:

Und da wirkte nun das Wort vom „linearen Kontrapunkt“ geradezu wie eine Erlösung. Auf neue Fasson und mit neuer Begründung fand man gerechtfertigt, was man schon eine Weile mit expressionalem Ernst getrieben. 128 And then of course the word of “linear counterpoint” sounded quite like a salvation. In a new style and with new rationale, one found justified what one had already been pursuing for a while with expressional austerity.

Again, Schoenberg served as scapegoat for all non-tonal aspirations of his day, as we have seen earlier in a comment about Toch’s String Quartet. From an indiscriminate conservative viewpoint (such as Heuß’s), Schoenberg’s compositional development epitomized the dystopian renunciation of functional harmony across all modernist compositional tendencies. The projection of “linear counterpoint” into this modernist compositional landscape at once decoupled the concept from the repertoire from which it was originally derived, and portrayed linear-melodic structures and traditional tonal-harmonic logic as incompatible musical principles in both compositional and analytical terms.

In this context, the ascription of linearity, let alone “linear counterpoint,” to compositions of the 1920s was as common as it was thoroughly contentious. Even particular attention to melodic developments could be read as an alignment with modernist tendencies. Notably, the vocabulary, and in particular the metaphor of the line, was shared between the two opposing ideological camps. The concept of the line formed a hinge across the divide between what, on the one hand, Toch tried to convey through the added annotations to his score and what his favorable listeners related as their impressions of the music, and on the other, what other critics sought to portray as utterly discordant and revolting.

128 Alfred Heuß, “Das 53. Tonkünstlerfest,” 278. 111

Kurth’s own position, meanwhile, was not quite as firm as his declarations might suggest.

As I review in Chapter III, he applauded the theoretical purview of Toch’s Melodielehre , which extended a linear understanding of melody to music from the fifteenth century to their contemporaries. He also maintained a friendly correspondence with Paul Bekker, and in a letter to him, Kurth mentioned Toch’s visit to his home in Spiez in Switzerland, implying that Toch was a shared acquaintance. On that occasion, Kurth also commended the compositions of Toch that he had already seen.129 Thus, despite his unconcealed partiality for the music of Bach, which he shared with the conservative voices in the debates delineated above, Kurth’s vision for linear- horizontal trajectories in music far exceeded their categorical renunciation of all modernist aspirations of their day.

In the next chapter, I turn in more detail to Toch’s Melodielehre , which was published in

1923. It will help to read this treatise in the cultural-political context cast in the present chapter, where melody and its discourse have been portrayed as contentious concerns in the history of music theory since the nineteenth century. Particularly in light of his aesthetic positioning, his compositional advancements, and notational innovation, Toch’s Melodielehre offers a valuable complementary perspective on the issues addressed above. In it, Toch solidified the mapping of melody and line in a theoretical framework—against all critique of the day.

129 Letter from May 22, 1924: “Ernst Toch gefiel mir sehr, ich will nun seine Kompositionen kennenlernen, der erste Eindruck davon ist sehr günstig.” Schmid and Hinden, eds., “Volltextbriefe.” The benevolent correspondence between Kurth and Paul Bekker is documented in their letters between August 1922 and December 1927. Kurth invited also Bekker to Spiez, and exchanged new publications with him, commenting as well with enthusiasm on any writings that Bekker shared with him. 112

III. MELODIC WAVE LINES , 1821 AND 1923:

TOWARD CONTINUITY IN ERNST TOCH ’S TONHÖHENLINIE

Figure III.1 : Friedrich August Kanne, melodic wave line, Der Zauber der Tonkunst (1821) 1

Figure III.2 : Ernst Toch, “small wave line,” Melodielehre (1923) 2

Both of these wave lines are drawn as continuous sine shapes, with a constant deflection and regular phase-length. Both come from music-theoretical sources, and present what the two theorists conceived as a (simplified and stylized) visual analog to melody. In both sources, melody takes center stage in the author’s music-theoretical agenda and in both it is discussed in the context of more comprehensive taxonomies, in which musical parameters are mapped onto visual ones. Yet, the century that separates the two renderings positions them in entirely different cultural and intellectual contexts. Between 1821 and 1923—the years of the two sources— already the definition and status of melody in music-theoretical and compositional discourse changed significantly, as I laid out in Chapter II. These changes occurred in parallel with developments in aesthetic and epistemic frameworks available not only to theorize melody itself,

1 Friedrich August Kanne, “Der Zauber der Tonkunst,” Wiener Allgemeine Musikalische Zeitung 5 (1821), 537. 2 Ernst Toch, Melodielehre: Ein Beitrag zur Musiktheorie (Berlin: M. Hesse, 1923), 27. 113 but moreover to conceive of relations between aural and visual phenomena, like those invoked in rendering melody through a wave line.

In exploring the foundations for such analogies between sound and image—or melody and line—I analyze each of the two depictions within the theoretical context in which they arose.

My investigations develop around a theoretical and aesthetic challenge that pertained to both music theories alike, namely the question of how to account for the line’s essential graphical property of continuity in musical terms. The explanatory frameworks for this conundrum provided by each of the two music theories will provide a rich foundation for comparing the aesthetic connotations of the lines in the figures above. I will propose that the emergence of research in Gestalt psychology and in auditive and visual cognition around the turn of the twentieth century significantly expanded the interpretative potential of the line in Figure III.2.

While looking strikingly alike, the lines in the two images above thus carry fundamentally different aesthetic and music-theoretical meaning.

This chapter investigates how to read these lines in light of the intellectual paradigms of their times. Following from the previous chapter, in which I situated theories of melody in their broader aesthetic debates from the nineteenth to the early twentieth century, this chapter will thus offer the opportunity to investigate the internal substance of two historically separated examples in more detail. As the wave line in Figure III.1 predates the era that constitutes the focus of my dissertation by about a century, it serves as a comparative reference to explore the theoretical developments through a concrete case study.

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Kanne’s Wave Line

In 1821, composer and music critic Friedrich August Kanne (1778–1833), editor of the

Allgemeine Musikalische Zeitung of Vienna, published an essay in that journal on “The Magic of

Music.” The evocation of “magic” (“Zauber”) was a common poetic theme at the time, such as in the “Zauberpossen” of Johann Nestroy and Ferdinand Raimund. These were theater pieces for the Volk, including such staples of the repertoire as Nestroy’s Der böse Geist

Lumpazivagabundus oder Das liederliche Kleeblatt (1833). As a composer, Kanne celebrated his biggest success with his “Zauberopern,” such as Lindane oder die Fee und der

Haarbeutelschneider (1824), a genre made famous by Wolfgang Amadeus Mozart’s Die

Zauberflöte (1791). In that vein, his article reveals insights into what Kanne considered music’s most central “magical secrets” (“zauberische Geheimnisse”) or organizing principles of musical composition—of which he considered melody the first. Building as well on such music-aesthetic tropes as the “Geisterreich der Musik” in which E.T.A. Hoffmann had positioned the music of

Ludwig van Beethoven, Kanne moreover likened melody to a language of the ghosts

(“Geistersprache”). He viewed melody as the expression of a composer’s innermost and truest emotions, which elude rationalization and verbal expression, but could still—mysteriously—be communicated to the listeners, hence a “ghost language.”3 Kanne himself juxtaposed this poetically rich understanding of melody with the technical and dry definition as a “succession of tones”—a perspective that he cynically ascribed to narrow-minded “mere musicians.” 4

3 “[Melodie ] ist die Geistersprache, die in dem Gemüthe allen Wiederhall findet, indess sie vom Verstande gar nicht begriffen wird.” Kanne, “Der Zauber der Tonkunst,” 507. See David Trippett, Wagner’s Melodies: Aesthetics and Materialism in German Musical Identity (Cambridge, UK: Cambridge University Press, 2013), 73; Kanne also writes, “Spricht [der Tonkünstler ] seine innersten und heiligsten Gefühle durch ein Mittel aus, welches wir eine Geistersprache nennen wollen.” Kanne, “Der Zauber der Tonkunst,” 250. 4 Kanne, “Der Zauber der Tonkunst,” 507. 115

The conception of melody as an intuitive expression that evades theoretical rationale is representative of discourses on melody in the nineteenth century at large, as I discussed in the previous chapter. By carefully couching his music-theoretical insights in multiple metaphorical layers, Kanne’s discussion upheld this sacrosanct status of melody. To start, the wave line—such as the one shown in Figure III.1—together with the broader imagery of water, served Kanne as the metaphorical fold to envelop the poetic richness of melody. 5 He evoked the imagery of oceanic waves to portray the aggregate of tonal forms contained in the ocean of the Ur-tonality of C major. 6 Within this pool of possibilities lie the musical forms (“Formen”)—also known as melodies—that a composer may devise. The invocation of “forms” to denote melodies involves another layer of metaphor in Kanne’s thinking, namely the assertion that his “magical secrets” tied across music and the visual arts. He proposed analogies between the two art forms, based on the functions he perceived in different artistic parameters. Of utmost importance, Kanne considered the molding of a distinct form or shape (“Form”) for the respective artwork. In music, he attributed this function to melody, and in painting and sculpting to contour:

In ihnen liegen zwey zauberische Geheimnisse geborgen, welche der menschliche Geist entfaltet hat, nähmlich das erste: eine Form zu bilden, welche sich als scharfer Umriss zeigt, wie bey der Aussenseite plastischer Werke, oder dem Conture der Mahlerey— durch die Aufeinanderfolge der Töne die Melodie .7

5 As Trippett has pointed out, water and waves were common metaphorical images for music and in particular melody in the nineteenth century. In “Der Zauber der Tonkunst,” Kanne reinforced the imagery by sprinkling in further water-related metaphors throughout the essay, such as “rauscht die Musik” or “Fluss der aufeinander folgenden Ideen.” Trippett has also pointed to passages such as Kanne’s description of melody as “ideal and invisible embodiment of all feelings and passions,” as well as the “successive wave play [Wellenspiel ] of all lines of beauty that float on the coexisting basis of harmony.” Quoted in Trippett, Wagner’s Melodies , 73. 6 “Die Fläche des Meeres in ihrer sanften Bewegung ist gleich der Urtonart C-dur, und in ihr wiederholt sich die Scala wie im Tonmass.” Kanne, “Der Zauber der Tonkunst,” 539. (C.f. Trippett, Wagner’s Melodies , 105). More than that, Kanne argues that no other phenomenon in nature represents melody (“the melodic scale”) as well as the moving surface of the ocean, which encapsulates all sensations, between repose and movement, dynamic striving and mathematical proportions. 7 Kanne, “Der Zauber der Tonkunst,” 249. The emphasis is original. 116

In it lie hidden two magical secrets, which the human spirit has unfolded, of which the first [is ] to build a form that manifests itself as a sharp outline, like the external shape of sculpted works, or contour in painting—through the succession of tones in melody .

Secondly, Kanne proposed that the form thus achieved had to be modeled to assume a specific character. For this purpose, he envisioned a correspondence between color and dark and light shading in painting on the one hand and harmony in music on the other. Lastly, Kanne referred to rhythm, his third secret, to which he likened the effect of determining the proportions of an artwork.

Kanne’s mapping of melody and contour is telling, if only tentatively explored in his own explication. As he intimated, contour captures the outline of a form, a three-dimensional body. In visual theory, it is a commonplace that this delineation is most commonly achieved by a line.

Indeed, in painting, drawing, sketching, etching, woodcuts and linoleum cuts, lines are often the sole graphical elements. In addition to shaping contours, lines might serve as well for shading and patterning, and to create the illusion of plasticity, of depth, stillness and motion. These lines are not independent means of expression, but rather serve a specific representational function, to imitate the three-dimensional world outside our eyes and brain. As I reviewed in Chapter I, visual artists of the twentieth century emancipated the line from this functionality to explore the versatile expressive potential of the line in its own right.

What happens when we transfer these relations and the definition of contour to music?

Kanne’s analogy implies that melody, like contour, delineates the outer shape of the multi- dimensional body of music. If contour in painting is bound by the three-dimensional object to be depicted, how did Kanne conceive of melody—and, concomitantly, of music? Let us consider the oceanic waves that Toch adduced as metaphor for melody. From the ocean to the two- dimensional sheet of paper, the physical materiality of water waves and their pulsation of mass

117 and energy are represented by a sine wave (as depicted in Figure III.1). This rendering captures the energetic fluctuations of the wave within the two predetermined parameters that are mapped onto the two axes of the illustration: the length and width of the wave. Furthermore, the regularity of the sine wave suggests constancy in the wave’s progression.

In Kanne’s music theory, a similar transformation maps a complex phenomenon onto the confines of a two-dimensional conceptual space. While referring to the multitude of forms contained in the “ocean of tonality,” the two-dimensional representation of these forms first of all reduces the parameters by which they are measured. As I discussed in Chapter I, and as is common in traditional music notation, the two dimensions of Kanne’s wave denote the passing of time on the horizontal axis, and variations in pitch “height” in the vertical deflection (with a peculiar twist, as I explore below). Moreover, the shape of the sine wave delimits the plurality of possible forms since it prescribes certain expectations about the shape that the melody should assume. Indeed, in Kanne’s theory, this normative shape is tied to an internal organizational principle, which Kanne derived from nature to further demonstrate how music was determined by natural principles. As Kanne observed, the upsurge of an oceanic wave exceeds its fall—or, in other words, a wave takes longer to swell than to break and recede. 8 This unevenness maps well onto the unequal subdivision of the octave: the rising of the wave represents the span of the lower fifth of a diatonic scale, ascending from the tonic pitch to the dominant, and the falling of the wave mirrors the quick return to its starting point (the tonic) in the upper fourth of the scale. 9

As obvious as Kanne made this analogy seem in his writing, at least two aspects reveal it as quite an intricate interpretation. First, in the 1820s, scientific research on water waves was far from unified. In 1804, František Josef Gerstner ( Theorie der Wellen ) had first proposed a

8 “Man wird die Länge des Aufschwungs bemerken, so wie die Kürze des Falls.” Kanne, “Der Zauber der Tonkunst,” 537. 9 Trippett has also discussed this aspect of Kanne’s theory. Trippett, Wagner’s Melodies , 106–8. 118 corresponding physical and mathematical theory of waves as deviating from the regularity of a sine wave. Gerstner’s theory of trochoidal waves acknowledged the irregularity not only with regards to the length of the respective phases of the wave, but also to their height (the amplitudes of the perpendicular deviation above and below the sea level at rest). Further calculations of such trochoidal waves followed only a half-century later, among others by George Gabriel Stokes

(“On the Theory of Oscillatory Waves,” 1847) and William John Macquorn Rankine (“On the

Exact Form of Waves near the Surface of Deep Water,” 1863), while mathematicians across

Europe continued to model waves after regular sine waves (such as like George Biddell Airy in

“On Tides and Waves,” 1841, in Encyclopedia Metropolitana ). In this context, Kanne must have pursued some research in physics as the foundation to his music theory, and he likely leaned specifically on Gerstner’s theory of the wave. Second, and more unusual in the history of music theory, Kanne relinquished the metaphorical logic of pitch space and its attendant vocabulary for the sake of justifying the wave’s return to its starting point. While the phase of the rising wave coheres with the metaphorical directionality of a “rising” scale segment, the “falling” of the upper fourth opposes this common denomination in which it would be similarly considered as

“rising” rather than “falling.”

Kanne annotated this process using the example of a C major scale in the illustration reproduced below as Figure III.3. Here, the unevenness between the rising and falling of the wave is graphically rendered in a slightly uneven waveform, a feature that is nearly indiscernible in the un-annotated, blank wave line of Figure III.1. Kanne also explained that this normative shape and process could be modified if the music continued to tonicize the dominant from the fifth scale-degree onwards. In that case, the wave would continue to rise.

119

Figure III.3 : Friedrich August Kanne, annotated wave line with C major scale 10

With the turning points of the wave being assigned exclusively to the tonic and dominant of the respective scale, the internal organization of Kanne’s wave relied firmly on the structural hierarchies of diatonic tonality. By implication, any melody was subordinate to the regulating function of harmony. Such a conception of the relation between harmony and melody was representative of the hegemony of harmony in early nineteenth-century music theory, which eclipsed almost entirely any consideration of melody as an independent parameter, as I reviewed in Chapter II. In this respect, Kanne’s allusion to the functionality of contour in painting is fitting: as contour, melody frames the harmonic essence of music. Even though Kanne’s essay is dedicated primarily to melody, his mapping of melody onto the wave line epitomized melody’s inherent dependency. It illustrates melody as bound not only by harmony, but also by the fixed shape of the metaphorical water wave, which inverts common denominations of melodic directionality. Moreover, and this will be relevant again for my discussion later, Kanne’s wave projected exclusively scalar passages. The harmonic organization of the scale, in turn, affirmed the sine shape as the sole form that Kanne’s wave line could take, with the systematic unevenness that Kanne applied between the rise and fall of the wave in Figures III.1 and III.3.

10 Kanne, “Der Zauber der Tonkunst,” 538.

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From Kanne’s Wave Line to Toch’s Tonhöhenlinie: A Preliminary Comparison

Much had changed by Ernst Toch’s time a hundred years later. For one, diatonicism—as it had been operating in the background in Kanne’s imagery—could no longer be taken for granted as an organizing principle of music in the early twentieth century. Moreover, by the early

1920s, melody had become a rather independent musical parameter. Indeed, as one of the leading composers of his day, Toch took a pioneering role in shaping stylistic tendencies and listening expectations in German music. With his works of the early 1920s, contemporary listeners acknowledged a new focus on linear-horizontal trajectories, with the dissolution of traditional harmonic ties. Toch’s String Quartet Op. 26, discussed in Chapter II, showcased both the compositional procedures associated with this “linear idiom,” as well as the debates that this terminology incited in music journalism.

With early twentieth-century ears thus attuned to linear-melodic processes in music, critics and theorists observed its relative scarcity in aesthetic and theoretical accounts on music.

In response, they wrote aesthetic pamphlets and theoretical treatises dedicated to melody, in an unprecedented quantity, as Michael Polth has found.11 Toch’s Melodielehre , his first music- theoretical treatise, which, as mentioned in the previous chapter, grew out of the doctoral dissertation that he completed in 1921, formed part of this trend. It was published in 1923, just a couple of years after the young composer took up his first teaching position in Mannheim, which he held from 1919–29. While Toch himself was skeptical of the pedagogical mission of his treatise, as I discussed in Chapter II, he still embodied a threefold perspective on the subject of linearity—as a composer, a theorist, and, indeed, a pedagogue.

11 Michael Polth, “Zwischen Gestaltpsychologie und Funktionalität: Anmerkungen zur Melodielehre von Ernst Toch,” in Spurensicherung: der Komponist Ernst Toch (1887-1964)—Mannheimer Emigrantenschicksale , ed. Hermann Jung (Frankfurt/Main: Peter Lang, 2007), 101–19. 121

In accordance with the aspiration of elevating melody as an independent musical parameter, Toch coined a theoretical concept to facilitate the discussion of his music-theoretical observations. In the first chapter on the “Begriff der Melodie,” he asserted:

Das Nacheinander von Tönen ergibt wohl eine “melodische Linie”—wir wollen sie gleich und ein für allemal “ Tonhöhenlinie ” nennen—aber noch keine Melodie. 12 The succession of tones certainly yields a “melodic line”—we want to call it right away and once and for all “ Tonhöhenlinie ”—but not yet melody.

Toch was surprisingly sparing in offering further explanation of the Tonhöhenlinie , even though it constitutes the treatise’s central concept. Occasional hints as to the rationale behind this mapping between melody and line are buried in his discussions, and form the basis of my analysis. Toch merely wrote that the Tonhöhenlinie (“pitch line”) pertained exclusively to a melody’s progression in pitch, as indicated by the term itself. It was “not yet melody,” since only through the addition of rhythm, as melody’s other constitutive parameter, could a real musical expression arise. This distinction between a “succession of tones” without artistic value on the one hand, and “melody” as true musical expression on the other echoes Kanne’s verdict about the creative agency of melody and the apposite theoretical inquiry that it demanded.

Comparable to Kanne’s approach, Toch’s line focused exclusively on the pitch content of melody. However, as mentioned above, in Kanne’s “Magic of Music,” the organization of pitch was subordinate to harmonic considerations, whereas Toch isolated melody from the complexities of the musical texture. Such an isolation was essential to the aesthetic-historical program of Toch’s Melodielehre , since the musical excerpts that Toch quoted across his treatise span over five centuries of music history, from Guillaume Dufay, Giovanni Pierluigi da

Palestrina, and Hans Leo Haßler to contemporaries like Arnold Schoenberg, Erich Wolfgang

12 Toch, Melodielehre , 7. The emphasis is original. 122

Korngold, and Hans Pfitzner. Due to this historical scope, the music covered in Melodielehre entails a variety of harmonic languages.

Accordingly, when Toch described the rising and falling of his melodic wave line as processes of accumulating tension and release, he matched these trajectories exclusively to variations in pitch height, independent of any tonal hierarchies. The shape of the Tonhöhenlinie thus adapts to the specific melody that it derives from, such that the turning points of the wave line correspond to the high- and low-points of the respective melody. This is the case, for instance, in the line that Toch drew above the excerpt from Beethoven’s Third Symphony (I consider his analysis at the end of this chapter; see Figure III.16). Unlike in Kanne’s theory, the shape of Toch’s Tonhöhenlinie thus orients itself after the melody’s development rather than a predefined sine form. Similarly, the regularity of Toch’s line in Figure III.2 captures at once a normative reference of maximal evenness that melodic contours might assume. Moreover, Toch cited a specific musical example that matches his wave line of Figure III.2, noting how composers used wave-like melodic contours to imitate waves of water, especially in such predestined genres as Venetian serenades, barcaroles, and gondola-songs. 13 The melody of the famous Barcarole from Jacques Offenbach’s Les contes d’Hoffmann , for instance, from which

Toch reproduced his musical examples 34 and 35, undulates in stepwise increments around a constant third scale degree, thus evoking the gentle swaying of the gondola, as Toch described.

Though he quickly clarified that he was interested primarily in the features of absolute music, rather than in such “musical onomatopoeia,” Toch could not resist a reference to the oceanic waves that also inspired Kanne’s choice of metaphor.

13 “Es ist klar, daß der Tondichter, dem die bewußte Nachahmung der Wellenbewegung des Wassers vorschwebt, auf diese Linie verfallen wird und ich kann mir wohl die Vorführung der zahlreichen venetianischen Serenaden, Gondellieder und Barcarolen ersparen, um so mehr als diese Art der Wellenlinie den Kern unserer Untersuchungen noch gar nicht trifft.” Toch, Melodielehre , 28–29. 123

Approximating Continuity

The Problem of Continuity in Kanne’s Theory

Waves of water thus underscored the smoothness in melody that both Kanne and Toch evoked in their theories of the wave line. This smoothness is manifest in the external appearance of the graphically rendered lines, like in Figures III.1 and III.2. But how is this seamlessness accounted for in musical terms in the internal structure of these wave lines? Put in more technical terms, the imagery of the melodic wave line, and in particular its graphical representation, portrays melody as a seamless, continuous, and coherent entity. Indeed, continuity is intrinsic to graphical and geometrical definitions of the line. But how, or to what extent, is melody a continuous, uninterrupted phenomenon? These questions pertain equally to Toch’s and Kanne’s wave lines, as to any other linear representations of melody (or music).

With respect to the 1820s, David Trippett has wondered about the transferral of precisely this visually constituted property of the line—as a continuous entity—in Kanne’s theory of melody and the depiction on the wave line. He writes:

One wonders why Kanne’s illustrative sine waves do not demand non-discrete intervals, i.e. glissandi, or vocal portamento. Though this may be implied by the continuous topography of water, the practical impossibility of justifying such anti-grammatical lines—essentially: pitch-continuous cries—in compositional terms perhaps rendered the full implications of this principle of motion unrealizable in 1821. 14

As Trippett rightly concludes, Kanne’s theoretical framework left no room for considerations of pitch-continuity as a possible translation of the line’s visual continuity. Indeed, Kanne had opened his essay on the “Magic of Music” by observing how the number of (diatonic) pitches

14 Trippett, Wagner’s Melodies , 107. 124 matched the “magical number seven” of colors on the rainbow. 15 Attributed to this magical number, the diatonic scale thus constituted music’s natural structure, as Kanne implied as well with the example of the C major scale that he annotated on his wave line in Figure III.3. As music’s “first material,” these diatonic subdivisions were the smallest conceivable increments in

Kanne’s metaphorical ocean of pitch, and they were indispensably part of his theory of melody.

While not envisioning continuous glissandi between successive tones of a melody, Kanne did conceive of the wave line as tying across the nearest possible discrete steps within the premises of his theoretical framework. This organizational principle applied not only to the clinically contrived context of the C major scale that Kanne annotated on the wave line of Figure

III.3, but also to the artistic wild. As Trippett reviews, Kanne believed that any melodic interval larger than a second would be mentally—or even audibly—filled in with step-wise motion.

Kanne referred to such “naturalist” vocal performers (“Naturalisten”) as farmers, old women, and children—in other words, the musically un-trained, or those otherwise deviating from the norm of the educated middle-aged white male—to demonstrate how they would tie across intervallic leaps by inserting scalar runs.

Daher zieht der Naturalist im Gesange (z.B. Bauern, alte Weiber, Kinder, Hirten etc.) die Secunden auch alle durch, und nimmt selten einen Sextensprung ohne die inmitten liegenden Secunden mit anzuschlagen. 16 Thus the naturalist in singing (e.g. farmers, old women, children, shepherds, etc.) ties seconds across all [intervals ], and rarely takes the leap of a sixth without articulating the seconds lying within.

Kanne illustrated this strategy through the example of a Lutheran melody:

15 “Die heilige Zahl ‘sieben’ ist’s, auf welche der Wunderbau des Regenbogens am Himmel seine farbigen Säulen stützt…. Dieselbe Zahl gibt nun auch der Tonkunst in den sieben Tönen ihr erstes materielles Wesen.” Kanne, “Der Zauber der Tonkunst,” 249. This argument is ironically fallacious, considering that Newton had expanded the color spectrum from six to seven colors just so to accommodate the seven pitches of the diatonic scale. 16 Kanne, “Der Zauber der Tonkunst,” 513; Trippett, Wagner’s Melodies , 106. 125

Figure III.4 : Friedrich August Kanne, examples of scalar fill-ins in a Lutheran melody 17

Kanne’s explanation for this performance practice was two-fold. Firstly, he construed the fill-ins as a sleight-of-hand amongst those who would otherwise have difficulty hitting the correct notes.

Secondly, and more to the point of his argument, Kanne staged this tendency of the musically untrained—or, perhaps, unspoiled—as the archetypal coherence with the laws of nature, with which they complied instinctively (“unwillkürlich”). These laws prescribe melody’s essence to lie in the step-wise progression of tones, which Kanne perceived to correlate with an innate feeling of pleasure incited by symmetry and order:18

Diese einfache Melodie singt der gemeine Mann häufig auf folgende Weise [example of Figure III.4 inserted ] … weil ihm da Lücken zu seyn scheinen, die das jedem Menschen innewohnende Wohlgefallen an Symetrie und Ordnung, ihn unwillkührlich auszufüllen zwingt. … Denn Melodie ist stets aus Secundenweise Fortschreitung gegründet, weil die Sprünge schon Beweise von poetischer Freyheit oder rhetorischer Kunst sind. 19

17 The examples are reproduced from Trippett, Wagner’s Melodies , 107, Examples 2.2a and 2.2b. In the original, both examples are found on page 513 in Kanne’s essay; Trippett’s indication of the page number in his Example 2.2b is mistaken. 18 Trippett similarly reads Kanne’s argument as “the proof [of the conception of melody as primarily step- wise ] lies in nature.” Trippett, Wagner’s Melodies , 105. My translation is adapted from Trippett’s partial rendering of the passage. Trippett translates “unwillkürlich” as “spontaneous” (106), while I read the word to mean more an instinctive act. Trippett expresses a similar understanding in different ways in his translation, which reads: “instinct for symmetry and order forces them spontaneously to fill in the gaps.” 19 Kanne, “Der Zauber der Tonkunst,” 513. 126

The common man often sings this simple melody in the following way [example of Figure III.4 inserted ] … since [the intervallic leaps ] appear to him as gaps that the feeling of pleasure for symmetry and order, which is innate in all human beings, forces him to instinctively fill in. … For melody is founded invariably on the step-wise progression [of tones ], since the leaps are already proof of poetic freedom or rhetorical art.

Earlier in the treatise, Kanne clarified even more explicitly that he believed melody to originate in the step-wise progression of tones. On this fundament, larger intervallic leaps stand out as aesthetic licenses, born out from an “act of freedom that the sense of beauty demanded,” and function thus as rhetorical devices and forms of poetic expression:

Melodie … ist (für blosse Musiker) die secundenweise Fortschreitung der Töne, nach den Gesetzen der Schönheit. Ich sage secundenweise Fortschreitung, weil alle bey Terzen-, Quarten-, Quinten- und anderen Sprüngen ausgelassenen Secunden doch ursprünglich mit gedacht, und nur durch einen Act der Freyheit, den das Gefühl der Schönheit geboth, weggelassen sind. 20 Melody … is (for mere musicians) the step-wise progression of tones, following the laws of beauty. I say step-wise progression because in all leaps of a third, fourth, fifth, or other intervals, the intervening seconds are implied, and are left out only through an act of freedom that the sense of beauty demanded.21

For Kanne, the step-wise fill-ins of the Lutheran melody in Figure III.4 are thus part of the melody’s underlying essence. Their diatonic structure (in this case, implying G major) and step- wise organization allowed for a representation of the melody on a wave line, though Kanne did not enact his theory at this applied level and depict this specific melody through a line. But within the framework of Kanne’s theory, the melodic progression by the smallest conceivable increments was the closest approximation to the wave line’s graphical continuity. The real seamlessness of the line remained, however, unaccounted for in Kanne’s essay.

20 Kanne, “Der Zauber der Tonkunst,” 508. 21 Translation adapted from Trippett, Wagner’s Melodies , 105. 127

Towards a Graphical Line in Toch’s Theory

In Toch’s theory, the continuity of the evoked wave line similarly posed an aesthetic challenge. As in Kanne’s time, the line’s continuity did not necessarily reflect non-discrete fluctuations in pitch, as Trippett concluded with regards to the early nineteenth century. The very question of what happens between the tones of a melody indeed remained a vital concern for music theorists throughout the twentieth century. 22 While Toch invoked an explanatory framework to account for notions of continuity in his concept of the Tonhöhenlinie , as I discuss below, he remained ambiguous when it came to its enactment.

To start, different visual representations of the Tonhöhenlinie coexist throughout Toch’s treatise. The realization as actual graphical lines—such as the ones of Figures III.2 and III.16— are exceptions in Melodielehre . Indeed, the absolute majority of the many musical excerpts featured across Toch’s treatise are rendered in conventional staff notation. Only in a few instances, he added straight brackets—predesigned shapes in typesetting—to highlight pertinent passages of the Tonhöhenlinie that he referred to. But even with those, Toch commented on the labor involved in adjusting the inclination of the brackets to reflect the upward or downward orientation of the melody.23 After a couple of examples illustrated in that painstaking way, he resorted merely to horizontal brackets, and finally refrained from annotating the examples altogether. As with his essay on simplifying music notation from 1926 that I discussed in

22 As I discuss in Chapter IV, Ernst Kurth contemplated the question as well. Notable contributions towards the concern come from phenomenological research, such as the work of Edmund Husserl and, a bit later, Victor Zuckerkandl. 23 “Anmerkung: Aus drucktechnischen Gründen wird in den folgenden Beispielen der Richtungswechsel in der Tonhöhenlinie nicht mehr angezeigt.” Toch, Melodielehre , 66n.: The emphasis is original. The comment refers to a series of musical examples (Toch’s Exx. 74–81 and 82–94), which illustrate the same principle, namely that a large intervallic leap should be followed by scalar motion in the opposite direction. In the first set of examples, Toch adjusted the brackets at angles to indicate the change of direction between the leap and scalar motion. In the second set, he resorted merely to horizontal brackets, and commented that this form of representation facilitated the typesetting. 128

Chapter II, the comment speaks to Toch’s careful consideration of the visual effect of his graphical examples despite the obvious typographical limitations that he faced. 24 That it was indeed Toch who determined the visual appearance of his musical examples in the treatise— rather than an editor or publisher of the treatise—is evidenced through a letter that Toch wrote to his doctoral advisor Theodor Kroyer. As Heiko Schneider has highlighted, Toch disclosed to

Kroyer that he typeset the musical examples himself in order to save costs and facilitate the publication of the treatise. 25 In a rare and fortunate instance in the history of music theory, the graphical design of the figures in Melodielehre can thus be ascribed directly and with certainty to

Toch.

These challenges aside, Toch still employed an idiosyncratic form of proto-notation in the early part of his treatise, through which he sought to highlight the linear qualities of his conception of melody and the essence of his Tonhöhenlinie . But precisely these graphical experiments pose more questions about the “linearity” of the concept than they answer.

Accompanying his initial proposition that melody could be mapped onto a line, Toch illustrated the difference between the Tonhöhenlinie as an analytical abstract on the one hand and melody as an animated musical entity on the other. The notational experiment of Toch’s Example 10

(here Figure III.5) rendered this abstraction as a series of open note heads on the staff:

24 See Ernst Toch, “Vorschläge zur Vereinfachung der Notenschrift,” Musikblätter des Anbruch 7 (1926): 308–12. 25 Heiko Schneider, Wahrhaftigkeit und Fortschritt: Ernst Toch in Deutschland 1919–1933 (Mainz: Schott, 2007), 66. 129

Figure III.5 : Ernst Toch, Melodielehre , Example 10

Commenting “this certainly is a Tonhöhenlinie , but not a melody,” 26 Toch further clarified the distinction by adding the musical excerpt in its full conventional notation—with rhythm—in the succeeding figure (his Example 11, here reproduced as Figure III.6):

Figure III.6 : Ernst Toch, Melodielehre , Example 11 (Beethoven, Sonata for Violin and Piano No. 5, Op. 24)

In the commentary on this pair of examples, Toch explicated the role of rhythm as the soul-giving force in melody, which—as if through “magical touch” (“wie von Zauberhand berührt”)—“enlivened” and “inspirited” the otherwise “inanimate” (“leblos”) Tonhöhenlinie of

Example 10:

Wie von Zauberhand berührt, springt aus diesem leblosen Gebilde [der Tonhöhenlinie ] eine Melodie hervor… wenn der Rhythmus es beseelt. Die Tonhöhenlinie war ein wächsernes Bild, der Rhythmus hauchte ihm Leben ein. Der Rhythmus wurde ihm zur Seele. 27

26 “Das ist wohl eine ‘Tonhöhenlinie,’ aber keine Melodie.” Toch, Melodielehre , 8. 27 Toch, Melodielehre , 8. Thought experiments of this kind about the dissociation of rhythm and pitch in melody and about their respective value for the creative originality of a composition were not uncommon 130

As if touched by a magical hand, the inanimate formation [the Tonhöhenlinie ] transforms into melody … when rhythm inspirits it. The Tonhöhenlinie was a wan image, rhythm infused life into it. Rhythm became its soul.

In the present case, the “magical hand” belonged to none other than Ludwig van

Beethoven: the re-addition of rhythmic information in Example 11 (Figure III.6) reveals the identity of the excerpt as the opening theme of his Violin Sonata No. 5 in F major, Op. 24. The evocation of magic (the magical hand) is the first instance of a rhetorical ploy that Toch used recurrently throughout the treatise. Incidentally conjuring up similarities with Kanne’s rhetoric,

“magic” and “mysterious forces” crop up in Toch’s Melodielehre as surrogates for technical explanations to account for some of the most profound and challenging questions that his project entailed, such as those that the following pair of examples raises. As we saw in Chapter II, these allusions also channeled music-aesthetic concerns of the time, such as, most famously, Hans

Pfitzner’s admonition against the “disenchantment” of music that he perceived in contemporary theoretical and analytical approaches.

A parallel set of examples only a couple of pages later similarly promised to expose the wave line visually through a notational experiment. Here, Toch first transcribed the famous

German Christmas carol “O du fröhliche, o du selige” in his example No. 41 (here Figure III.7).

In the following example, he enacted the same separation between pitch and rhythm as in the case of Beethoven’s Op. 55. He explicitly disintegrated aspects of pitch and rhythm as they are encoded in conventional notation and reproduced only the plain note heads of the tune, leaving out their different stems and colorings (see Figure III.8, Toch’s Example 42). Even more at the time. A famous case pertains to the alleged similarity between the opening of the finale to Mozart’s Symphony in G minor, No. 40 (KV 550) and the scherzo movement of Beethoven’s Symphony No. 5 (Op. 67). German musicologist Gustav Nottebohm first observed that Beethoven had copied Mozart’s triadic motive amidst the sketches for his own scherzo, “betraying” thus their intervallic similarities (Nottebohm called the proximity on the page a “Verrätherin”). Around 1900, various critics debated about the degree of resemblance that they perceived in the two themes. Gustav Nottebohm, Zweite Beethoveniana: Nachgelassene Aufsätze , ed. Eusebius Mandyczewski (Leipzig: C.F. Peters, 1887), 531. 131 consequential as a notational experiment than the previous case, Toch also dispensed with the symbols for the key and time signature.

Figures III.7 and III.8 : Ernst Toch, Melodielehre , Examples 41 and 42 (Christmas carol “O du fröhliche” and Tonhöhenlinie )

Toch commented on this series of black dots in Example 42, as follows: “now one sees the wave line without difficulty.” 28 So he claimed that this example laid bare the consistency of the Tonhöhenlinie as intrinsic to the (notational) identity of the melody, being covered only by the veil of graphical information pertaining to rhythm. Yet, while the notational intervention promised to expose this line visually—so one could “see [it ] without difficulty”—Toch did not go as far as to produce it graphically as an actual line, so that it would indeed be blatantly visible.

Rather, he clearly assumed that his readers would have no difficulty in seeing a line in the graphical appearance as a row of separate dots. The framework Toch invoked to facilitate this cognitive translation will be the focus below.

28 “Nun sieht man die Wellenlinie ohne weiteres.” Toch, Melodielehre , 32. 132

The discrepancy between Toch’s alluded line and the notational reality of discrete dots highlights the limitation of music notation with respect to assimilating the concept of melodic linearity. In particular when approaching music from the angle of conventional notation with its separate note heads, as in Toch’s examples above, the ambition of describing melody as a linear entity raises the questions of how and under which conditions the discrete tones, captured as separate note heads, could indeed be viably connected. Moreover, the coexistence of graphical lines, such as in Figures III.2 and III.16, with the disjunct rendering of Figures III.5 and III.8 above challenges us to inquire as to the reasons behind their difference. Toch hinted at answers to all these questions through the broader framework proposed in Melodielehre . Analyzing these intimations will uncover how Toch conceived the line’s continuity, and how it functions in the larger agenda of the treatise. I will pursue this task in three steps. First, I scrutinize Toch’s examples through the observations made with respect to Kanne’s theory. While this examination draws out similarities in the approaches of the two theorists, I subsequently turn to investigating the cognitive translation that Toch invoked in his notational experiments above. I frame this analysis by exploring the historical contingencies to such a psychological framework, thereby substantiating the paradigm shift in the history of melodic thinking that I pointed to in Chapter II.

Finally, the last part of the chapter inquires what aesthetic potential the graphically continuous line afforded Toch in comparison to a rendering as a row of dots.

Approximating Continuity in Toch’s Tonhöhenlinie

To start, let us return to the examples of Figures III.5–8 above, and to Toch’s claim that they visualize the Tonhöhenlinie , even through the appearance of separate note heads. In this invocation, Toch relied on an approximation of the line that is reminiscent of the strategy that we

133 encountered in Kanne’s theory. Indeed, the allusion to a line in Figure III.8 (Toch’s Example

42s) “works” mostly because the excerpt minimizes intervallic distances between adjacent tones.

In fact, both of the melodies that Toch chose in the illustrations of Figures III.5–8, namely the theme of Beethoven’s Violin Sonata and the German Christmas carol, are composed almost exclusively of step-wise motion. The only exception is the octave-leap ( f’–f’’ ) in the penultimate bar of the excerpt from Beethoven’s violin sonata.

Similarly, the example from Beethoven’s Third Symphony (see Figure III.16, featured at the end of this chapter) is composed almost exclusively of step-wise progressions. Here as well,

Toch subsumed all successions of tones under this scalar paradigm. This assimilation is evinced in the graphical line that Toch drew above the staff to highlight the respective Tonhöhenlinie in

Figure III.16, which does not show any distinction in shape between the step-wise progressions of tones and the melody’s opening leap of a fourth ( b-flat’—e-flat’’ ). 29

The implicit constraint of choosing melodic excerpts that progress uniformly by step is typical of Toch’s application of the Tonhöhenlinie more broadly. Indeed, all the musical examples cited in the first part of Melodielehre —the section dedicated to the Tonhöhenlinie — progress predominantly in step-wise motion. More generally, two out of the three shapes that

Toch considered for the Tonhöhenlinie are defined by their step-wise progression. As I discuss below, these are the “Gerade” and the “small wave line.” With regards to the “Gerade,” Toch

29 Wassily Kandinsky’s Beethoven-analysis discussed in Chapter I and V demonstrates how such a distinction could be rendered quite easily through variations in the line’s steepness. Confronted incidentally with the same opening intervallic leap in another Beethovenian melody (the fourth b-flat’—e- flat’’ ) as Toch, Kandinsky drew a steeply ascending line which then recedes more gradually, at a flatter angle, to portray the succeeding scalar descent. Alternatively, as we have seen with Kanne’s annotated wave line in Figure III.3, variations in the steepness of the wave line could also be used to adjust the length of the respective phase—for instance, so as to render the unevenness between ascending and descending segments. 134 himself fittingly referred to the excerpts that he isolated as “Tonleiter-Melodien” (which can be translated as “scalar melodies”). 30

Only in the later part of Melodielehre , starting on page 79 of the treatise’s 180 pages total, did Toch turn his attention away, also nominally, from the Tonhöhenlinie to the artistic realm of “melody.” Concomitantly, his focus expanded to include a variety of melodic formations, starting, for instance, with melodies made out of triadic arpeggiations in his Chapter

VI, under the heading “Die Melodie im Lichte der Harmonik.” Tellingly, Toch discussed more diverse intervallic progressions besides step-wise constellations under the heading of “melody,” rather than as formations of a Tonhöhenlinie . It thus seems that also in Toch’s time, intervallic leaps—or “gaps,” as Kanne had called them more suggestively a hundred years earlier—were still difficult to account for with regards to a perceived coherence that bound leaps together. Just like Kanne, Toch evaded the question by minimizing the gap that had to be bridged between adjacent tones.

But while Kanne had limited the shape of his wave lines to a pre-defined curvature, which could only vary between the representation of tonic and dominant scale segments, Toch derived the shape of his lines from the specific melodies at hand. The external shape of Toch’s

Tonhöhenlinie was thus more variable than Kanne’s wave line. Internally, however, Toch restricted the applicability of his concept through a different means, which ultimately fostered a similar preconception about the internal organization of the line as Kanne’s. While Kanne had filled in any freely chosen melody with scalar runs between intervallic leaps in order to attain a smooth succession of tones by the smallest possible increments, Toch applied a selective lens to the repertoire, to focus only on those excerpts that suited his theoretical agenda.

30 Toch, Melodielehre , 24. 135

A Psychological Perspective on Music Theory: Cognition as Methodological Anchor in Toch’s Melodielehre

The allusion to the readers’ ability to see a line where none was physically present that

Toch conjured up in Figure III.8 (his Example 42) entailed more than a limitation to step-wise motion. Indeed, there was more at play in how Toch thought of the line in the first place, and how he conceived of the senses involved in the perception of the Tonhöhenlinie . From the outset of the treatise, Toch established the primacy of sensory perception to his approach to music. This proclamation aligns Toch with the trend of early twentieth-century music theorists more broadly, as I discussed in Chapter II. In what Alexander Rehding has coined the “age of psychology” in the history of music theory, music theorists aspired increasingly to a more psychologically founded conception of music that would be oriented by the listener’s perception of music.31

Tapping insights from contemporaneous research in cognition and psychology, notably from the emerging fields of experimental psychology and Gestalt theory in German academia, the setup of

Toch’s treatise thus marks a foundational difference to the premises operative as Kanne’s model.

Let us thus investigate the episteme of perception and cognition with which Toch framed his

Melodielehre .

He opened the treatise by considering the capacity of the various senses, deeming the aural and visual senses “höherwertig” than all others. 32 These two senses stand out, Toch argued, through the potential multidimensionality of their sensations, thus superseding in complexity the sensations yielded by the “tiefwertige” senses. Deducing compatibility between aural and visual sensual impressions, Toch concluded that the respective mental images were transferable

31 Alexander Rehding, Hugo Riemann and the Birth of Modern Musical Thought (Cambridge: Cambridge University Press, 2003), 34. Rehding describes this paradigm shift by the example of changes in Hugo Riemann’s thought, summarizing the period as, “the age of psychology was about to supersede the age of acoustics.” 32 Toch, Melodielehre , 1. 136 between them: a visual image could be mapped onto an aural one, and vice versa. Following from this logic, Toch proposed to map musical parameters onto visual ones, by establishing equivalence in terms of their mental representations.

As the referential framework of visual relations, Toch invoked the hierarchical structure of Euclidian geometry. To determine the available parameters, he described how the multidimensionality of the physical world was projected onto mental images of varying dimensions:

Was wir sehen ist ein dreifaches. Da ist zunächst als einfachste Form des Gesichtseindruckes die Linie . Die einfachste, weil sie der Ausdruck der ein dimensionalen Ausdehnung ist. Die mehrdimensionale Ausdehnung offenbart sich dem Auge als Eindruck des Flächen - und Körper haften. … Dem Linien- und Flächeneindruck gesellt sich als dritter der der Farbe hinzu. Die Qualität dieses Gesichtseindruckes ist grundsätzlich verschieden, weil nicht mehr an Ausdehnungsbegriffe geknüpft. 33 What we see is threefold. First, there is as the simplest form of visual impressions the line . [It is ] the simplest because it is the expression of one -dimensional extension. More- dimensional extension manifests itself to the eye as impressions of planes and bodies . … The impression of lines and planes is joined by that of color as a third kind. The quality of this visual impression is fundamentally different because it is no longer tied to terms of extension.

Toch further explained that due to the perceptual limitations of human vision, the plane and the body occupy the same dimension in their cognitive representations. A differentiation between the two is only possible through recourse to the sense of touch and the knowledge thus acquired. In terms of visual cognition, Toch thus established a tripartite hierarchy—line, plane, and color.

This foundational tripartition also applied to aural cognition, Toch maintained, with emphasis:

Dieselbe Dreiteilung der Sinneswahrnehmungen gilt, wenn wir an die Stelle der Raumbegriffe Zeitbegriffe setzen, auch für alle Gehörswahrnehmungen. 34

33 Toch, Melodielehre , 1–2. The emphases are original. 34 Toch, Melodielehre , 2. In the original, this entire passage is emphasized through broad spacing. 137

The same tripartition of sensations applies—if we replace the terms of space through terms of time—also to all auditory sensations.

On this basis, he started to propose an equivalent order of musical parameters, proceeding, as with the visual impressions, in increasing order. Having declared the line as the

“simplest form of visual impressions,” Toch’s first analogy related the line to the smallest unit in music—the pitch or tone. Toch called this line a “Tongerade” (“tone-line”), and he explained that it extends from a temporal point (“Zeitpunkt”). 35 This explanation ties back to his proposition of the line as an “expression of one -dimensional extension” (“Ausdruck der ein dimensionalen Ausdehnung”). The temporal extension of the tone-line retrospectively illuminates the importance of “extension” that Toch invoked as the guiding principle in his exposition of visual phenomena. 36 In the juxtaposition of the point (time-point) and line (tone- line), only the line assumes aesthetic meaning as a cognitive entity, whereas the point—which

Toch tacitly omitted from his classification of visual impressions—serves merely as a reference.

This classification, and in particular the omission of the point as both an icon of creative agency and cognitive signifier, resonates equally with theories in the visual arts, as I discussed in

Chapter I, as well as with principles of Gestalt theory. Paul Klee, for instance, asserted that the point was “without time” (“zeitlos”), and hence “dead,” in contrast to the line as the “first moveable deed:”

Über den toten Punkt hinweggesetzt sei die erste bewegliche Tat (Linie). … Wenn ein Punkt Bewegung und Linie wird, so erfordert das Zeit. Ebenso, wenn sich eine Linie zur

35 See Toch, Melodielehre , 3. 36 The centrality of “extension” in Toch’s classification furthermore evokes the reception of Henri Bergson’s Time and Free Will (1889), and Duration and Simultaneity (1922). Much like “duration” formed the basis of consciousness in Bergson’s thought, “extension” provided the fundamental criterion for Toch’s exposition of a cognitive imagery. Rather than from deliberate engagement with Bergsonian phenomenology, however, this resonance more likely resulted from Toch’s practical musical experience. 138

Fläche verschiebt. Desgleichen die Bewegung von Flächen zu Räumen. … Zeitlos ist nur der an sich tote Punkt. 37 The dead center being the point, our first dynamic act will be the line. … When the dot begins to move and becomes a line, this requires time. Likewise, when a moving line produces a plane, and when moving planes produce spaces. … Only the dead point as such is timeless.

Emphasizing the quality of extension as a condition of his perceptual hierarchies, Toch’s thought aligned with Klee’s theory of the point and line and their energetic constitution. As we shall review momentarily, from a psychological point of view, Gestalt theorists similarly disregarded the single point as an aural or visual impression in favor of the perception of more holistic phenomena, which trumped the perception of any smaller, constituent parts.

From the available parameters, Toch further likened the musical interval to a geometrical angle—an intermediate step in the originally proposed tripartition of cognitive levels—and the concurrence of even more tones in a chord to a plane. Moreover, as we have seen, in the taxonomy, the line doubled as analogy not only of the single tone, but also of melody (in the

Tonhöhenlinie ).

The itemization of parameters available in the above quotation clarifies that the entities with which Toch operated in his taxonomy were not exterior phenomena of the physical world, but rather their corresponding representation as internal, cognitive images. This perspective sets

Toch’s mapping between aural and visual phenomena clearly apart from analogies such as those that Kanne, for instance, had proposed. Kanne’s likening of melody to contour, harmony to color, and rhythm to proportion in painting was based on an ideological correspondence between

37 Paul Klee, “Schöpferische Konfession,” in Schöpferische Konfession , ed. Kasimir Edschmid, Tribüne der Kunst und Zeit 13 (Berlin: Reiss, 1920), 29 and 33. Translated in Paul Klee, Creative Confession and Other Writings , trans. Matthew Gale (London: Tate Publishing, 2013), 7–14, at 7, 9, and 10. See also Régine Bonnefoit, Die Linientheorien von Paul Klee (Petersberg: Michael Imhof, 2009), 25. 139 these parameters in terms of their functionality within the respective art forms. Toch, by contrast, sought to understand musical and visual parameters as perceptual entities.

In the quote above about the tri-partite hierarchy in visual perceptions, Toch distinguished sharply between spatial and temporal terms, envisioning them as dimensions exclusive to aural and visual cognition respectively. By replacing “the terms of space with terms of time,” he suggested that the order of spatial sensations transformed into an order of auditory sensations. 38 In Toch’s theory, then, only aural sensations involved—and, concomitantly, accounted for—the passage of time. Conversely, Toch implied that spatial sensations occurred as immediate, quasi-timeless impressions.

This polarity of terms underpinned the analogies between aural and visual phenomena that Toch proposed. For instance, he opposed the “temporally-audible line” (“zeitlich-hörbare

Linie”) of melody to the “spatially-visible” line that extends in graphical space. 39 Within this dichotomy, melody constituted a dynamic principle that unfolded in time, whereas the

Tonhöhenlinie remained a static entity—and, by implication, spatially defined. After all, the

Tonhöhenlinie was merely an abstract representation of one specific aspect of melody, as Toch had clarified (“it is not yet melody”). It is the static visual shape that melody as a “temporally- audible line” yields in the mind of the listener. In other words, a “temporally-audible line”

(“zeitlich-hörbare Linie”) finds its cognitive representation in a “spatially-visible” line, and vice versa. Thus, when Toch claimed that one could easily see the wave line in Figure III.8, this seeing refers to the mental image of a line that hearing the (purely audible) line inherent in melody conjures up. In other words, only when listening to the melody—and its Tonhöhenlinie or “Wellenlinie”—can one see the line in one’s mind. An interpretation of the images of Figures

38 “Dieselbe Dreiteilung der Sinneswahrnehmungen gilt, wenn wir an die Stelle der Raumbegriffe Zeitbegriffe setzen, auch für alle Gehörswahrnehmungen.” See above, from Toch, Melodielehre , 2. 39 Toch, Melodielehre , 6. 140

III.5–8 thus entails recourse to theories of analogies between aural and visual imagery. It thus merits examining how such analogies, or indeed processes of aural and visual cognition, were understood at the time.

Backdrops for Toch’s Cognitive Framework

Principles of aural and visual cognition and the relation between them constituted a burgeoning field of research in the late nineteenth and the early decades of the twentieth century.

Models for Toch’s ideas were rife in philosophical and psychological thinking of his day. Even if

Toch did not acknowledge explicitly any sources of reference or inspiration, his propositions regarding correlations between aural and visual mental images are clearly indebted to this trajectory of research.

Ernst Mach

An influential point of departure for studies in cognition was Ernst Mach’s theory of

Sinnesempfindungen (“Sensory Perception”), as delineated in his Beiträge zur Analyse der

Empfindungen (1886). 40 In 1896, Mach illustrated a theory of perception in a diagrammatic sketch, which is preserved at the Archive of the Deutsches Museum in Munich (reproduced in

Figure III.9). 41

Seeking to elucidate the formation of scientific knowledge from perceptions of the physical world, Mach’s diagram features the two senses of vision and audition, which dominated

40 Ernst Mach, Beiträge zur Analyse der Empfindungen (Jena: G.Fischer, 1886). Mach’s essay appeared in expanded editions under the title Die Analyse der Empfindungen und das Verhältniss des Physischen zum Psychischen starting in 1900 (Jena: G.Fischer). 41 The sketch is catalogued as CD 73503 in the Archive of the Deutsches Museum in Munich. See also Wilhelm Füßl and Johannes-Geert Hagmann, Licht und Schatten: Ernst Mach - Ludwig Mach , Catalogue of the Exhibition (Munich: Deutsches Museum, 2017), 70. 141 studies of perception, and which Toch considered “höherwertig.” The thicker line in the diagram and its accompanying arrows trace how stimuli from these two senses are first transformed into an aural or visual image (“Lautbild,” “Schriftbild”) respectively. These images then converge in a concept (“Begriff”)—which, as the target of Mach’s inquiries, assumes due prominence in the central field of the sketch. Because the concept is shared between stimuli from both senses, the mental images can be translated equally into aural or visual forms of representation (which Mach termed “Lautbezüge” and “Schriftzüge”). 42 The illustration shows precisely the kind of mapping that Toch invoked. In the case of Toch’s analogies, for instance, the central “concept”

(“Begriff”) could be populated with the “line,” as the mental imagery that the perception of either a melody or a geometrical line might trigger, and which, in turn, could be represented again in either medium. I have recreated this analogy in the diagram of Figure III.10.

42 I translated “Lautbezüge” and “Schriftzüge” as “aural” and “visual representations” to reflect the parallelism between them. More literally, they denote “sonic relations” and “written strokes.” 142

Figure III.9 : Ernst Mach, Sinnesempfindungen (1896), sketch

Figure III.10 : Mach’s diagram populated with Toch’s theory of the line in aural and visual cognition 143

The arrows in Mach’s diagram suggest a unidirectional process in the transformation between sensations, mental images, and the formation of conceptual representation. Such an understanding of perception as a successive rather than a simultaneous act was indeed a critical achievement of nineteenth-century psychological research, as Benjamin Steege has chronicled. 43

A view that conflicted with “the Idealist’s treasured ‘unity of the living act’ (Einheit des lebendigen Actes),” Steege portrays the “temporalization of the distance between a person and the world” as one of Hermann von Helmholtz’s notable agendas in the psychophysical discourse of the 1850s and 60s. 44 Since Mach was an avid champion of Helmholtz’s work (having published an unsolicited Einleitung in die Helmholtz’sche Musiktheorie in 1866), Steege subsumes Mach’s theory of “Beiträge zur Analyse der Empfindungen” under the propagation of this paradigm shift. 45

Christian von Ehrenfels

Yet, in 1890, which is some six years before the drawing of the sketch in Figure III.9,

Christian von Ehrenfels critiqued Mach for not having gone far enough with regards to the temporality of perception. Ehrenfels took Mach’s theory, and specifically his comparison between aural and visual cognition, as the starting point for his own pioneering article “On

‘Gestalt Qualities,’” which would pave the way for the emergence of Gestalt theory in German

43 Benjamin Steege, Helmholtz and the Modern Listener (Cambridge: Cambridge University Press, 2012), esp. “Temporalities of Attention,” 83–96. 44 Steege, Helmholtz and the Modern Listener , 88. 45 See esp. Steege, Helmholtz and the Modern Listener , 89n21. On the relation between Helmholtz’s and Mach’s thought see Steege Helmholtz and the Modern Listener , 23, and Alexandra Hui, The Psychophysical Ear: Musical Experiments, Experimental Sounds, 1840-1910 (Cambridge, MA: MIT Press, 2013), 103. For Hui’s discussion of Mach’s theory, see esp. 114–21. 144 academia. 46 Citing from Mach’s “Beiträge zur Analyse der Empfindungen,” Ehrenfels highlighted that in that treatise, visual and aural sensations (“Raumgestalten und selbst

‘Tongestalten’”) were still portrayed as yielding immediate and holistic images. Ehrenfels summarized Mach’s proposition:

Mach stellt (…) die für manchen gewiß paradox klingenden Behauptungen auf, daß wir Raumgestalten und selbst “Tongestalten” oder Melodien unmittelbar zu “empfinden” vermögen. 47 Mach made the (certainly for many somewhat paradoxically sounding) claim that we are able directly to “sense” spatial shapes and even tone-Gestalten or melodies. 48

Focusing on the example of melody, Ehrenfels countered:

Denn daß, wenn nur Gegenwärtiges “empfunden” wird, die zeitlich sich abspielende Melodie jedenfalls kein Objekt der Empfindung abgeben könne, das wird selbstverständlich von Mach ebensogut zugestanden werden, wie von jedem, welcher sich scheut, Widersprechendes zu behaupten. 49 If we can sense only that which is simultaneously present to us, then a melody, which is played out in time , cannot serve as an object of sensation. This would of course be admitted by Mach as much as by anyone who wishes to avoid asserting what is contradictory. 50

Melody, as a phenomenon that defies perception as a single momentary sensation, became Ehrenfels’s test case. His study explored how melody could be grasped as a coherent and holistic entity after all, despite its inherent evanescence. Ehrenfels thus reconceived Mach’s theory of aural and visual cognition by accounting for the temporality inherent in aural perception. Falling chronologically between the publication of Mach’s treatise (1886) and his

46 Christian von Ehrenfels, “Über ‘Gestaltqualitäten,’” Vierteljahrsschrift für wissenschaftliche Philosophie 14, no. 3 (1890): 249–92. In what follows, I refer to a later edition that appears in Ehrenfels, Das Primzahlengesetz, entwickelt und dargestellt auf Grund der Gestalttheorie (Leipzig: Reisland, 1922), 7–29 and 77–95, which also contains the related “Weiterführende Bemerkungen.” Apart from Mach’s essay, Ehrenfels mentions Alexius Meinong’s “On the Psychology of Complexions and Relations” (1891) as an important source of reference, a draft of which he must have seen before the text’s publication. 47 Ehrenfels, “Über Gestaltqualitäten,” 7. 48 Translation from Ehrenfels, Foundations of Gestalt Theory , ed. and trans. Barry Smith (Munich: Philosophia Verlag, 1988), 82. 49 Ehrenfels, “Über Gestaltqualitäten,” 7–8, emphases in original. 50 Translation amended from Ehrenfels, Foundations of Gestalt Theory , 82–3. 145 drawing of the sketch of Figure III.9 (1896), Ehrenfels’s critique might even have inspired Mach to explore such a temporal account in the diagram. At the same time, Ehrenfels had not yet spoken the last word on the topic in his 1890 essay either.

In 1922—after a gestation period of over thirty years—he published an addendum to “On

‘Gestalt Qualities’” in which he revised in particular a theoretical frame for the temporality of the cognitive processes that he had proposed. 51 The addendum was instigated by criticism that

Ehrenfels’s theory had faced regarding the temporal framework, which he had implied only rudimentarily in 1890. Part of this critique was founded on scientific and philosophical advances made in the meantime, involving prominently Albert Einstein’s theory of special relativity and

Hermann Minkowski’s attendant model of space-time, which integrated time as a fourth dimension into a spatial model, as I reviewed in Chapter I.

In his response, Ehrenfels attempted to re-model the Einsteinian space-time continuum to better account for processes of memory and anticipation. Ehrenfels took issue in particular with the representation of time as an arrow pointing in two opposite directions. While Ehrenfels accepted such a representation for the arrow extending into the past, he refuted the model for its implied conception of the future, which seemed too pre-determined. Instead, Ehrenfels advocated for the future to be conceptualized through a “chronomorph” model, in which the signification of time would constantly change to transform the present into the past. 52 While Ehrenfels only mentioned the impact of Einstein’s theory as a frame of reference to his thoughts, the perceptual orientation of his account of time aligns more with Henri Bergson’s position, who in 1922

51 Ehrenfels, “Über Gestaltqualitäten,” introducing the addendum with “nach einer mehr als dreißigjährigen Pause” (77). 52 Ehrenfels, “Über Gestaltqualitäten,” esp. 106–9. 146 similarly countered Einstein’s physically based theory of time.53 Together, Ehrenfels’s addendum and the debate between Einstein and Bergson document the lively and far-reaching discussions concerning the temporality of cognitive processes that occurred at the time when

Toch was revising his dissertation to prepare the publication of his treatise.

These concerns with the temporality of aural perception, which Ehrenfels—and before him, Helmholtz—emphasized, are equally crucial as context to Toch’s propositions as are such theories of aural and visual cognition as demonstrated in Mach’s diagram. At the same time,

Ehrenfels posited that not only aural, but also visual cognition relied on temporal processes. He suggested that spatial Gestalten might equally arise from the cognitive re-composition of multiple, temporally dispersed sensory impressions. As he emphasized, this applied even to what he termed “atemporal” (“unzeitliche,” Smith translates as “non-temporal”) Gestalt qualities. 54

Unlike the temporal (“zeitliche”) Gestalt qualities, “atemporal” qualities are not defined through the temporal order of their component sensations, and they might even be grasped as a single sensation. This, however, did not negate the passing of time that the sensation entailed in its cognitive processing, as Ehrenfels explicitly pointed out.

53 Henri Bergson, Duration and Simultaneity: Bergson and the Einsteinian Universe , ed. and trans. Robin Durie (Manchester, UK: Clinamen Press, 1999), originally Durée et simultanéité . À propos de la théorie d'Einstein (Paris, 1922). See also my discussion in Chapter I. The book continues the famous debate over their theories of time that Bergson led with Einstein in 1922. 54 “Dagegen können wir sämtliche Gestaltqualitäten durch eine vollständige Disjunktion in zeitliche und in unzeitliche einteilen, wobei wir unter letzteren nicht etwa diejenigen verstehen, zu deren Perzeption keine Zeit nötig wäre, auch nicht diejenigen, für deren Auftauchen im Bewusstsein ein gleichzeitiges Umfassen aller Elemente ihrer Grundlage unerlässlich ist ... sondern diejenigen, für deren Grundlage nicht wie bei den zeitlichen Gestaltqualitäten verschiedene zeitliche Bestimmtheit der Vorstellungsobjekte erforderlich ist.” Ehrenfels, “Über Gestaltqualitäten,” 20. “[Non-temporal Gestalt qualities are ] those for whose foundation distinct temporal determinations of the separate objects of presentation are not required. Non-temporal Gestalt qualities are qualities whose foundation can be given completely in perceptual presentation (called by many ‘sensation’).” Translation from Foundations of Gestalt Theory , ed. and trans. Barry Smith (Munich: Philosophia Verlag, 1988), 94. 147

This central advancement of Ehrenfels’s theory clearly exceeded Toch’s understanding of cognitive principles, who theorized visual impressions as quasi time-less and immediately holistic perceptions: Toch differentiated between the aurality of temporal dimensions and the visuality of spatial dimensions—a dichotomy that Ehrenfels had sought to eliminate.

Other Gestalt Theorists

This fundamental theoretical divergence complicates Luitgard Schader’s reading of

Toch’s Melodielehre as a direct offspring from the theories of the Viennese school of Gestalt theory. 55 Schader suggests that—like Toch—this group of scholars gave precedence to the aural and visual senses over the others, and she conjectures that Toch would have been familiar with their research through his brief studies in 1907–10 at the philosophy department of the

University of Vienna, where he took seminars with Friedrich Jodl and Wilhelm Jerusalem. 56 For instance, Schader draws attention to a passage from Jodl’s Lehrbuch der Psychologie from 1896, in which Jodl contemplates the kinship between these two senses, observing that the sensation of pleasure arising from them commonly springs from the intuitive combination of different sensual

55 “So kann Tochs Melodielehre … als ein Ergebnis seines Studiums am Wiener Philosophischen Seminar gedeutet werden.” Luitgard Schader, “Das Verhältnis von Ernst Tochs ‘Melodielehre’ zu Ernst Kurths ‘Grundlagen des linearen Kontrapunkts,’” Musiktheorie 18, no. 1 (2003): 58. Michael Polth perpetuates Schader’s conclusions, though somewhat more cautiously, in Polth, “Zwischen Gestaltpsychologie und Funktionalität,” 110–11. 56 Schader, “Das Verhältnis von Ernst Tochs ‘Melodielehre’ zu Ernst Kurths ‘Grundlagen des linearen Kontrapunkts,’” 53. Toch was enrolled in the Philosophy department of the University of Vienna between fall 1907 and fall 1910. Ulrike Kienzle has pointed out, however, that Toch effectively lived and studied in Frankfurt in the years 1909–11 and presumably did not actually take any classes in Vienna after his move—which limits the expanse of Toch’s philosophical studies to a maximum of four semesters. Ulrike Kienzle, “‘Ich bin der meistvergessene Komponist des Jahrhunderts:’ Ernst Toch - erfolgreich und verfemt,” in Neue Töne braucht das Land: die Frankfurter Mozart-Stiftung im Wandel der Geschichte (1838-2013) (Frankfurt am Main: Frankfurter Bürgerstiftung, 2013), 225 148 impressions. 57 The level of complexity that Jodl ascribed to sensory experiences in these two senses does indeed parallel Toch’s classification of “hochwertige” and “tiefwertige” senses, as discussed above. 58 But Jodl’s Chapter IX, “Wichtigste psychische Gebilde der Reproduction,” portrays again a much more nuanced account of “time” and “space” than the one reflected in

Toch’s theory.

Schader has also proposed that Toch molded his theory after the Gestalt-theoretical principles of the Viennese school following Ehrenfels’s contributions, and that he adapted in particular the principle of “Übersummenhaftigkeit” (“supra-summativity”):

Based on Christian von Ehrenfels, Toch interprets musical structures through the lens of Gestalt psychology. … Toch’s description of the “Übersummenhaftigkeit der Gestalt” had also been anticipated by Christian von Ehrenfels likewise by the example of melody. 59

Schader’s language suggests Toch’s direct reception of Ehrenfels’s work and might even mislead the reader to assume explicit quotations in Toch’s text. Yet, Toch did not use the term “Gestalt,” let alone that of “Übersummenhaftigkeit.” The passage from Melodielehre , which Schader cites to illustrate the manifestation of these ideas in Toch’s thought, reads:

Natürlich darf nicht übersehen werden, daß diese Teilung in Tonhöhenlinie und Rhythmus nichts mit den genetischen Vorgängen, dem Werden der Melodie zu tun hat, sondern lediglich der getrennten und darum geordneten Untersuchung der beiden Elemente dienen soll. Neben und über dem sichtbaren, auf diese Weise zusammengesetzten Resultat bleibt das Geheimnis seines Werdens als das Wesen der

57 Schader, “Das Verhältnis von Ernst Tochs ‘Melodielehre’ zu Ernst Kurths ‘Grundlagen des linearen Kontrapunkts,’” 57–8, quoting from Friedrich Jodl, Lehrbuch der Psychologie (Stuttgart: J.G. Cotta, 1896), 406. 58 See Toch, Melodielehre , 1. 59 “In Anlehnung an Christian von Ehrenfels interpretiert [Toch ] musikalische Strukturen im Sinne der Gestaltpsychologie … Tochs Beschreibung der ‘Übersummenhaftigkeit der Gestalt’ war von Christian von Ehrenfels ebenfalls am Beispiel der Melodie vorweggenommen worden.” Schader, “Das Verhältnis von Ernst Tochs ‘Melodielehre’ zu Ernst Kurths ‘Grundlagen des linearen Kontrapunkts,’” 57: Schader also writes, “Beide Autoren [Kurth and Toch ] lenken das Augenmerk der Interpretation auf die Melodie als selbständigen Träger des musikalischen Geschehens und beide verankern ihre Theorie in der Gestaltpsychologie,” 60. 149

musikgestaltenden Urkraft , ähnlich wie man das Wesen eines Baumes nicht damit erklären kann, daß man ihn als eine Summe von Holz, Rinde, Blättern usw. definiert. 60 Of course we must not overlook that this separation into Tonhöhenlinie and rhythm has nothing to do with the genetic processes, the becoming of melody, but merely serves as a separated analysis of both elements and the issues around them. Apart from and above the visible composite result remains the mystery of its becoming as the essence of the music- generating Ur-force ; [this is ] comparable to the fact that one cannot explain the essence of a tree by defining it as the sum of wood, bark, leaves, and so forth.

It is Toch’s construal of the tree that caught Schader’s attention. Melody is like a tree, Toch argued, which is composed of multiple different elements, but in its essence is more than the sum of these diverse components—a single “composite result.” Such an interpretation of the whole as more than the sum of its parts certainly illustrates the very principle of “Übersummenhaftigkeit,” as Ehrenfels had defined it as one of Gestalt theory’s foundational premises. 61 Schader conjectures that Toch adopted this idea and its representation through the imagery of the tree from Wilhelm Jerusalem’s Einleitung in die Philosophie from 1903. 62 She draws a parallel with a passage from that treatise in which Jerusalem—another one of Toch’s teachers in Vienna— invoked a “blossoming tree” to illustrate how the combination of the two terms “blossoming” and “tree” could still yield a single holistic mental image. 63 Unlike Toch, who considered the complexity of the tree itself, Jerusalem specified the impression through an attribute

60 Toch, Melodielehre , 9. The emphases are mine. 61 Ehrenfels, “Über Gestaltqualitäten,” esp. 16. Max Wertheimer, Kurt Koffka, and other protagonists of the Berlin school of Gestalt theory were quick to revise this theorem. They asserted that the whole was not more , but other than the sum of its parts. In the further development of Gestalt theory, this view mostly supplanted Ehrenfels’s pioneering concept of “Übersummativität” or “Übersummenhaftigkeit.” 62 Schader, “Das Verhältnis von Ernst Tochs ‘Melodielehre’ zu Ernst Kurths ‘Grundlagen des linearen Kontrapunkts,’” 57. She also considers the influence of Kurth’s theory in Grundlagen des linearen Kontrapunkts for the invocation of an “Urkraft,” but then relates this concept more decisively to Wilhelm Jerusalem. 63 See Schader, “Das Verhältnis von Ernst Tochs ‘Melodielehre’ zu Ernst Kurths ‘Grundlagen des linearen Kontrapunkts,’” 57, quote from Jerusalem, Einleitung in die Philosophie , 2 nd rev. ed. (Vienna: W. Braumüller, 1903), 32. 150

(“blossoming”), to accentuate our capacity to grasp and imagine complex entities with all their idiosyncrasies.

A much closer model to Toch’s specific use of the tree as a symbol of composite entities can however be found in an earlier source. In fact, this takes us back again to Ehrenfels’s reception of Mach’s Beiträge zur Analyse der Empfindungen . In his “On ‘Gestalt Qualities,’”

Ehrenfels disclosed that he developed the very theorem of “Übersummativität” on the basis of

Mach’s work. To illustrate how he saw the idea ingrained already in Mach’s writing, he cited in his own essay the following passage from Beiträge zur Analyse der Empfindungen , in which

Mach observed the holistic consistency of a tree:

Der Baum mit seinem grauen, harten, rauhen Stamm, den zahllosen, im Winde bewegten Ästen, mit den glatten, glänzenden Blättern erscheint uns zunächst als ein untrennbares Ganze. 64 The tree with its grey, hard, rough trunk, the many branches moving in the wind, with its sleek, glossy leaves, appears to us at first as an indivisible whole.

Mach’s description of the tree as an “indivisible whole” encapsulates the principle of

“Übersummativität” as Ehrenfels theorized it. Moreover, in its emphasis on the diversity of the tree’s component elements—its trunk, branches, and leaves—it bears a striking similarity to the description in Toch’s writing, who listed as the tree’s parts the “wood, bark, leaves, and so forth.” Like Toch, Mach stressed the unified appearance of the tree despite its complex structure, and unlike Jerusalem, he referred to a general, unspecified example of a tree.

While this correlation again suggests a lineage of influence from Mach via Ehrenfels to

Toch, it is important to bear in mind that Toch restricted his reflections on these ideas to the short passage quoted above. He explored neither possible sources for his ideas nor their

64 Ehrenfels, “Über Gestaltqualitäten,” 8–9, referring to Ernst Mach, Beiträge zur Analyse der Empfindungen , 40. 151 theoretical consequences. Instead, he confined the explanatory potential of the allegory in the metaphorical black box of “mystery.” To it, he attributed both the generative processes that form melody—a “music-generating Ur-force” (“musikgestaltende Urkraft”)—as well as the principles that account for a holistic perception of a tree. Unlike in Kanne’s days, which, as mentioned, featured plenty of precedents for the tropes of magic and mystery, in the context of the early twentieth century, this rhetoric sustained Toch’s evasion of the pertinent scientific discourses.

Ernst Kurth’s reaction to Melodielehre appositely captured this dichotomy between the potential of Toch’s approach and the limitations of its enactment. Toch had mailed his colleague a copy of Melodielehre for review. In his response letter, Kurth applauded Toch’s endeavors and commented in particular that the introduction (in which Toch addressed possible analogies between aural and visual cognition) articulated “the most difficult problems that extend far beyond musical concerns.” 65 Kurth’s generally enthusiastic reception frames these “most difficult problems” as part of the shared agenda that he perceived for the development of music theory, which he himself had proclaimed only a couple of years earlier in the opening of his

Grundlagen des linearen Kontrapunkts (1917) as the orientation towards a psychologically founded approach. But while Kurth welcomed Toch’s efforts in outlining pertinent issues in his introduction, he acknowledged that they remained “problems” that extended into realms far outside of music.

65 The letter is contained in Nora Schmid and Lea Hinden, eds., “Volltextbriefe zum Inventar Nachlass Ernst Kurth (Vers. 4.0)” (Bern: University, Institut für Musikwissenschaft, September 2007), http://www.musik.unibe.ch/dienstleistungen/nachlass_kurth/index_ger.html . See also Schader, “Das Verhältnis von Ernst Tochs ‘Melodielehre’ zu Ernst Kurths ‘Grundlagen des linearen Kontrapunkts,’” 56: “Die schwersten, noch weit aus der Musik herausführenden Probleme scheint mir die Einleitung zu enthalten.” 152

Achieving Continuity

Despite the hesitation expressed in Kurth’s review, the cognitive paradigm that Toch invoked as the frame to his taxonomy of musical parameters opens up a valuable perspective on how to construe the aesthetic richness of a mapping between melody and line in the early twentieth century. In particular, under the auspices of inquiries into Gestalt theory and cognition, as discussed above, the conundrum of melody’s coherence could be transferred from a quasi- acoustical to a psychological and phenomenological concern. This conceptual shift explained the continuity of Toch’s Tonhöhenlinie to reflect the experienced coherence of melody as a cognitive entity unfolding in time. 66 When read through Mach’s diagram of aural and visual cognition

(Figures III.9 and III.10), Toch’s Tonhöhenlinie can moreover be construed as the visual mental imagery that corresponds to the impression of melody in the listener’s mind, which could then be rendered into a visual or aural form of representation. In this context, the graphical continuity of the line thus assumed aesthetic and music-theoretical meaning when applied to melody.

This scheme well exceeded the explanatory backdrop available at Kanne’s time. While

Kanne’s wave-line of Figure III.1 is visually just as continuous as Toch’s in Figure III.2, its graphic continuity is not aesthetically accounted for within his music-theoretical framework. To

Kanne, the scalar progressions, with which he filled melodic leaps, remained an approximation to the pre-defined shape of the wave line and its continuous fluctuation. In Toch’s treatise, the limitation to step-wise motion in the Tonhöhenlinie constitutes an oddity, perhaps, but one that facilitated conjuring up the cognitive imagery that the concept denoted.

66 This explanation accounts for Heiko Schneider’s observation that “in Melodielehre , Toch used terms that imply the perception of melodies as holistic units of motion.” Wahrhaftigkeit und Fortschritt , 70: “In der Melodielehre verwendete Toch Begriffe, welche die Wahrnehmung von Melodien als ganzheitliche Bewegungseinheiten implizieren.” 153

Of course, the aspiration to match the line’s continuity in full conceptual depth was and remained an intellectual game. After all, as Paul Souriau, whom we first encountered in Chapter

I, rightfully observed,

Le mouvement mélodique a encore cette ressemblance avec le mouvement visible, qu’il sera très mal perçu quand il sera continu. Soit une sirène acoustique dont le disque se met en mouvement avec une vitesse uniformément accélérée. Nous entendons un son d’abord très grave qui monte peu à peu, d’une façon continue. Mais ces variations de tonalité ne pourront être reconnues que part intermittences, quand elles se seront assez accumulées pour que notre oreille s’en aperçoive. … Le sensation du mouvement mélodique nous sera donc mieux fournie par des variations brusques, saccadées, que porteront sans transition le son d’un degré á l’autre de l’échelle musicale. 67 Melodic movement also has this resemblance to visible movement: it is very poorly perceived when it is continuous. Suppose we have an acoustic siren whose disk gets into motion at a uniformly accelerated speed. We first hear a very deep tone that rises little by little in a continuous way. But these variations of tonality can only be detected intermittently, when we have accumulated enough for our ear to observe them. … Melodic movement will therefore be better perceived by sudden variations that carry the sound from one degree to the next of the musical scale without any transition.

What Souriau described is the effect of an actual pitch-glissando, as it might be produced on a siren. He observed that a tune made of such continuously changing sound would really be much harder to recognize than a melody that progresses by immediately noticeable gradations, such as those of the musical scale. Souriau thus established a boundary around the ideal of continuity in the melodic line, by drawing attention to necessary thresholds of auditory perception.

With theories of embodiment and cognition providing new explanatory frameworks in

Toch’s time to enliven his metaphor of choice, they also opened up further aesthetic potential. In

Toch’s case, tying melodies together into single coherent entities brought out their idiosyncrasies and predisposed them to holistic analysis. As I discuss below, Toch deduced aesthetic principles pertaining to the overall shape that the Tonhöhenlinie would yield. These principles, in turn,

67 Paul Souriau, L’esthétique du mouvement (Paris: F. Alcan, 1889), 319. The translation is from Souriau, The Aesthetics of Movement , trans. Manon Souriau (Amherst: University of Massachusetts Press, 1983), 153. 154 were indicative of the effect of the melody on the listener. This additional step in Toch’s theoretical agenda finally demonstrates the affordance of a representation of the Tonhöhenlinie as a continuous line in contrast to a row of disjunct tones, as discussed above.

The Shape of the Tonhöhenlinie as Expressive Seismograph

Toch classified three general shapes for the Tonhöhenlinie . As noted, the first two of these progress predominantly in step-wise motion. The first shape is that of the “Gerade” (or

“straight line”), which portrays continuous scalar passages in a single direction. As Michael

Polth observes, the “Gerade” is the only shape that Toch did not depict in an abstract graphical form. 68 The illustration of Figure III.11 reproduces Polth’s extrapolation of the shape. Toch’s omission of a respective graphical figure in the treatise might easily relate to the efforts involved in typesetting such illustrations—an issue that he was wary of, as I will address in more detail later. When highlighting a straight Tonhöhenlinie in a musical example, Toch preferred to resort to horizontal brackets as a predefined typeset, if annotating the music at all.

Figure III.11 : “Gerade” Tonhöhenlinie , as represented by Michael Polth 69

Toch’s second shape is the “small wave line” (“Wellenlinie im engeren Sinne,” also referred to simply as “Wellenlinie”), which depicts step-wise undulations around an implied horizontal axis, without ever deviating too far from it:

68 Polth, “Zwischen Gestaltpsychologie und Funktionalität,” 109n18. 69 Taken from Polth, “Zwischen Gestaltpsychologie und Funktionalität,” 109. 155

Ich denke bei der Wellenlinie im engeren Sinne an eine Tonhöhenlinie , welche sich in möglichst kleinen Schritten, vorwiegend also stufenweise, auf- und abwärts bewegt, ohne sich von der Durchschnittshorizontalen—wenn wir beim Bilde bleiben wollen: dem Spiegel oder Niveau—allzuweit zu entfernen. Sie wird also ungefähr vorstehende Gestalt [represented in Figure III.2] annehmen. 70 With the waveline in the narrow sense I think of a Tonhöhenlinie that progresses mostly in small steps, principally in step-wise motion up and downwards, without ever deviating too far from an average horizontal axis—if we want to remain in the imagery, from the mirror or level. It thus takes approximately the shape depicted [in Figure III.2] above.

Toch’s graphical illustration of the “small wave line” is the curvilinear shape shown in Figure

III.2 at the outset of this chapter.

After these two shapes that focus on melodic formations on a small scale, Toch introduced as his third shape the “Wellenlinie im weiteren Sinne” or “large wave line” (also referred to as “große Welle”), which not only deflects much more widely along the vertical axis than the “small wave line” but also traces melodies over longer spans of time (see Figure III.12).

Figure III.12 : Ernst Toch, “large wave line,” Melodielehre 71

With the “große Welle,” Toch’s musical examples also started to encompass larger melodic intervals besides purely step-wise progressions. They are still more constrained, though, than in later sections of the treatise, which feature the full variety of intervallic constellations under the heading of “melody.”

70 Toch, Melodielehre , 27. 71 Toch, Melodielehre , 34. 156

Already with respect to the “straigt line” and the “small wave line,” Toch intimated an aesthetic interpretation of these shapes, as indicative of specific expressive qualities in music.

For instance, he referred to the “Sanglichkeit” of the “small wave line,” and described a short

(three-measure) excerpt from Hans Pfitzner’s opera Palestrina (Toch’s Example 52), which adhered strictly to his definition of the “small wave line” as conveying “tenderness, intimacy, and passion.” 72 As noted earlier, Toch was more interested in such emotionally oriented interpretations of music than in blatant pictorial mimesis, such as the invocation of oceanic waves in Offenbach’s Barcarole.

Toch theorized this expressive potential of the Tonhöhenlinie -shapes more fully with regards to the “large wave,” for which he conjured up the functionality of the seismograph and barometer, as follows:

Ich verstehe unter der “großen Welle” jene eigentümliche Linie, welche sich aus den Spitzen—[image of Figure III.12 inserted ] den höchsten und tiefsten Punkten der Tonhöhenbewegung ergibt und welche etwa vergleichbar ist der Linie, die der Stift unserer feinen Meßinstrumente (Barometer, Seismograph usw.) zeichnet. 73 As the “large wave” I understand this idiosyncratic line which arises from the peaks— [image of Figure III.12 inserted ] the highest and lowest points of the movement in pitch—and which is comparable for instance to the line that the pen of our fine measuring instruments (barometer, seismograph etc.) draws.

In a next step, Toch charged the evocation of seismographic and barometric graphs— records of exerted pressure and energetic vibrations—aesthetically, as representations of music’s expressive development. Like a technical measuring instrument, he perceived the wave line to trace fluctuations in affective tension in music. Since in Toch’s conception, the wave line

72 The reference to “Sanglichkeit” appears in Toch, Melodielehre , 31. Toch makes the following comment on his Example 52: “Man muß durch das Erlebnis der Pfitznerschen Schöpfung durchgegangen sein, um die ganze Zartheit, Innigkeit, Liebeskraft dieser wenigen Noten mitzuempfinden, welche zu einer unscheinbaren, unterbrechungslosen kleinen Welle vereinigt, nach außen hin wie das konstruierte Klischee einer solchen wirken.” Toch, Melodielehre , 34. 73 Toch, Melodielehre , 34–35. 157 projected directly the shape of melodic contour, he hereby established a direct analogy between the rising and falling of melodic contour and the increase and decrease in affective tension. In other words, the peaks of the wave line depict not only climaxes in pitch height, but also in expressive tension. The “large wave line” can thus be construed as Toch’s seismogram of melody’s expressivitiy and, concomitantly, of its effect on the listener.

Toch solidified this metaphorical analogy between seismographic and emotive fluctuations by proposing an overarching triangular shape that encased these fluctuations of the large wave to delineate the music’s general emotive development. Here, Toch invoked the authority of another art form, and cited Gustav Freytag’s Die Technik des Dramas , a nineteenth- century standard reference on dramatic form and development. 74 He also reproduced a graphical depiction of Freytag’s theory in the form of a triangle that reflects the proportions allotted to the different parts of the drama and the position of the ideal dramatic climax (Figure III.13). He further specified that he conceived of the climactic moment in the drama, which in Freytag’s triangle is annotated with a “K” (for “Katastrophe,” or catastrophe), as corresponding to his own concept of “tonischer Höhepunkt.” Furthermore, Toch expanded on the comparison by suggesting that melody had to be structured by caesuras into phrases and sections just like a drama divides into acts and scenes.75

74 Gustav Freytag, Die Technik des Dramas (Leipzig: S. Hirzel, 1863). Toch cites Freytag’s work in Melodielehre , 36. 75 Toch, Melodielehre , 36. 158

Figure III.13 : Ernst Toch, triangle of dramatic organization, adapted after Freytag’s theory, Melodielehre . “K” denotes the dramatic climax (“Katastrophe,” or catastrophe), which corresponds to Toch’s concept of “tonischer Höhepunkt.”

Like with the Tonhöhenlinie , Toch construed the contour of the triangle as fluctuations both in pitch height and in dramatic tension. This reductive equation between pitch and dramatic effect has attracted critique from readers across the treatise’s reception history. The first to take issue with Toch’s interpretation of Freytag’s scheme for musical composition was Arnold

Schoenberg. In the comments that he added to his copy of the treatise, Schoenberg protested:

das soll er gefälligst zeigen! Ich finde das Gegenteil! Das ist dramatische aber nicht musikalische Technik. … Beweis? Wo? Ueberall? Siehe meine Harmonielehre! Ich habe Notizen über anderes. 76 he’d better prove this! I find the opposite! This is dramatic technique but not musical technique. … Proof? Where? Everywhere? See my Harmonielehre ! I have notes on differing views.

To counter the conventions for musical composition that Toch derived from Freytag’s diagram, Schoenberg cited examples from the repertoire (notably, the first movement of

Beethoven’s Sixth Symphony), which “evades a climax” altogether. Further, he elaborated that climactic moments in music could equally be achieved through means other than pitch, as a movement of his own Second String Quartet demonstrates:

76 See Schoenberg’s copy of Toch’s Melodielehre , held at the Arnold Schoenberg Center in Vienna. Transcriptions of this copy are found in Julia Bungardt, “Die Bibliothek Arnold Schönbergs mit einem kommentierten Katalog des nachgelassenen Bestandes sowie einer Edition seiner Glossen in den Büchern” (Ph.D. dissertation, University of Music and Performing Arts Vienna, 2014), Erläuterungen, 31. In the original, some of these comments are written on an extra sheet of paper that Schoenberg inserted between the respective pages of Melodielehre (36–37). 159

Es ist ein Irrtum, dass die Darstellung des Gedankens unbedingt zu den Höhepunkten führen muss und dass an diesen der Vortrag oder die Stimme gehoben werden muss. Aber auch nicht die Tonhöhe. Zum Bsp die Pastoralsymph. 1. Satz weicht einem Höhepunkt aus. Wie aber Höhepunkt anders als durch einen Ton-Höhepunkt ausgedrückt werden kann, zeigt z.B. das Nachspiel wieder des 3. Satzes aus meinem II. Quartett. 77 It is a misbelief that the presentation of ideas needs to lead to climaxes and that these have to be emphasized in performance by raising the voice. But also pitch [does not necessarily need to rise ]. For example the “Pastoral Symphony,” first movement, evades a climax. How, however, a culmination can be expressed by means other than pitch, demonstrates, for instance, the postlude (again) of the third movement of my Second Quartet.

Schoenberg’s opposition thus targeted the limitation in scope of Toch’s considerations and contested in particular his attribution of musical expression exclusively to variations in pitch. 78

Schoenberg’s criticism anticipated Michael Polth’s much later assessment of Toch’s treatise, which similarly takes issue with Toch’s “infelicitous” isolation of melody from the complexities of the musical texture. 79 Deeming the resulting insights superficial, Polth criticizes

Toch’s overly narrow consideration of immediately consecutive tones. Moreover, he laments

Toch’s ignorance towards the structuring affect of harmony, presuming instead all tones as homogeneous entities without any hierarchical differentiation. He illustrates this critique by the

77 Bungardt, “Die Bibliothek Arnold Schönbergs,” Erläuterungen, 31I. 78 In more recent music theory, Kofi Agawu’s work provides the most comprehensive study of the notion of structural “highpoints” in music, and of the various forms it may take, including “a simple melodic peak, a point of textural culmination, or the point of greatest harmonic tension.” V. Kofi Agawu, “Structural ‘Highpoints’ in Schumann’s ‘Dichterliebe,’” Music Analysis 3, no. 2 (1984): 162. To depict these structurally significant moments, Agawu adopts “dynamic” and “narrative curves”—concepts visualized as graphical lines—from the work of musicologist Leonard Ratner (1966) and composer Barney Childs (1977). Drawing as well on empirical and cognitive studies, Zohar Eitan has similarly studied the phenomenon of “highpoints in music.” Zohar Eitan, Highpoints: A Study of Melodic Peaks (Philadelphia: University of Pennsylvania Press, 1997). 79 “Der Elan Tochs wird allerdings durch einige theoretische Vorentscheidungen behindert, die man als unglücklich empfinden kann: durch die Beschränkung der Melodie auf das ‘rein Melodische’ und durch den gestaltpsychologischen Ansatz.” Polth, “Zwischen Gestaltpsychologie und Funktionalität,” 101. Polth’s claims regarding the “Gestalt-theoretical inclinations” of Toch’s theory follow Schader’s, as discussed above. 160 example of Toch’s analysis of the opening melody of Chopin’s Mazurka in B-flat major, Op. 7,

No. 1 (Toch’s Examples 19 and 20, as well as 116). 80

Figure III.14 : Ernst Toch, Melodielehre , Example 20 (Chopin, Mazurka in B-flat major, Op. 7, No. 1, mm. 1–4)

Polth points out how Toch undiscerningly subsumed tones under the Tonhöhenlinie as he saw fit, indifferent to their harmonic support and relative structural weight. In his Example 20

(reproduced as Figure III.14), for instance, Toch bracketed off the extension of the

Tonhöhenlinie over the b-flat’’ that is supported through a subdominant-harmony (including, moreover, even the harmonically unsupported, ornamental c’’’ from the trill), rather than extending the line to the same pitch in the following measure which is harmonized with the tonic. Polth points to the irony that Toch asserted his intentions to observe harmonic considerations in his annotation of this particular example. 81 Polth demonstratively counters

Toch’s reading of the passage by imposing a quasi-Schenkerian lens onto the same musical excerpt, and delineating a hierarchical sub-structure among the tones of the melody based on a harmonic analysis of the passage (see Figure III.16). Through this juxtaposition of analytical

80 Polth, “Zwischen Gestaltpsychologie und Funktionalität,” 113–16. Toch’s examples are from Melodielehre , 15 and 75. Example 116 is strikingly similar to Example 20. In the later example, Toch did not spell out the participant tones of the trill ( b-flat’’ and c’’’ ), but extended the excerpt to include two more measures, across which Toch spanned a second horizontal bracket. 81 Following his Examples 116 and 117, Toch stated: “Die Stellen der Einkerbungen erscheinen nicht willkürlich, sondern sind, neben rhythmischen, von harmonischen Rücksichten diktiert.” Toch, Melodielehre , 75. The emphasis is original. 161 readings, Polth argues that Toch prioritized the unity of the Tonhöhenlinie over the unity of harmonically coherent musical phrases.

Figure III.15 : Michael Polth, analysis of the same passage (Chopin, Mazurka in B-flat major, Op. 7, No. 1, mm. 1–4) 82

Polth’s analysis (as depicted in Figure III.15 above) further curtails the span of the structurally significant ascent of the melody to the octave span f’–f’’ , denoting the g’’ and its underlying subdominant harmony a “Wechselbewegung” that prolongs the f’’ and its tonic support. Though a reference to his own methodological framework is conspicuously absent from

Polth’s intervention, the Schenkerian undertones of his analytical reading are difficult to miss.

Implicitly, Polth thus judges Toch’s theory through the lens of Schenker’s analytical approach. Enacted on more equal and overt terms, this comparison is indeed revealing and—not least due to the conceptual term of the line shared between Schenker’s Urlinie and Toch’s

Tonhöhenlinie —also called for. When evaluating both theories in their own right, such a reading illuminates the ways in which the two theoretical approaches diverged in the degree of independence granted to horizontal developments of individual voices over their tie to a vertical-

82 Polth, “Zwischen Gestaltpsychologie und Funktionalität,” 115. 162 harmonic organization. Based on this observation, we might inquire as to what prompted Toch’s decisions and what kinds of analytical insights he targeted.

As Polth rightly highlights, the Tonhöhenline that Toch presented of Chopin’s Mazurka reflects the relation of consecutive tones, depicting thus phenomena that would be situated on the very surface of a Schenkerian graph. Consequentially, Toch’s annotations of the melody do not parse the underlying harmonic structure. Instead, they bracket distinctive shapes of melody that

Toch sought to scrutinize for their internal organization. Ultimately, the shapes of the

Tonhöhenlinie indicate a catalogue of typical structuring principles in melodic composition.

From the perspective of a composer—who, as we have seen, explored the limits of how far he could stretch horizontal-melodic coherence—this seems like a useful ambition. Moreover, the imagery of the seismograph that Toch conjured implies a continuous recording of all melodic events, considering equally all its constituent tones. Indeed, a seismograph draws a continuous line. It tracks the steady progression of events—or tones participating in the melody—rather than leaping between them to collect disjunct data points. The resulting image yields a distinctive shape that Toch could compare with the normative shapes he established in order to achieve case-specific analytical insights. In other words, only in combination with the principles of melodic composition that Toch proposed throughout his treatise did the Tonhöhenlinie assume aesthetic meaning beyond a direct mapping of tension and release.

Another aspect makes Toch’s allegory of the seismogram yet more elucidating. A seismograph captures fluctuations of only a single parameter in time—seismic waves.

Correspondingly, Toch’s Tonhöhenlinie traces the rise and fall of melody’s diastematic trajectory. While the resulting shape is commonly referred to as “melodic contour,” the term appears problematic in light of its connotations in theories of painting as discussed earlier. As I

163 proposed, the analogy between melody in music and contour in painting in Kanne’s theory demonstrated the dependency of both, as serving merely as the exterior “delineation” of a more complex entity in either art form. In Toch’s theory, by contrast, melody is the entity of interest. It is not an outer frame or delineation of harmonic progressions and phrase structures. Instead, it is the very phenomenon that the seismogram of the Tonhöhenlinie records. This line assumes more independence than the contouring line in painting: it is not tied to representing something else, but rather moves in direct correlation with the motion that it records. In that sense, the notion of line in Toch’s concept of Tonhöhenlinie has evolved significantly from the line of Kanne’s reference to painterly contour. A final example illustrates the functionality of Toch’s

Tonhöhenlinie in practice.

Beethoven and the Aesthetic Function of Toch’s Tonhöhenlinie

Among five musical excerpts—all by Beethoven—that Toch cited (Examples 36–40) to demonstrate the ubiquity of the small wave line in the context of absolute music, he annotated only the last one with a curved line, a melody from the Marcia funebre movement of the Third

Symphony, Op. 55 (see Figure III.16).

Figure III.16 : Ernst Toch, Tonhöhenlinie for Beethoven, Symphony No. 3, Marcia funebre , mm. 36–40, Melodielehre , Example 40 83

83 Toch, Melodielehre , 31. 164

This particular example stands out across the entire treatise as the only one for which Toch drew a graphical line whose shape matched precisely the respective melody. While the reasons for this exclusivity were grounded in the mechanical constraints of typesetting, as discussed above, it merits inquiring as to why Toch deemed this particular example from Beethoven’s Third

Symphony—notably, a selection from the slow movement of a symphony most famous for its arpeggiaic opening theme of the first movement—worthy of a hand-drawn graphical annotation.

I propose that among the many examples of the treatise this particular one fulfils most of the aesthetic criteria that Toch discussed for what makes for good melodic composition. To start, the opening leap b-flat’–e-flat’’ is balanced out by the succeeding step-wise descent down to b-flat’ again, adhering thus to the recommendation that a leap be followed by step-wise motion in the opposite direction. Within these opening five tones, the b-flat’ could perhaps even be considered a “melodischer Stützpunkt” —roughly translated a “staging point in melodic development,” a reference tone recurrently articulated—as Toch proposed elsewhere in the treatise.

Moreover, Beethoven’s melody conforms to the central aesthetic principle that Toch endorsed with regards to the overall development of tension in larger spans of music, which he discussed under the heading of the “große Wellenlinie.” Attending in particular to the distribution of melodic low and high points in the Tonhöhenlinie , Toch deduced three essential rules: 1) That the melody reach only one single real peak, which Toch termed “tonischer

Höhepunkt;” 2) that the respective pitch had to be surpassed in case the melody subsequently continued to build up tension and 3) that the highest peak (“Höhepunkt”) must be reached only in the last third or fourth of the melody. 84 Also the curvilinear shape that Toch drew to exemplify the general shape of the “large wave” (as discussed and depicted earlier, Figure III.11), encapsulates these principles, as does the triangle of overall dramatic proportions that he adopted

84 Toch, Melodielehre , 35. 165 from Freytag’s theory of drama. Even though Toch ostensibly envisioned this theory of the

“large wave” to apply to larger spans of music than the mere four measures excerpted in

Example 40, Beethoven’s symphonic melody similarly conforms to all these rules. This cannot be said of any of the other melodies that Toch cited in the surrounding examples, all of which either start with their respective highpoints, or do not reach them within the apposite proportion of the musical excerpt.

More than that, the particular example exposes the greatest rhythmic variety—perhaps even the most idiosyncratic rhythmic profile—among the five excerpts of Beethovian melodies that Toch chose. Most pertinently, this rhythmic profile emphasizes the two local “Höhepunkte”

(e-flat’ and a-flat’’ ) through their coincidence with the longest note values of the excerpt (quarter notes)—in addition, of course, to the metric placement of these tones. In this particular case, the peaks of the Tonhöhenlinie thus condense the expressive potential in both of the two parameters that Toch perceived crucial to melody: rhythm and pitch.

While not constitutive for the concept of the Tonhöhenlinie , Toch did regard rhythm as important, describing it poetically as melody’s “soul,” which “vivified” the otherwise

“inanimate” Tonhöhenlinie .85 Toch also argued that taken by itself, rhythm was more effectual than the Tonhöhenlinie for recognizing a known melody. While the rhythmic profile of

Beethoven’s melody depicted in Example 40 must have fulfilled this aspiration, Toch was surprisingly expedient in accurately reproducing the rhythm of Beethoven’s melody. Together with omitting any agogic marks originally included in Beethoven’s score (comprising two slurs and six staccato dots), Toch also left out the tie that prolongs the b-flat’ on beat one in the second full measure by a sixteenth note. While this omission might amount to a tampering with the

85 “Wenn der Rhythmus es beseelt. Die Tonhöhenlinie war ein wächsernes Bild, der Rhythmus hauchte ihm Leben ein. Der Rhythmus wurde ihm zur Seele.” Toch, Melodielehre , 8. 166 rhythmic identity of Beethoven’s theme, it can also be subsumed under Toch’s efforts in cleaning up the visual impact of the example, or under the convenience he sought for typesetting.

In order to achieve the clearest visual result, he also took further editorial licenses in the register in which he represented the music on the staff. Without accounting for his choice, Toch notated

Beethoven’s symphonic melody not in the lower octave in which it is first introduced by the first violins in mm. 16–20, but in the octave in which it is played in mm. 36–40 by the oboe. This choice meant that Toch could annotate the Tonhöhenlinie above the staff and relatively close to the note heads, and avoided a cluttered result in which the line might have graphically interfered with the stems and beams.

With the unique status that it assumes in Melodielehre , the melody from Beethoven’s

Third Symphony thus epitomized Toch’s compiled observations of good melodic composition.

Moreover, by implication, the honor was conferred on Beethoven himself, as the paragon from across the five centuries of music history that Toch’s treatise covers. Not coincidentally, this predilection conforms to Pfitzner’s ideology, which, as I discussed in Chapter II, exerted some influence on Toch’s thought. In Pfitzner’s writings, Beethoven personified the genius composer whose melodic inventions arose from subconscious intuition.

This twist accentuates the somewhat two-sided nature of Toch’s Tonhöhenlinie . Taken by itself, the line that Toch drew above Beethoven’s melody appears utterly unremarkable, and, in merely tracing the melodic outline, is also void of analytical impact per se. Yet, at the same time, it encapsulates a cornucopia of theoretical and aesthetic ideals, and captures a partisan outlook on music-historical evolution. This clash of attributes and desired functionalities that merge in

Toch’s Tonhöhenlinie , is representative of the aesthetic richness that the line assumed over centuries of serving as imagery for melody. The success of such mappings, however, was greatly

167 enhanced through the psychological paradigm of the early 1900s that I reconstructed as the premise for Toch’s theory. This context revealed that the line’s simplicity belies the complexity of the cognitive process required for translating aural and visual processes. This intricacy, in turn, opened up new potential for interpreting the aesthetic qualities of the line and of melody.

Indeed, only in the realization as a coherent and continuous line did the mapping of melody onto the metaphorical wave line unfold its full aesthetic potential. Toch’s seismographic analysis of the constitutive parameters in melodic composition demonstrates this affordance of the line, as does Kandinsky’s rendering of another Beethovian symphonic melody that I discuss in Chapters I and V. These graphical translations abstract an exterior shape of the melodies in question, and thereby re-center the attention onto a holistic perception of the music, away from the minute increments of tones and intervals from which it is composed. Yet, this chapter has shown that careful consideration of these internal structures reveals critical aspects of the theoretical conceptualization at play. After all, it is mostly through internal details that the two wave lines of Figures III.1 and III.2 eventually represent fundamentally divergent music- aesthetic conceptions: the one bound by harmonic logic and the higher principles of natural order and magic, the other a direct, and emotionally suggestive image of a specific melody’s unbound trajectory.

The very principle that united the two attendant theoretical frames—Kanne’s and Toch’s music theories—meanwhile, is representative of linear conceptions of melody more broadly. As I will attend to in more detail in the following chapter, Ernst Kurth—who has been closely tied to

Toch in the historical reception of their respective theories—also limited his linear-melodic concepts to primarily step-wise musical progressions. Incidentally, in this principal restriction,

168 the music theorists intuited additional cognitive principles that featured in the continued Gestalt- theoretical research of the 1920s.

169

IV. INTERWEAVING LINES IN ERNST KURTH ’S THEORY OF LINEAR COUNTERPOINT

“in die Kontrapunktik von der Linie als Einheit und Urgebilde aus einzudringen.” 1 “to penetrate counterpoint using the line as unit and primordial entity.”

Already in the title of Ernst Kurth’s treatise Grundlagen des linearen Kontrapunkts:

Einführung in Stil und Technik von Bach’s melodischer Polyphonie , first published in 1917, the line takes center stage. Its prominence was only enhanced when Kurth adopted the shorter version Grundlagen des linearen Kontrapunkts: Bachs melodische Polyphonie , starting with the treatise’s second edition in 1922. 2 That later, crisper title is also reflected in English-language

scholarship, which commonly renders it as Foundations of Linear Counterpoint: Bach’s Melodic

Polyphony .3 In this rhetorical construction, “linear” defines Kurth’s approach to counterpoint, and, based on the parallelism between “counterpoint” and “polyphony,” “linear” appears as analog to “melodic.” 4 Indeed, the treatise lays out a theory of the melodic line, as the guiding principle with which Kurth envisioned the examination of polyphonic music. He dedicated the first large section of Linear Counterpoint entirely to “foundations of melody,” before turning, in the later parts, to the actual agenda of advancing a theory of counterpoint, and specifically a

1 Ernst Kurth, Grundlagen des linearen Kontrapunkts: Einführung in Stil und Technik von Bach’s melodischer Polyphonie (Bern: Max Drechsel, 1917), ix. The emphasis is original. 2 Ernst Kurth, Grundlagen des linearen Kontrapunkts: Bachs melodische Polyphonie , 2nd rev. ed. (Berlin: Max Hesse, 1922). In the following, I quote from this edition, abbreviated as Linearer Kontrapunkt . For ease of reading, I refer to the English title as Linear Counterpoint in the text. 3 There is, as of yet, no comprehensive translation of Kurth’s writings, including Linear Counterpoint . Lee Allen Rothfarb, trans. and ed., Ernst Kurth: Selected Writings , (Cambridge, UK: Cambridge University Press, 1991) provides translations of selected passages across Kurth’s entire output. Where available, I refer to Rothfarb’s translation; all other translations are my own. 4 Kurth himself addressed how he perceived a distinction between the expressions “counterpoint” and “polyphony.” He specified that he understood “counterpoint” to carry more intrinsic “contrast to a harmonic structure,” while “polyphony” conditioned a “linearly designed structure” by (etymologically) designating a style that involved the confluence of multiple voices. See Rothfarb, Ernst Kurth: Selected Writings , 38, referring to Kurth, Linearer Kontrapunkt , 59. 170 study of the polyphonic music of Johann Sebastian Bach. Here, Kurth argued for conceiving counterpoint as the interweaving of multiple linearly oriented melodic strands—or, as he declared his ambitions in the opening pages of the treatise, “to penetrate counterpoint using the line as unit and primordial entity.” 5 As I discuss in more detail below, Kurth perceived this as an intervention against the prevailing theory of counterpoint at the time, which he considered too preoccupied with moment-to-moment harmonic analysis. Approaching music through a profoundly cognitive lens, Kurth argued that such an understanding failed to account for the horizontal coherence and unity of individual voices as they govern the listening experience.

Across the treatise, the centrality of the line for Kurth’s project could not be more apparent. Already an early reviewer of Linear Counterpoint discerned this and put it in a nutshell:

Wer Kurths Logik folgen will, muß von vornherein seinen Begriff der melodischen Linie übernehmen. Er gibt der ganzen Denk- und Darstellungsweise die Richtung. Für ihn ist die Melodie nicht eine Folge von Tönen, sondern ein Bewegungszustand, zu dem die Töne nur gleichsam als notwendige Begleiterscheinung hinzutreten. 6 Whoever wants to follow Kurth’s logic, has to adopt from the outset his concept of the melodic line. It determines all his thought and presentation. For him, melody is not a succession of tones, but a state of motion, to which the tones merely appear as a requisite concomitant effect.

As that review conveys, the line encapsulated Kurth’s ideas, which at once entailed a profusion of further metaphors, notably that of a “state of motion.”

Kurth’s idiosyncratic and suggestive vocabulary has in fact motivated most scholarly inquiry to date.7 Scholars such as Lee Rothfarb, Wolfgang Krebs, Helga de la Motte-Haber, and

5 “In die Kontrapunktik von der Linie als Einheit und Urgebilde aus einzudringen.” Kurth, Linearer Kontrapunkt , ix. The emphasis is original. 6 Anonymous review of Linear Counterpoint by Ernst Kurth (signed with “L.”) in Neue Zeitschrift für Musik 86, nos. 9–10 (March 1919): 60. 7 Patrick McCreless’s verdict about the “obstacle” that Kurth’s terminology poses for the appreciation of his ideas has become a commonplace, even as many scholars have worked on overcoming these linguistic 171

Youn Kim have traced some of the most prominent expressions from across Kurth’s writings—

such as “force,” “gravity,” “weight,” “mass,” “cohesion,” “energy,” “motion,” and

“becoming”—in scientific, philosophical, phenomenological and psychological discourses of his

day. 8 Their studies have situated Kurth’s work under the heading of an “energetic” school of

music theory in the early twentieth century, and illuminated many critical aspects of Kurth’s

thought. The line, however, has remained overlooked across these contributions. Rothfarb’s

comment that “the notions of melodic ‘line’ and ‘linear counterpoint’ lie at the heart of the

mystique of Grundlagen ,” goes into little detail, yet Rothfarb acknowledges its importance for

“those who decide to read it [and who ] will want to know what Kurth meant by those

expressions.” 9 Also the short explication that Rothfarb cites from Ian Bent does not do justice to

the complexity of the “line” in Kurth’s thought, nor does it clarify much of its theoretical

function:

Ian Bent has explained “linear” as deriving from three levels of the creative process: Will, which gives music its dynamic thrust (kinetic energy); the manifestation of Will in the creative psyche, which fashions a play of forces ( Kräftespiel ) from the primordial energy;

hurdles. He writes, “Kurth’s dependence upon an analytical terminology which is psychological and metaphorical in character, and which indeed constitutes a personal and almost mystical language unique to his theories, was an obstacle to the acceptance of those theories in his own day and remains so for us now.” Patrick McCreless, “Ernst Kurth and the Analysis of the Chromatic Music of the Late Nineteenth Century,” Music Theory Spectrum 5 (April 1983): 57. Daphne Tan has discussed how such skepticism towards Kurth’s terminology as expressed by McCreless and others has historical precedents in Heinrich Schenker’s criticism of Kurth’s work. Daphne Tan, “Beyond Energetics: Gestalt Psychology in Ernst Kurth’s ‘Musikpsychologie,’” Theoria 22 (2015): 100. 8 Wolfgang Krebs, Innere Dynamik und Energetik in Ernst Kurths Musiktheorie: Voraussetzungen, Grundzüge, analytische Perspektiven (Tutzing: H. Schneider, 1998), Helga de la Motte-Haber, “Kräfte im musikalischen Raum: musikalische Energetik und das Werk von Ernst Kurth,” in Musiktheorie , ed. Helga de la Motte-Haber and Oliver Schwab-Felisch, vol. 2 of Handbuch der systematischen Musikwissenschaft (Laaber: Laaber, 2005), 283–310, Lee Allen Rothfarb, Ernst Kurth as Theorist and Analyst (Philadelphia: University of Pennsylvania Press, 1988), and Youn Kim, “Theories of Musical Hearing, 1863-1931: Helmholtz, Stumpf, Riemann and Kurth in Historical Context” (Ph.D. dissertation, Columbia University, 2003). 9 Rothfarb, Ernst Kurth: Selected Writings , 24. 172

and the sonic realization of the play of forces in melody and, more complexly, in polyphony. 10

This chapter follows up on the obvious importance of the line for Kurth’s theory. It asks how Kurth conceived of the “primordial entity” that characterized his theoretical appraoch, how the line relates to the “state of motion” as invoked by the reviewer quoted above, and how it featured in his analyses. Tracing the line’s aesthetic connotations and functionality within the larger aims of Linear Counterpoint will not only show how it drew Kurth’s ideas together and marked his theoretical intervention, but moreover reveal yet unconsidered analytical consequences of his appraoch. Moreover, the line’s inherent interdisciplinarity will allow me to relate Kurth’s ideas to broader trends of his day.

Melody as Experienced Motion

From the outset, Kurth established the fundamentally psychological orientation of his explorations, writing in his introduction:

Hier wie dort sind es vornehmlich die psychologischen Voraussetzungen, nach welchen eine Vertiefung der Erscheinungen geboten war. 11 In either aspect, the investigation of these phenomena has to occur primarily through their psychological conditions.

Such a “psychological” lens on music had long determined Kurth’s music-theoretical agenda. As early as his first monograph, Die Voraussetzungen der theoretischen Harmonik und der tonalen

Darstellungssysteme from 1913, which grew out of his habilitation in Bern, Kurth indicated that future work in music theory had to pursue a more psychologically-oriented direction:

Wenn man besser noch von unbewussten als von unbekannten Wurzeln der Musiktheorie zu sprechen hat, so ist darauf hingewiesen, dass diese mehr noch als in akustischen in

10 Rothfarb, Ernst Kurth: Selected Writings , 24, referring to Ian Bent, Analysis (New York: Norton, 1987), 46. 11 Kurth, Linearer Kontrapunkt , x. 173

psychologischen Erscheinungen liegen, deren Erklärungsversuche überhaupt die Grundideen der theoretischen Systeme bilden, die Hypothesen bezüglich des Zusammenhanges der tonpsychologischen und der akustisch-physikalischen Tatsachen. 12 One should talk of the unconscious rather than the unknown roots of music theory, and I would point out that these roots lie in psychological phenomena more than in acoustical ones. Attempts at explaining these psychological phenomena form precisely the foundational ideas of theoretical systems, entailing hypotheses regarding the relation between tone-psychological and acoustic-physical circumstances. 13

This objective of examining music as a primarily psychological phenomenon remained at

the center of Kurth’s attention throughout his career, up to his final monograph

Musikpsychologie from 1931. 14 Also in Linear Counterpoint , Kurth explained that he targeted

the deep-seated unconscious roots of music theory, rather than contending himself with the

superficial appearance of music in the acoustic-physical realm.

Daher sind die akustisch-physikalischen Erscheinungen und die physiologischen Erscheinungen, die ihre Reizaufnahme vermitteln, nicht tiefster Uranfang musikalischen Geschehens und nicht in diesem Sinne als Grundlagen der Musik zu werten. 15 Thus the acoustic-physical phenomena and the physiological ones that transmit their stimuli are not the deepest primordial beginning [“Uranfang” ] of musical events and are in this vein not to be valued as music’s foundation.

Concomitantly, music theory had to dive deeper to locate the genuine foundation for its inquiries.

12 Ernst Kurth, Die Voraussetzungen der theoretischen Harmonik und der tonalen Darstellungssysteme (Bern: Drechsel 1913), 6. Both Luitgard Schader and Daphne Tan have interpreted Voraussetzungen as the foundation of Kurth’s later music-psychological work. Luitgard Schader, “Ernst Kurth und die Gestaltpsychologie oder Von der Prägung eines Aussenseiters in der deutschsprachigen Musikwissenschaft der 1920er Jahre,” in Musikwissenschaft - eine verspätete Disziplin? , ed. Anselm Gerhard (Stuttgart: J.B. Metzler, 2000), 175–96; Daphne Tan, “Ernst Kurth at the Boundary of Music Theory and Psychology” (Ph.D. dissertation, Eastman School of Music, University of Rochester, NY, 2013). For a broader context of psychologically oriented music theories, see for example Elizabeth West Marvin, “Tonpsychologie and Musikpsychologie: Historical Perspectives on the Study of Music Perception,” Theoria 2 (1987): 59–84. 13 Translation amended from Rothfarb, Ernst Kurth as Theorist and Analyst , 7. 14 Ernst Kurth, Musikpsychologie (Berlin: Hesse, 1931, reprint Bern: Krompholz, 1947). Tan, “Ernst Kurth at the Boundary of Music Theory and Psychology” provides a comprehensive study of this treatise. 15 Kurth, Linearer Kontrapunkt , 6. On the same page, Kurth also described these physical phenomena as the “surface” of musical form: “Die physikalischen Grundlagen der Musiktheorie, die Erscheinung von Tonschwingungen und Klängen bestimmen erst die Gesetze, welche diese ‘Oberfläche’ der musikalischen Erformung erfassen.” And later again, he equated the acoustic sensations with the “Oberschicht” of musical expression. Moreover, he emphasized, “ wie überhaupt bei psychologischen Vorgängen stets der bedeutungsvollere Teil im Unbewussten liegt.” Kurth, Linearer Kontrapunkt 3. 174

Die Wurzeln der Theorie tauchen ins Unterbewusste hinab. … Um die Musiktheorie zu begründen, gilt es nicht bloß zu „hören“ und immer wieder nach den Erscheinungen des Erklingenden zu fragen, sondern tiefer zu den Urvorgängen in uns selbst hinabzutauchen. 16 The roots of theory submerge into the unconscious. … In order to build music theory [on a solid foundation ], we have to not merely “hear” and repeateldy ask about the sounding phenomena, but rather to dive deeper to the originating processes within ourselves.

With this conceptual displacement between the superficial appearance of sounding music on the one hand and a profound, genuine truth located in the depth of the human unconscious on the other, Kurth propagated a long-standing lineage of how these metaphors had pervaded

German musical thought. As Holly Watkins has cogently elucidated, similar spatial attributions of unconscious processes and a “deeper” truth in music animated analyses and theories from

E.T.A. Hoffmann to Kurth’s contemporaries Heinrich Schenker and Arnold Schoenberg. 17

Notably, this meant that Kurth’s line was decisively not a surface phenomenon, but instead resided in the inner depths of the listener’s unconscious.

In that way, Kurth’s conception of the line deviated significantly from most other applications of the line in music, which adopted the line’s graphical essence as a surface appearance. Indeed, when understood as a graphical icon, the line not only appears on surfaces, but might even define them, as artists and media theorists have equally emphasized. 18 This observation pertains not only to the visual realm, but to musical textures as well. Schenker’s

16 Kurth, Linearer Kontrapunkt , 6–7. 17 Holly Watkins, Metaphors of Depth in German Musical Thought: From E T. A. Hoffmann to Arnold Schoenberg (Cambridge: Cambridge University Press, 2011). 18 Sybille Krämer has described the processes by which lines might not simply appear on surfaces, but rather create and define surfaces. See for instance Sybille Krämer, “Punkt, Strich, Fläche: Von der Schriftbildlichkeit zur Diagrammatik,” in Schriftbildlichkeit: Wahrnehmbarkeit, Materialität und Operativität von Notationen , ed. Sybille Krämer, Eva Cancik-Kirschbaum, and Rainer Totzke (Berlin: Akademie Verlag, 2012), 79, and Sybille Krämer, “Flattening as Cultural Technique: Epistemic and Aesthetic Functions of Inscribed Surfaces,” as part of the Colloquy “Discrete/Continuous: Music and Media Theory after Kittler,” ed. Alexander Rehding, Journal of the American Musicological Society 70, no. 1 (2017): 240. 175 theory of layers (“Schichten”) most prominently and comprehensively demonstrated how the excavation of a linear structure in music—an Urlinie -formation—necessarily identified an attendant layer of the musical texture. As is well known, Schenker’s gradual reduction of these layers targeted the “deepest” background of a composition.

In comparison, Kurth was less concerned with demonstrating the line as a material manifestation in music. While he observed linear progressions on rather superficial layers of the pieces that he analyzed, he did not postulate them as the ultimate constructive principle in music.

Rather, Kurth construed the “primordial entity” of his theory as an essentially experiential phenomenon. I address Kurth’s analyses in a later part of this chapter, where I will also expand on the comparison with Schenker’s theory.

In music-aesthetic terms, Wolfgang Krebs has likened Kurth’s position, which located the essence of music outside its physical and physiological constituency and instead in the listener’s experience, to Eduard Hanslick’s famous distinction between music as “tonally moving forms” on the one hand, and the listener’s emotional interpretation of it on the other. 19 His reading is based on such assertions in Kurth’s writing as, “Das musikalische Geschehen äussert [sic ] sich nur in Tönen, aber es beruht nicht in ihnen” (“The musical essence [lit. events] is merely expressed through the tones, but it does not reside in them”).20 However, in opposition to

Hanslick’s notion of “tonally moving forms,” Kurth understood motion to occur precisely not in the external, physical appearance of music as sounding tones, but rather in the listener’s experience of them. He contended:

19 Eduard Hanslick, Vom Musikalisch-Schönen: Ein Beitrag zur Revision der Aesthetik der Tonkunst (Leipzig: R. Weigel, 1854); Krebs, Innere Dynamik und Energetik in Ernst Kurths Musiktheorie , esp. 13– 14. Also Rothfarb has portrayed the experiential quality of Kurth’s approach, differentiating it primarily from theories concerned with a “material” outlook on music. See Rothfarb, Ernst Kurth as Theorist and Analyst , esp. 218 and 223. 20 Kurth, Linearer Kontrapunkt , 7. 176

Wir “hören” nicht bloss eine melodische Linie, sondern wir erleben auch als den eigentlichsten und tiefsten melodischen Impuls den Zug bewegender Kraft in ihr. 21 We do not merely “hear” a melodic line, but we experience through it the propulsion [”Zug” ] of moving force as the most essential and deepest melodic impulse.

This sensation of motion took absolute primacy in Kurth’s approach. The proper first chapter of Linear Counterpoint opens with the declaration: “Melody is motion” (“Melodie ist

Bewegung”). 22 The anonymous reviewer quoted earlier already rephrased this to explain,

“melody is a state of motion.” In the context of the framework discussed above, Kurth understood motion as an experiential quality, to be sensed as “the propulsion of a moving force.”

This sensation is induced by melody. And, as we shall see, the line captured this dynamic essence of melody.

Building on a close reading of Kurth’s Musikpsychologie (1931) and the psychological sources referenced in that later treatise, Daphne Tan has advanced this interpretation further. She argues that for Kurth, the sense of motion that he inscribed in melody in his well-known opening statement stemmed from an embodied understanding that invoked the experience of locomotion in the listener. As Tan puts it, “the experience of listening to a melody is like the experience of being in motion.” 23

Reflecting in particular on Kurth’s conception of “phases of motion”

(“Bewegungsphasen”), Tan construes such “uniform spans of [experienced ] motion” as a reflection of Kurth’s Gestalt-theoretical inclinations. This analysis expands on Luitgard

Schader’s research, which has similarly highlighted affinities with Gestalt psychology in Kurth’s

21 Kurth, Linearer Kontrapunkt , 3. 22 Kurth, Linearer Kontrapunkt , 1. 23 Tan, “Beyond Energetics,” 121. 177 thought (and in particular in Linear Counterpoint ). 24 Neither of these readings, however, accounts for how precisely the line fits into this network of ideas, how Kurth justified its primacy, and what further connotations it introduced. Tan adopts Kurth’s mapping of the experienced motion onto the line by stating: “The melodic line (as linear succession) is the quintessential expression of the energy of motion.”25 Continuing from the above observation that

Kurth theorized melody and the melodic line as the unconscious foundation to music—and, concomitantly, music theory—in the following, I first review further Tan’s and Schader’s research on the Gestalt-theoretical resonances in Kurth’s understanding of melody, and then investigate how these accounts might map onto the line as Kurth’s favored imagery.

Gestalt-Theoretical Aspects in Kurth’s Understanding of Melodic Motion

Both Tan and Schader position their portrayal of Kurth as a “Gestaltist,” or even a

“Gestalt psychologist,” as a complementary view to the prevalent classification of Kurth as an

“energeticist.” 26 Their research significantly refines what has surfaced as a commonplace in

Kurth scholarship, but more often than not, in the form of assertions that lacked documentary evidence and precision in argument. “Kurth’s ideas of psycho-auditive perception of curvilinear developments are clearly related to Gestalt-psychological notions of perception,” Lee Rothfarb, for example, maintained without further commentary in Ernst Kurth as Theorist and Analyst , the

24 Schader, “Ernst Kurth und die Gestaltpsychologie,” and Schader, Ernst Kurths “Grundlagen des linearen Kontrapunkts”: Ursprung und Wirkung eines musikpsychologischen Standardwerkes (Stuttgart: J.B. Metzler, 2001). 25 Tan, “Beyond Energetics,” 121. 26 Tan, “Beyond Energetics,” esp. 124. Earlier investigations into the psychological impetus of Kurth’s theory are presented in Hans-Peter Rösler, Die Musiktheorie von Ernst Kurth und ihr psychologischer Hintergrund (Hamburg: Verlag an d. Lottbek, 1998), and Helga de la Motte-Haber, “Die Musikpsychologie von Ernst Kurth,” Schweizer Jahrbuch für Musikwissenschaft 6-7 (1986–87), 95–108. 178 first comprehensive English-language study on Kurth’s work and still an authoritative source of reference. 27

While Tan focuses most extensively on Kurth’s Musikpsychologie , Schader explores the

Gestalt-theoretical resonances in Foundations of Linear Counterpoint . As I mentioned in

Chapters II and III, Schader has in particular undertaken historical-biographical research into possible personal connections between music theorists like Kurth and Ernst Toch on the one hand, and members of the Viennese and Berlin schools of Gestalt theory on the other. As with

Toch, Schader suggests that Kurth learned about Gestalt-psychological principles through the philosophical seminars that he attended at the University of Vienna, especially with the professors Wilhelm Jerusalem and Friedrich Jodl. Both of these philosophers pursued interests in cognitive research and built on the work of their Viennese colleague Christian von Ehrenfels, as well as his teacher Ernst Mach. Most likely, they also disseminated these discourses in their seminars at the University. 28

Schader documents a possible exchange of ideas between Kurth and Gestalt theorist Max

Wertheimer, one of the founders of the Frankfurt, and later the Berlin, schools of Gestalt psychology.29 Together with Wolfgang Köhler and Kurt Koffka, Wertheimer adjusted

Ehrenfels’s principle of “supra-summativity” to declare that the whole was not more but other

27 Rothfarb, Ernst Kurth as Theorist and Analyst , 100. Rather than expand on this insight, Rothfarb proceeded to draw parallels with much later psychological investigations into Gestalt-based perception in music, such as by Diana Deutsch, Leonard Meyer, and Fred Lerdahl and Ray Jackendoff—comments that illuminate little about Kurth’s understanding of Gestalt psychology, or even what this might have meant at his time. Only in his later edition of Kurth’s Selected Writings , did Rothfarb provide a more historically situated account on correspondences with Gestalt-theoretical research occurring in Kurth’s time. Rothfarb, Ernst Kurth: Selected Writings , esp. 21 and 43. 28 Schader furthermore contends that Kurth’s endeavors in reform-pedagogy (such as his work at the Freie Schulgemeinde Wickersdorf where he taught in 1911–12), were inspired by the ideology of these two professors. Schader, “Ernst Kurth und die Gestaltpsychologie,” 182–84. 29 See Schader, Ernst Kurths “Grundlagen des linearen Kontrapunkts ,” 59–75 179 than the sum of its parts. 30 As we saw in Chapter I, Ehrenfels had focused on explaining the various ways in which a sequence of perceptions could be grasped as a larger whole. The later theorists, by comparison, based their investigations on holistic perceptions as a priori manifestations, from which they derived details about the constituent parts. Schader observes that in Wertheimer’s view, the essence of the parts consequentially depended on their role within the whole. 31 This premise, in turn, allowed him to investigate in more detail the internal coherence of larger units of perception. Wertheimer’s Untersuchungen zur Lehre von der

Gestalt , published in 1922–23, accumulated insights from his concomitant studies, many of which were conducted as early as 1910–14. 32 While she summarizes the principles presented in that publication, Schader’s explanations about how she perceives a resonance with Kurth’s thought remain cursory. I will return to this source and its correlation with ideas in Linear

Counterpoint , and with other linear conceptions of melody, later in this chapter.

Schader also suggests that Kurth must have been familiar with Wertheimer’s studies on the perception of motion, as presented in his Experimentelle Studien über das Sehen von

Bewegung (1912). 33 This insight follows from an observation made by Helga de la Motte-Haber, who noted a “curious” similarity between Wertheimer’s theory and Kurth’s understanding of melody as the sensation of motion. 34 As Schader argues, La Motte-Haber excluded the

30 For a comprehensive study on the history of Gestalt theory in German academia, see Mitchell G. Ash, Gestalt Psychology in German Culture, 1890-1967: Holism and the Quest for Objectivity (Cambridge, UK: Cambridge University Press, 1995), on Wertheimer see esp. 122–34. 31 Schader, Ernst Kurths “Grundlagen des linearen Kontrapunkts ,” 64. 32 Wertheimer’s “Untersuchungen” were published in two parts: Max Wertheimer, “Untersuchungen zur Lehre von der Gestalt,” Psychologische Forschung: Zeitschrift für Psychologie und ihre Grenzwissenschaften 1 (1922): 47–58, and Wertheimer, “Untersuchungen zur Lehre von der Gestalt, II,” Psychologische Forschung: Zeitschrift für Psychologie und ihre Grenzwissenschaften 4 (1923): 301–50. The latter will be particularly relevant to my discussion. 33 Max Wertheimer, “Experimentelle Studien über das Sehen von Bewegung,” ed. F. Schumann, Zeitschrift für Psychologie 61, no. 1 (1912): 161–265. 34 Helga de la Motte-Haber, Psychologie und Musiktheorie (Frankfurt am Main; Berlin; Munich: M. Diesterweg, 1976), 35–40, esp. 40: “eine sehr merkwürdige Parallele,” quoted from Schader, Ernst 180

possibility of an actual interaction or exchange of ideas between Wertheimer and Kurth. Schader,

by contrast, traces various connections through which Wertheimer and Kurth could have known

of each other’s work, such as their similar educational backgrounds and their shared

acquaintance with Carl Stumpf and Erich Moritz von Hornbostel in Berlin. She concludes that it

can be considered “very likely” that Kurth was aware of Wertheimer’s research already in the

late 1900s or 1910s. 35 After all, she recounts that already in earlier texts, Wertheimer intimated notions of melody as a Gestalt-like entity, in publications that should have been easily accessible to Kurth and attracted his attention. 36

In the face of this rich historical research into a variety of pertinent sources that document their shared interests, Schader again does not explore in more detail the extent to which Kurth’s ideas actually mapped onto Wertheimer’s. Apart from lacking absolute certainty about her

Kurths “Grundlagen des linearen Kontrapunkts ,” 67. Also in her later article, La Motte-Haber argued that Kurth must have developed his Gestalt-theoretical ideas independently from the contemporary emergence of psychological research. Like Rothfarb, she surmises that Kurth only learned of Ehrenfels’s and Wertheimer’s studies in the 1920s, when they gained a broader readership in general, and when Kurth started to make reference to them in his bibliographies. La Motte-Haber, “Kräfte im musikalischen Raum,” 296, esp. n54. Compare, for instance, Rothfarb, Ernst Kurth: Selected Writings , 20–21. At the same time, however, Tan cautions us in her studies on Musikpsychologie that Kurth’s writing does not reveal in-depth engagement with most of the sources that he cited, which rather exposes a cherry-picking of quotes suited to his own agenda. Even a contemporary of Kurth’s, Albert Wellek, expressed reservations about Kurth’s contribution to psychological research, commenting, in a generally favorable review, “on the foundation of psychology [Kurth ] is an outsider.” Quoted in Tan, “Beyond Energetics,” 124. Notably, Wellek was himself researching in the realm of Gestalt psychology (as part of the “Leipzig school”) following in lineage from his teacher Felix Krueger, who, in turn, was a vital source of reference to Kurth in Musikpsychologie . See Tan, “Beyond Energetics,” 109n32. Incidentally, Wellek was also the advisor of La Motte-Haber. 35 Schader, Ernst Kurths “Grundlagen des linearen Kontrapunkts ,” 60 and 66–75. For instance, Schader surmises, “ dass mit einiger Sicherheit angenommen werden kann, das Ernst Kurth Wertheimers Namen und dessen Forschungsrichtung bereits kannte, noch ehe im Jahre 1912 der Artikel zum Phi-Phänomen erschien.” Schader, Ernst Kurths “Grundlagen des linearen Kontrapunkts ,” 71. 36 Schader refers to Max Wertheimer, “Musik der Wedda,” Sammelbände der Internationalen Musikgesellschaft 11, no. 2 (January–March 1910): 300–9. Based on phonograph recordings collected in the Berlin archive, the article presents Wertheimer’s transcription and analysis of a song performed by members of this Sri Lankan indigenous community. Wertheimer characterized his perception, “eine Melodie ist nicht durch individuell bestimmte Intervalle und Rhythmen gegeben, sondern ist eine Gestalt, deren Einzelteile eine in charakteristischen Grenzen freie Variabilität besitzen . Die Melodiegestalt wird dabei exakt durch die negativen Bestimmungen (hier z.B. ‘kein Aufwärts’) charakterisiert.” Wertheimer, “Musik der Wedda,” 305. The emphasis is original. 181 biographical-historical findings, she expresses hesitations about the necessary translation that

Kurth would have had to perform from a theory dedicated primarily to visual cognition to the realm of music and auditory perception. 37 As I portrayed in Chapter I, however, such transferences and comparisons, particularly between the visual and aural senses, were quite common in psychological and humanistic research around the turn of the century, and even served as the foundation for the study of these two ways of sensory perception.

The conceptual similarities between Wertheimer’s theory of the perception of motion and

Kurth’s notion of melody are indeed striking. In his experiments, conducted between 1910–12,

Wertheimer projected with a tachistoscope two static images in quick succession. Among the three possible kinds of perception that they induced—simultaneity, movement, or succession— depending on the speed of projection, Wertheimer inquired in particular the creation of apparent motion. 38 Importantly, in this perceived movement, which Wertheimer termed a “phi- phenomenon,” he theorized the illusion of a continuous transition between two stimuli, each a physically static image. 39 In other words, the perception of motion in Wertheimer’s study of visual cognition did not derive from an actual physical event or physiological stimulus.

Precisely such an illusory transition between static events (the individual tones) was central also to Kurth’s conception of melody and his invocation of the motive experience that melody elicited. From the outset, Kurth drew attention to the moments of transition between the tones, in assertions such as, “Das Wesentliche ist die Empfindung der Verbindung der Töne” (“The

37 Schader, Ernst Kurths “Grundlagen des linearen Kontrapunkts ,” 70. 38 For a discussion of Wertheimer’s theory, see also Romana Karla Schuler, Seeing Motion: A History of Visual Perception in Art and Science (Berlin; Boston: De Gruyter, 2016), 132–39, and Ash, Gestalt Psychology in German Culture , 122–34. 39 Herbert Fitzek and Wilhelm Salber summarize Wertheimer’s insights: “Wertheimer erkannte, dass im Nacheinander der Bilder … auch da Übergänge gesehen [werden ], wo eine entsprechende Reizgrundlage fehlt.” Herbert Fitzek and Wilhelm Salber, Gestaltpsychologie: Geschichte und Praxis (Darmstadt: Wissenschaftliche Buchgesellschaft, 1996), 28, quoted in Schader, Ernst Kurths “Grundlagen des linearen Kontrapunkts ,” 63. 182 essential quality is the perception of the connection between the tones”). 40 He located the origin of the perceived motion in these transitions:

Der Grundgehalt des Melodischen ist im psychologischen Sinne nicht eine Folge von Tönen, … sondern das Moment des Übergangs zwischen den Tönen und über die Töne hinweg; Übergang ist Bewegung. 41 The essence of melody is, in a psychological sense, not the succession of tones, … but the moment of transition between the tones and across them. Transition is movement.

Kurth was also quick to clarify that these perceived transitions were a purely psychological phenomenon, and neither physically nor physiologically conditioned. On that question, he paused to correct previous music-theoretical accounts, notably Hugo Riemann’s, who had sought to explicate these phenomena on a physical-acoustic level. 42 Cautious throughout his treatise about contradicting the popularity of Riemann’s thought, Kurth cited a longer passage from

Riemann’s Die Elemente der musikalischen Ästhetik (1900), so that the readers could judge

Riemann’s argument for themselves. 43 In that section of his collection of essays, Riemann attempted to account for a perceived “continuous change in pitch” (“kontinuierliche

Veränderung der Tonhöhe”) in melody across different kinds of musical articulation (legato and staccato). Arguing that in either form of articulation this sliding simply happened too quickly to be consciously perceived, Riemann also suggested that on instruments with fixed pitch increments, such as the piano, the ear inferred such a continuous change in pitch. The vocal portamento, in contrast, performed this continuous shift audibly and thus to a hyperbolic effect.

40 Kurth, Linearer Kontrapunkt , 2. 41 Kurth, Linearer Kontrapunkt , 2. Based on Kurth’s focus on these moments of transition, Wolfgang Krebs has captured Kurth’s theory under the maxim of “Kunst des Übergangs” (“art of transition”) as Richard Wagner had coined it. Krebs summarizes Kurth’s ideology as “Music does not consist of transitions, but music is permanent transition.” Krebs, Innere Dynamik und Energetik in Ernst Kurths Musiktheorie , 28. The emphasis is original: “Musik ‘besteht’ nicht aus Übergängen, sondern Musik ist Übergang in Permanenz.” 42 Kurth, Linearer Kontrapunkt , 9–10. 43 Hugo Riemann, Die Elemente der musikalischen Aesthetik (Berlin: W. Spemann, 1900), 40, quoted in Kurth, Linearer Kontrapunkt , 10–11. 183

Kurth rejected these insinuations of a pitch glissando occurring in the listener’s unconscious. 44

Following from my discussion in Chapter III, this stance dissociated Kurth not only from

Riemann’s ideas, but also from tentative appraisals of other linear-melodic conceptions, such as

David Trippett’s comments on Friedrich August Kanne’s wave line from his “Magic of Music”

(1821). 45 In distinction from construing the perception of continuous motion in music as pitch glissandi, Kurth countered that the explanation for such a perceived continuity in melody had to be sought out not in acoustic phenomena, but in the energetic nature of music: “Dieser Übergang ist jedoch nicht akustischer, sondern energetischer Natur” (“This transition is, however, not acoustic, but energetic in nature”). 46 It is not the tones themselves that move, Kurth elaborated; rather, the listener projects into them the propagation of a dynamic energy:

Was die Kluft zwischen den einzelnen sinnlich-gehörsmässigen Eindrücken der Melodie, den einzelnen Tönen, überbrückt, sodass sich eine melodische Linie nicht als Folge abgerissener Gehörseindrücke, sondern als ein geschlossener Zug darstellt, ist die Energie des tief unter der aufscheinenden Tonreihe erspannten Bewegungsvorgangs.47 What bridges across the gap between the individual auditory sensations of melody, the individual tones, so that a melodic line emerges not as the succesion of disrupted auditory impressions, but instead as a unified projection, is the energy of a motion process that extends deep beneath the appearing row of tones.

Rather than being moments of stasis or interruption (“Stillstand, Unterbrechung”), the transitions between the tones were infused with an energetic drive. 48 These energetically charged transitions

44 Kurth, Linearer Kontrapunkt , 10: “demnach müsste geradezu ein im Unbewussten vorgehendes, allmähliches Hinüberschleifen nach Art des ‘Glissando’ zwischen zwei aufeinanderfolgenden Melodietönen angenommen werden.” 45 See Chapter III. David Trippett, Wagner’s Melodies: Aesthetics and Materialism in German Musical Identity (Cambridge, UK; New York: Cambridge University Press, 2013), 107, referring to Friedrich August Kanne, “Der Zauber der Tonkunst,” Wiener Allgemeine Musikalische Zeitung 5 (1821): 537. 46 Kurth, Linearer Kontrapunkt , 10. 47 Kurth, Linearer Kontrapunkt , 9. 48 “Was zwischen den einzelnen aufeinanderfolgenden Tönen vorliegt, ist nicht Stillstand, Unterbrechung des melodischen Empfindens überhaupt.” Kurth, Linearer Kontrapunkt , 9. 184 guaranteed the perception of a coherent motive process in melody. Moreover, they tied these processes together into a unified dynamic development.

With these propositions about the illusion of motion as a phenomenon rooted in the transitional moments between two sensory stimuli, Kurth’s theory resonated strongly with

Wertheimer’s research on the perception of motion, as reviewed above. In two brief instances,

Wertheimer also hinted at the possible transference of his insights to other realms of sensory perception, such as to the acoustic one, where he perceived the “movement of tones”

(“Tonbewegung”) as a possible analogous phenomenon to the optical “phi-phenomena.”49 But he was also quick to point out that the perception of auditory phenomena, such as the progression of melodic intervals, exceeded his investigations and would merit a separate study in its own right. 50 While Kurth might have opposed Wertheimer’s term of a “movement of tones,” his study of melody in Linear Counterpoint , in many respects, accomplished precisely the desideratum that Wertheimer had exposed. Ehrenfels had also addressed the issue, but left his conclusions vague, arguing simply that “by movement of sound [‘Tonbewegung’] we understand not a spatial dislocation, but a change in sound quality.”51

49 “Zeigten sich so spezifische optische ϕ-Phänomene, so sei erwähnt, daß es in manchem Bezuge analoge Problemgebiete auch auf anderen Sinnesgebieten gibt. So zeigt—z.B.—bei prinzipieller Verschiedenheit im akustischen Bereiche die schon einmal erwähnte Erscheinung des ‚lebenden Intervallschritts,’ die ‚Tonbewegung’ als charakteristisches, gerichtetes Erlebnis, nicht statischer Art, einiges Verwandte.” Wertheimer, “Experimentelle Studien über das Sehen von Bewegung,” 253. Wertheimer is referring to an earlier passage in his text, in which he differentiated between “lively” and “dead” intervals in music (“lebende und tote Intervalle,” 202–3). 50 “Die Erforschung des psychologischen Wesens von Intervall schritten , des lebenden Intervallvorgangs, seiner Entstehung und seiner Gesetzmäßigkeiten ist eine Aufgabe für sich.” Wertheimer, “Experimentelle Studien über das Sehen von Bewegung,” 203. 51 Christian von Ehrenfels, “On ‘Gestalt Qualities,’” in Foundations of Gestalt Theory , trans. and ed. Barry Smith (Munich: Philosophia Verlag, 1988), 100. [Christian von Ehrenfels, “Über ‘Gestaltqualitäten,’” in Das Primzahlengesetz, entwickelt und dargestellt auf Grund der Gestalttheorie (Leipzig: O.R. Reisland, 1922), 28: “Unter Tonbewegung versteht man keine Dislokation, sondern eine Veränderung der Tonqualität.” ] 185

Kurth substantiated the Gestalt-theoretical interpretation of his propositions in his concluding remark on the discussion of Riemann’s theory. After all, he argued, music-theoretical inquiries should not merely target the essence of the transition between melodic tones, but rather attend to melody as a holistic phenomenon. The sensation of larger spans of motion not only carried across the increments of tones and the transitions between them, but should in fact be considered primary phenomena (“Primärerscheinung”) 52 :

Das Primäre ist der Zusammenhang des Melodischen, erst das Sekundäre ist die Herauslösung der Einzeltöne, über welche der Bewegungszug hinüberträgt, der zur geschlossenen Empfindung eines Kontinuums, der “Linie” führt. 53 Of primary importance is the coherence of melody. The isolation of individual tones is only secondary. The propulsion of motion [“Bewegungszug” ] carries across them and leads to the unified perception of a continuum, the “line.”

—and, similarly,

Das Primäre [ist ] auf eine gewisse Ausdehnung immer das Ganze, das Geschlossene eines melodischen Zuges, die “Linie;” die Einheit einer ganzen Bewegungsphase ist auch das Primäre an der auftauchenden melodischen Vorstellung. 54 The whole, the coherence of a melodic progression, the “line,” is, within a certain extension, always primary. The unity of a whole phase of motion is also primary in the emerging melodic imagination.

The perception of the whole thus took precedence in Kurth’s approach, rather than a focus on its constituent elements. On multiple occasions throughout the treatise, Kurth argued for the primacy of holistic perceptions, for the “unity of the linear motion as a primary phenomenon in

52 “Auf einen weiteren, wesentlicheren Gegensatz zu dieser Darstellung, der in der Auffassung eines gesamten, größeren melodischen Bewegungszuges als Primär erscheinung, nicht aber der von Ton zu Ton fortschreitenden Verbindung besteht, wird noch hinzuweisen sein.” Kurth, Linearer Kontrapunkt , 10. 53 Kurth, Linearer Kontrapunkt , 15. 54 Kurth, Linearer Kontrapunkt , 14. 186 contrast to the individual tones,” and for the “unity of the melodic process” (“Geschlossenheit eines melodischen Zuges”), as quoted earlier. 55

In positing such holistic perceptions as his premise, Kurth’s ideas aligned more closely with the Gestalt-theoretical conceptions of the Berlin school around Wertheimer than with

Ehrenfels’s earlier definitions, which took constituent perceptions as their starting point, as I explained above. This interpretation is consistent with Tan’s analysis of how Kurth theorized the unity of a “phase of motion” (“Bewegungsphase”) in his later Musikpsychologie. There, as well,

Kurth emphasized the primacy of a holistic perception, which would encompass the “retention of a ‘simultaneous’ image of motion,” or, in other words, a holistic image of melody as a “dynamic experience.” 56

In the two quotes above, the line entered as the quintessential image to capture the unifying processes that Kurth argued for. The line, Kurth contended, perfectly expressed the continuity and coherence that he considered central to the experience of melody, and to the state of motion that it evoked.

Andererseits kennzeichnet aber aus diesem Grunde gerade der Ausdruck “ Linie ,” wenn er auch aus der Uebertragung auf räumliche Anschauung hervorging, besonders treffend das Wesen der melodischen Bewegung, weil er das Moment des Geschlossenen, des Kontinuums , heraushebt und plastisch vor Augen führt. Und auf der Kraft, welche den Zusammenhang zwischen den einzelnen Tönen herstellt, sie zu Komplexen zusammenrafft, zum Gesamtbild einer Reihe schliesst, beruht die Melodik. 57 Still, the expression “ line ”—even if it originates in the translation from spatial perception—captures precisely and particularly well the essence of melodic movement, because it brings out the moment of cohesion, the continuum , and visualizes it graphically. Melody relies on the force that forges a coherence across the individual

55 “Die Einheit des Linienzuges als Primärerscheinung gegenüber den Einzeltönen.” Kurth, Linearer Kontrapunkt , 14. 56 See Tan, “Beyond Energetics,” 121–23. 57 Kurth, Linearer Kontrapunkt , 3. The context to Kurth’s affirming use of “still,” “even if,” and “precisely” is a previous comment about the appearance of music in conventional notation, which disrupts the linear quality of melody into disjointed note heads. I discuss these allusions to the visual aspect of Kurth’s theory later in this chapter. 187

tones, that ties them together to complexes, consolidates them in a unitary image of a row.

The line thus encapsulated the Gestalt-theoretical unity that Kurth ascribed to the perception of melody, as he already indicated in his opening declaration of the “line as unit and primordial entity.” The line at once depicted all the qualties that characterized Kurth’s conception of melody: continuity, cohesion, coherence, and unity (“Kontinuum,”

“Geschlossenheit,” “Zusammenhang,” “Gesamtbild”). 58 Much like Tan’s suggestion of melody

(in all linguistic variants, as “die Melodie,” “das Melodische,” or “die Melodik”) standing as “a proxy for Bewegungsenergie ,” I advance the line in Kurth’s theory as a proxy for the holistic impression that the flow of energy in melody conveys to the listener. 59 Indeed, the “retention of a

‘simultaneous’ image of motion,” as Tan has described Kurth’s unified conception of the “phase of motion,” would most certainly assume the shape of a line if imagined visually.

In Kurth’s theory, then, the line really constituted a “unit and primordial entity” to the extent that it symbolized the wealth of aesthetic qualities that he inscribed in melody.

Conversely, Kurth capitalized on the line’s properties to encapsulate these connotations. In particular, Kurth employed the line’s continuity as an essential asset—unlike Kanne and Toch, as

I discussed in the previous chapter. These two theorists left the aesthetic interpretation of this visual property, in large part, up to the reader, and prompted reviewers to inquire as to the possibility of inferring in their lines pitch-continuous glissandi. Kurth, by contrast, was quite explicit about how the line, in all its capacities, fit into the larger framework of his ideas. As stated above, he also vehemently objected to the idea of construing the perceived continuity in

58 It is worth noting that “cohesion” (“Kohäsion”) also had a more specific connotation in Kurth’s vocabulary, namely the harmonic, and thus vertically oriented forces that bind sonorities together, as I discuss more extensively below. 59 Tan, “Beyond Energetics,” 121. 188 melody as a manifestation of glissandi. Like the two other theorists, however, he still prioritized step-wise melodic progressions, as I will discuss later in this chapter.

In addition to the connotations mentioned above—continuity, cohesion, coherence, and unity—across the various quotations, Kurth also projected onto the line the depiction of movement and the propagation of dynamic energy. As we have seen, Wertheimer’s studies on the perception of motion provided a psychological and Gestalt-theoretical backdrop to the evocation of motion in melody. But in order to illuminate how the connotation of motion, alongside that of motive energy, mapped onto the line, we have to turn to yet another framing discourse.

Models for Kurth’s Melodic Line in the Visual Arts and Other Domains

Other aspects of Kurth’s terminology become apparent when following up on his comments about the origins of the line. In addition to the instance quoted earlier, Kurth hinted at the visual essence of the line in the following passage:

Wollte man daher den im Sprachgebrauch schon einer geometrischen Anschauung entnommenen Ausdruck “melodische Linie” in die wirklich vorliegenden Verhältnisse zurück übertragen, so hätte man nicht in Anwendung rein zeitlicher Begriffe von einer “Tonfolge” zu sprechen, sondern besser von dem “Treiben” oder dem “Zug,” um die immanente Bewegungs-empfindung, den lebendigen Willen im Melodischen, herauszufassen. 60 When transferring back the expression “melodic line,” which is adopted from a geometrical viewpoint, onto the actual circumstances, one would have to resist talking of a “succession of tones” in applying a purely temporal lens, but rather talk of the “drive” or the “propulsion,” in order to accentuate the immanent sensation of motion, the lively will in melody.

60 Kurth, Linearer Kontrapunkt , 2. 189

Kurth acknowledged not only the visual, geometrical connotations of the line, but also its potential to encapsulate more abstract qualites. As established above, he was particularly interested in the line’s capacity to denote liveliness and the “immanent sensation of motion.”

In Chapter I, I chronicled that precisely such attributes were attached to the line in the visual arts around the turn of the twentieth century. Particularly in Paul Klee’s conception of the

“active line” (reproduced as Figure I.1), motion assumed a constitutive artistic-aesthetic function.

As Klee explained, the “active line” generated itself through a point set in motion. As we have seen, this generative process could be projected onto the creative act of the draughtsman, in that drawing a line “starts with the point that sets itself into motion.” 61 In this conception of the line, which Régine Bonnefoit has described as “genetic” (“genetisch”), the two constitutive elements are a single point, as it manifests itself in the initial moment, and an energetic impetus, which instigates forward motion. 62

This visual-artistic theory corresponds fully to Kurth’s conception of the energetic forces at play in the propagation of melody. Borrowing more metaphors from physical parlance, Kurth inscribed kinetic energy in the melodic tones, a state of tension that propels forward to continue the melodic motion:

Es liegt ein Weiterwirken des melodischen Impulses [im Einzelton ] latent, ein Spannungszustand, der sich in Fortbewegung, d.h. in weiterem melodischen Übergehen auszulösen strebt. Diesen ... mithin auch den Einzeltönen innewohnenden Spannungszustand bezeichne ich in Anlehnung an die Ausdrucksweise der Physik als „kinetische (=Bewegungs–) Energie .“ 63 The continued effect of a melodic impulse lies latent in the individual tone; a state of tension that strives to dissolve in forward motion, that is in the continued melodic

61 “[mit dem ] Punkt, der sich in Bewegung setzt.” This observation is cited from Klee’s first lecture at the Bauhaus in November 1921, in Régine Bonnefoit, Die Linientheorien von Paul Klee (Petersberg: Michael Imhof, 2009), 23. 62 See Chapter I. The term “genetic geometry” is introduced in Bonnefoit, Die Linientheorien von Paul Klee , 23. 63 Kurth, Linearer Kontrapunkt , 11. 190

transition. I call this state of motion that is inherent in the tones “ kinetic energy ,” following the parlance of physics.

Kurth moreover explicated that these processes were instigated by an “initial melodic impulse,”

(“melodische Anfangsenergie, oder Anfangsimpuls”) that inhibited the first tone. 64 Much like the line in Klee’s theory, then, Kurth’s melody grew out of an initial single tone, through the propagation of kinetic energy. Kurth even coined this conception the “genetic process in melody” (“Der genetische Vorgang im Melodischen”). 65 In Chapter V, I will address the ways in which Klee, conversely, modelled artistic conceptions of the line after Kurth’s theory of Linear

Counterpoint .

As I also explored in Chapter I, the genetic line in artistic discourse also became a metaphor for describing two kinds of embodied processes: the act of its creation through the draughtsman’s hand, and its reception through the tracing eye (“tastendes Auge”) of the spectator. Both of these layers of interpretation emerged from the cross-fertilization with psychological research, and both map onto Kurth’s theory of melody as well. Kurth’s line denoted first and foremost the coherent perception of melody by the listener. Moreover, Kurth argued in the later parts of the treatise that linear-melodic entities should also be understood as the primary constructive material in Bach’s polyphony. Unlike in the visual domain, however, in music, the performance and perceptive process coincide in simultaneity: the listener experiences motion in melody as it emerges in performance. In painting, by contrast, the spectator usually

64 Kurth, Linearer Kontrapunkt , 12. 65 Kurth, Linearer Kontrapunkt , 14. 191 relives an artwork’s creation at a significant temporal remove from the moment in which the painter moved the brush over the canvas. 66

Further parallels animate these analogies between artistic theories of the “active,” or

“genetic” line on the one hand, and Kurth’s theory of melody on the other . The re- conceptualization of the line that I discussed in Chapter I entailed new aesthetic connotations, such as immediacy, expressivity, continuity, and coherence. In contrast to an earlier Euclidian definition of the line as a connection of predefined points, the energetic line could extend its coherence indefinitely. Moreover, like melody, the energetic line took shape as it emerged. Kurth described this in music as a “process of formation” (“Erformung”):

Darum ist auch im psychologischen Sinne bei der Melodik statt von Form besser von Erformung (= Ur-Formung) zu sprechen, dem Werden zur wahrnehmbaren Erscheinung überhaupt. 67 Therefore one should speak in a psychological sense of melody not as form , but rather as formative process (=Ur-formation), the actual becoming of a sensible phenomenon.

Tied as such to an organic growth process, all moments in the “genetic” emergence of the line and of melody were equally constitutive of their eventual shape. This conception at once emphasized the unitary cohesion of these formed entities. The combined backdrops of Gestalt theory, psychology, and the visual arts illuminate the line as an essential and vivid imagery in

Kurth’s theory of melody.

66 I reviewed this duality through Cécile Guédon’s reading of Paul Souriau’s L`Esthéstique du mouvement (1889). Cécile Guédon, “Abstraction in Motion: A Choreographic Approach to Modernism” (University of London, Birkbeck, 2014), 190. 67 Kurth, Linearer Kontrapunkt , 10. Kurth seems to be playing with the etymological relation between the two German prefixes “Ur-” and “er-” (one commonly used for nouns, the other for verbs—in that sense, “Erformung” is the derivative of “erformen”). By employing both in his analogy (“Erformung” and “Ur- Formung”), Kurth harnessed all the possible connotations of these prefixes, entailing both a formative process and a primordial state. I am grateful to Alex Rehding for pointing this out to me. Rothfarb has translated “Form” as “shape” and “Erformung” as “shaping.” For a more extensive discussion of these ideas in Kurth’s writings see Daphne Tan, “‘As Forming Becomes Form:’ Listening, Analogizing, and Analysis in Kurth’s Bruckner and Musikpsychologie,” Journal of Music Theory 61, no. 1 (April 2017): 1–28. 192

Besides its metaphorical potential, Kurth also addressed the line in more superficial terms—literally, in its appearance and function in music notation. Already in the early pages of his treatise, he contextualized the visual origins that he observed of the line in the graphical rendering of music in notation. Here, Kurth noted primarily the line’s absence from the representational vocabulary of conventional staff notation, and criticized the ways in which that notational system disrupted the linear unity of melody into disjunct note heads:

Bei Anklammerung an die Niederschrift gelangt man zudem leicht dahin, die in Notenköpfe zerrissene Linie nicht mehr genügend als übergehenden und fliessenden Zusammenhang zu empfinden; das Bild der einzelnen Notenköpfe fördert im Musikbewusstsein stark und zum Nachteil des wirklich darzustellenden Gehalts im Melodischen die Lösung der Linie in ihre einzelnen Töne.” 68 When clinging to the written image [of music ], one easily arrives at perceiving the line that is torn up into note heads, and not sufficiently as continuous and flowing coherence. The image of the discrete note heads forcefully prioritizes, in the musical consciousness, the dissolution of the line into its constituent tones at the expense of the actual content of melody (which would have to be rendered).

A couple of pages later, he lamented the irony that that system of “ line -notation”—by which he referred to the introduction of diastematic staff-lines—ultimately subverted music’s linear conception:

Erst indem die Notenschrift (seit dem 10. Jahrhundert) durch die Linien notation bestimmte Tonhöhen herauszufassen beginnt, wird auch der graphische Ausdruck auf den Weg gewiesen, durch die Zersetzung in Einzelnoten den Linien begriff gänzlich zu verdrängen. 69 Only when music notation started to accentuate pitch through the integration of lines (since the tenth century), it also instigated the graphical expression to supplant entirely the linear conception [of music ] by disintegrating it into individual tones [note heads ].

Arne Stollberg has commented that this nostalgia for neumatic notation was not unique to

Kurth, and representative of a by-now outdated understanding of neumes as reflections of

68 Kurth, Linearer Kontrapunkt , 2–3. 69 Kurth, Linearer Kontrapunkt , 29,. The emphasis is original. 193

melodic-energetic coherences in Gregorian chant. 70 Stollberg’s source of reference is Alexander

Truslit’s theory of musical kinesthetics as presented in his 1938 monograph Gestaltung und

Bewegung in der Musik .71 The music pedagogue Truslit, too, expressed his dismay over modern staff notation as a regression from the standard set by neumes, which he furthermore construed as matching the gestural movements of the choral conductor. Truslit’s theory, and the discourse in which Stollberg situates it, provide yet another context for the invocation of motion in melody.

As Stollberg frames it through Truslit’s own words, the “attempt at understanding everything in music somehow through the human body [had been ] virtually omnipresent since the 1910s and

20s.” 72 Thereby, Truslit asserted that his ideas of Gestaltung und Bewegung in der Musik traced

back to these earlier decades before the book was eventually published. With reference to that

earlier context, Kurth’s ideas of melody as motion contribute a music-theoretically founded

backdrop to Stollberg’s narrative.

Conversely, Stollberg contextualizes Kurth with these concerns that Truslit perceived so

widespread in the early twentieth century, and that were closely connected as well with the

emergence of modern dance.73 But while Kurth focused on the aesthetic and music-theoretical

70 Arne Stollberg, “‘Mimische Ausdruckshandlungen.’ Der Dirigentenkörper im anthropologischen Musikdiskurs des 19. und 20. Jahrhunderts,” in DirigentenBilder. Musikalische Gesten - verkörperte Musik , ed. Florian Henri Besthorn, Arne Stollberg, and Jana Weißenfeld (Basel: Schabe, 2015), 40. 71 Alexander Truslit, Gestaltung und Bewegung in der Musik: ein tönendes Buch vom musikalischen Vortrag und seinem bewegungserlebten Gestalten und Hören , ed. Hans Brandner and Michael Haverkamp, Reprint of the original (Berlin, 1938) (Augsburg: Wißner, 2015). Like the reprint, Truslit’s monograph was accompanied by three gramophone records containing the musical examples to the text. 72 “Truslits Buch Gestaltung und Bewegung in der Musik erschienen erst 1938, aber gedanklich und methodisch—wie der Autor selbst schreibt—fest eingebunden in die seit den 1910er und 1920er Jahren beinahe allgegenwärtigen ‘Bestrebungen, das Musikalische irgendwie vom Körper aus erfassen zu wollen.’” Stollberg “Mimische Ausdruckshandlungen,” 38. Brandner, editor of the reprint of Truslit’s treatise, has also offered a contextualization of his kinesthetic ideas. See Hans Brandner, Bewegungslinien der Musik: Alexander Truslit und seine Lehre der Körpermusikalität, der Kinästhesie der Musik (Augsburg: Wißner, 2012). 73 Arne Stollberg, “Mimische Ausdruckshandlungen,” 38–44. I attend to another source that Stollberg discusses—an essay from 1904 by Erich Moritz von Hornbostel on “Melodischer Tanz” —in the Conclusion of this dissertation. 194 significance of the experience of motion in music, and here in particular with respect to select repertoires, Truslit took a more comprehensive and applied approach. Though similarly propounding the centrality of “inner motion” in music, Truslit extended his inquiries to music performance and actual physical movements of musicians and conductors—the focus of

Stollberg’s study. More eclectically than Kurth, Truslit compiled references to motion in music from acoustic, embodied, biological, anthropological, sensory-motor and psycho-physiological perspectives. 74 Notably, too, Truslit developed a notational system to capture and categorize patterns of musical motion. As reproduced in Figure IV.1, for instance, he theorized different shapes for an “up-and-down movement.” Not surprisingly, this notation featured lines, and more specifically curvilinear shapes, because “in nature, everything moves in curves.” 75 Hence, Truslit considered the first shape of Figure IV.1 “unnatural.”

74 See also Bruno H. Repp, “Music as Motion: A Synopsis of Alexander Truslit’s (1938) ‘Gestaltung und Bewegung in der Musik,’” Psychology of Music 21, no. 1 (1993): 48–72. 75 Repp, “Music as Motion,” 53. 195

Figure IV.1 : Alexander Truslit, Gestaltung und Bewegung in der Musik , Plate 2. All four figures can be paired with the same musical excerpt, such as a C major scale, ascending and descending over one octave. 76

The trajectory of these lines corresponded to a perceived motion in pitch space, depending on “pitch, intensity, and duration of the tones—that is, on the melodic-rhythmic motion in the music.” 77 The pedagogue Truslit conceived of these shapes to address both the musical performer and the listener. He conducted experiments to demonstrate that the different shapes of Figure IV.1 elicited considerable nuance in the performance of the same musical excerpt, for instance a scale. Using an oscilloscope, Truslit recorded and measured these samples, to show how the versions differed in amplitude and duration at the various moments of the scale. These illustrations are included in an accompanying booklet with his treatise. In

76 Figure reproduced from Repp, “Music as Motion,” 54. 77 Repp, “Music as Motion,” 50. 196 addition to teaching how to “shape” (“gestalten”) these different musical motion curves in performance, Truslit also sought to help listeners experience the “original motion pattern” by learning to draw the above patterns to assimilate their shapes according to respective auditive conditioning.

These pedagogical experiments and exercises channeled in many ways what artists and art critics described as the “immediate” and “expressive” qualities of the line, as I discussed in

Chapter I. Truslit also attributed liveliness to the resulting notational artifacts, claiming, “modern notation encloses the living music like a rigid and cold armor. Yet it is not difficult to cut through this armor and to make the imprisoned shape come gloriously alive.” 78 The mapping of musical motion onto the curvy line moreover corresponds to the paradigm of the active, genetic line in the visual arts that I reviewed above. 79 Crucially, the graphical realization of the different curved shapes was essential to Truslit’s approach, both for conveying their essence and for modeling the physical gestures for the listener.

This takes us back to Kurth, who, by contrast, avoided the visual representation of his linear-melodic conceptions. Indeed, despite its essential function for tying together his ideas, as I charted above, Kurth did not enact the line as a graphical icon at all throughout Linear

Counterpoint . In the few instances in which he annotated musical examples, he did so through the addition of such punctual symbols as “+” or “*” signs to highlight tones that he perceived as connected in a melodic line. I will discuss a pertinent example later in this chapter in Figure

IV.2. The absence of a graphical display of his linear-melodic conceptions distinguishes Kurth’s

Linear Counterpoint from most other sources discussed in this dissertation. Apart from the

78 Quoted from Repp, “Music as Motion,” 51. 79 However, the three shapes in Figure IV.1 that Truslit considered “natural” (“naturgemäß”) contradict my proposition from Chapter I that melodic lines do not curve back to the left since they depict trajectories in passing time. Truslit’s shapes thus present abstractions of specific melodic patterns, which reflect a retrospective and holistic view on a musical excerpt. 197 efforts that it would have entailed in typographical terms, Kurth’s reluctance towards graphical illustrations appears fully consistent with his theoretical propositions and convictions. As we have seen, for Kurth, the line connoted a phenomenon that he rooted deep in the listener’s unconscious; projecting it onto the surface of a sheet of paper would not do justice to it.

Therefore, while skeptical of the disruptive effect of traditional music notation, Kurth did not invest in advancing an alternative—unlike Truslit, for instance, who aspired to liberate music from the “rigid and cold armor” of conventional notation. While the discourse around kinesthetic theories of music might have been a source of inspiration to Kurth, his approach also diverged in notable ways from it. Kurth’s line remained inherently invisible.

Horizontality and Verticality in History: Kurth’s Music-Theoretical Intervention

In multiple instances throughout his treatise, Kurth described the two-dimensional manifestation of music in notation as a merely superficial representation of music’s actual essence. Nevertheless, he construed this two-dimensionality of the notational artefact to epitomize the central dichotomy that he claimed to lie at the heart of his approach in Linear

Counterpoint —namely the dualism of horizontality and verticality in musical textures and music-theoretical perspectives. 80 As he explained, the kinetic energy in the melodic line faced as its counter-force a vertical gravitational pull, which Kurth called “cohesion” (“Kohäsion”). 81

Expanding Kurth’s palette of physical-energetic metaphors, “cohesion” accounted for the harmonic tie of chordal sonorities, and correlated, as Krebs observes, with molecular adhesion in

80 See Kurth, Linearer Kontrapunkt , esp. 58–67. Rothfarb, Ernst Kurth: Selected Writings , 38. 81 As various scholars have highlighted, Kurth advanced his theory of chordal cohesion as an attempt at overcoming Carl Stumpf’s “Verschmelzungstheorie” (theory of tonal fusion). Kurth addresses Stumpf’s theory in Linearer Kontrapunkt , 64–65. See for instance La Motte-Haber, “Kräfte im musikalischen Raum,” 290–91, and Kim, “Theories of Musical Hearing, 1863-1931,” 315–17. 198 physics. 82 In Kurth’s conception, both linear-horizontal and harmonic-vertical forces exerted their influence on the individual tones, thus infusing the tones with energy. Kurth perceived this interplay of forces to overpower the meaningfulness of the individual tone in isolation. 83 While he portrayed the two forces to interact in a form of synergetic confluence in the frame of the musical texture, Kurth also argued that compositional techniques might prioritize one over the other. 84 Concomitantly, music theory had to be prepared to recognize and examine both dimensions equally.

In precisely this stipulation, Kurth discerned the roots for his necessary intervention. For while he credited previous theories with having expansively attended to harmonic forces in music, he criticized them for subsuming melodic linearity within them, thereby failing to acknowledge its independent creative drive. In Linear Counterpoint , Kurth sought to rectify this imbalance. Though ironically, early critics of Kurth’s treatise reproached him for precisely the same pitfall in the other extreme, for losing sight of the tonal-harmonic foundation to his linear- melodic perspective. While this overly oppositional reaction was a product of its time, as we have seen in Chapter II, Kurth’s presentation of his position might well have fuelled the tensions.

In a historical survey that he framed through the dualism between horiztonal (linear- contrapuntal) and vertical (harmonic) conceptions of polyphony, Kurth sought to vindicate his ambitions through historical cases of precedence. As I chronicle below, this portrayal shows that

Kurth was well aware of disrupting established music-theoretical traditions. In Kurth

82 Krebs, Innere Dynamik und Energetik in Ernst Kurths Musiktheorie , 224. Krebs discusses the interplay of verticality and horizontality in Kurth’s theory more broadly at pp. 223–35. A similar term, “Kohärenz,” meanwhile featured in Gestalt-theoretical research of the 1920s, as I review later in this chapter. 83 See Kurth, Linearer Kontrapunkt , 66, Rothfarb, Ernst Kurth: Selected Writings , 43. 84 Kurth, Linearer Kontrapunkt , 66: “Eine gegensätzliche Tendenz kennzeichnet aber darum auch die technischen Grundzüge von linear-kontrapunktischer und andrerseits von harmonischer Satzlage, und deren Verschiedenheit ist durchgreifend, sie reicht bis zu den Wurzeln der Satztechnik hinab, die hier vom Akkord, dort aber von der Linie als Einheit und Ursprung auszugehen hat.” (Emphases in original). See also Rothfarb, Ernst Kurth: Selected Writings , 43–4. 199 scholarship, many authors have reviewed these narratives about how Kurth’s writings might be situated in the history of music-theoretical thought. Below, I will focus only on those aspects that pertain directly to the role of the line and the way in which Linear Counterpoint interfered with non-linear conceptions of counterpoint. This survey will complement the contextualization of

Kurth’s ideas and their reception that I initiated in Chapters I and II.

In his narrative concerning the historical primacy of a “linear-melodic principle”

(“melodisch-polyphone Schreibweise,” or “mehrstimmiges Linienprinzip”) in polyphony, Kurth recounted how music theorists periodically obscured the linear qualities in music in favor of vertical-harmonic concerns. 85 Covering a period from the tenth century to Johann Sebastian

Bach, Kurth discerned such tensions from the very beginning of this timespan. Despite the linear-scalar organization of the modal system, he saw the “ominous principle of ‘punctus contra punctum’” lying latent already in musical discourse around early organum. 86 (That motto, which allegorically encapsulated the target of Kurth’s agenda through its emphasis on the “point,” will resurface again in my discussion later.) While recognizing a culmination in melodic fluidity in the “Ars nova” style of the fourteenth century, Kurth diagnosed the decreasing independence of polyphonic voices in the following centuries, leading to a veritable “crisis” (“Übergangskrise”) in compositional style around 1600. 87 The standardized use of the leading tone in cadential gestures constituted for Kurth a symptom of this decline of linear polyphonic writing, since it not only disturbed the modal organization of music, but moreover emphasized moments of vertical- harmonic coordination of all voices. 88 Kurth observed these tendencies equally in the music of

Orlando di Lasso and Giovanni Pierluigi da Palestrina and aligned these compositional shifts

85 See Kurth, Linearer Kontrapunkt , 117–45. 86 “Bereits die Keimform des verhängnisvollen Prinzips ‘punctum contra punctum’ enthält.” Kurth, Linearer Kontrapunkt , 117–9. 87 Kurth, Linearer Kontrapunkt , 124. 88 Kurth, Linearer Kontrapunkt , 122. 200 with the theoretical codification of the triad in Gioseffo Zarlino’s Le istitutioni harmoniche

(1558). Zarlino’s treatise planted the seed for the development of harmonic thought in the following centuries, typified, for instance, in Jean-Philippe Rameau’s Traité de l’harmonie

(1722), as well as in Johann Joseph Fux’s theory of counterpoint in Gradus ad Parnassum

(1725).

While the emerging basso continuo practice and its notation aided this conceptualization of music’s harmonic structures in the early seventeenth century, Kurth highlighted that at the same time the flourishing of instrumental music afforded unprecedented technical possibilities of melodic elasticity. 89 Indeed, because of the agility he perceived in instrumental performance and the wider ambitus of musical instruments over the human voice, Kurth promoted instrumental polyphony as the ideal expression of the linear-polyphonic idiom. Therefore, unlike most other counterpoint treatises, Linear Counterpoint focuses not on vocal, but on instrumental polyphony as its primary object of study, and here specifically the oeuvre of Johann Sebastian Bach, his keyboard and organ works and the compositions for solo violin and solo cello. 90

Bach arises as the pinnacle of Kurth’s narrative of linear-melodic polyphony, uniting the benefits of the outlined theoretical and technical conditions. Bach integrated the highest condensation of harmonic organization in music with the fullest fruition of contrapuntal linearity, afforded by unconstrained instrumentality:

So zeigt die Entwicklung vom Beginn des siebzehnten Jahrhunderts an das fruchtbare Ineinanderdrängen der beiden Grundkräfte des musikalischen Satzes, das die Vorbedingung zur vollreifen Durchbildung der kontrapunktischen Linientechnik bildet, wie sie in Bach’s Schaffen zugleich mit der höchsten Kraft harmonischer Konzeption ihre nie wieder erreichte, höchste Entfaltung zeigt. 91

89 Kurth, Linearer Kontrapunkt , 124–26. 90 Kurth, Linearer Kontrapunkt , 144–45. Following Philipp Spitta, Kurth also pointed out that Bach allegedly built his own teaching around instrumental polyphony. See Kurth, Linearer Kontrapunkt , 145. 91 Kurth, Linearer Kontrapunkt , 126. 201

Since the early seventeenth century, the development shows the fertile intertwining of the two essential musical forces, which constitutes the precondition for the fully mature formation of a contrapuntal linear technique, as it achieved its highest evolvement in Bach’s oeuvre, at once with the highest power of harmonic conception, as it has never been attained again.

Through this convergence of aesthetic ideals, Kurth justified the choice of Bach’s polyphonic music as the primary object of study in Linear Counterpoint : “den Kontrapunkt aus seiner reinsten und eigentlichsten Quelle zu schöpfen.… Das Studium des Kontrapunkts ist von dem des Bachschen Stiles nicht zu trennen” (“to draw counterpoint from its purest and truest wellspring.… The study of counterpoint cannot be divorced from [the study of] the Bachian style”).92

With Bach’s death, Kurth saw these achievements vanishing quickly as they gave way to harmonic-homophonic composition and its symmetrical, periodic forms in the classical era. As I reviewed in Chapter I, the stylistic shift after 1750 also marks a rift in Kurth’s theoretical coverage, with his later monographs reentering, in chronological succession, with the music of

Richard Wagner and Anton Bruckner. 93 But while the historical survey of compositional styles provided in Linear Counterpoint broke off with Bach’s death, Kurth continued to delineate the propagation of harmonic thinking in counterpoint treatises from Johann Georg Albrechtsberger and Luigi Cherubini to contemporaries like Hugo Riemann, Felix Draeseke, and Heinrich

Schenker. In this lineage of thought, Kurth identified in particular two authors for their sustained impact on music-theoretical discourse up to his day: Fux and Riemann.

With regards to the latter, whom he recognized as the contemporary doyen in the field,

Kurth was particularly wary of expressing his objections, as we have seen earlier. Already in the

92 Kurth, Linearer Kontrapunkt , ix. 93 See also Rothfarb, Ernst Kurth as Theorist and Analyst , esp. chap. 5 “Kurth’s Historical View of Harmony.” 202

foreword, Kurth stressed that he did not seek to initiate polemical confrontation, and at various

occasions throughout the treatise, he paid tribute to Riemann’s achievements. 94 For instance,

Kurth credited Riemann with the comprehensive classification of harmonic relations that can arise in contrapuntal textures. 95 Still, he asserted that Riemann’s harmonically driven approach to

counterpoint, which derived polyphony from the gradual “figuration” of a harmonically

structured texture, did not properly account for the essence of Bach’s polyphonic music. 96 The

problem, Kurth analyzed, boiled down to one of music theory’s notorious chicken-and-egg

questions, namely the primacy of melody or harmony as entry-points to music analysis. 97 Bach’s

music, Kurth was certain, arose from the primacy of the melodic line. Ultimately, he thus could

not help but revive this century-long debate, which, as we have seen, caught up with him quickly

in the critical reception of his treatise.

Not surprisingly, with respect to the other, earlier source of contention—Fux’s theory of counterpoint—Kurth felt less need for being complimentary. The prevailing doctrine of counterpoint at the time still built on Fux’s Gradus ad Parnassum (1725), with its five species

(“Gattungen”) of contrapuntal composition. 98 Kurth took issue with the way in which Fux’s

94 Kurth, Linearer Kontrapunkt , x. 95 “Das Hauptverdienst, den ganzen tonalen Zusammenhang der im Kontrapunktieren entstehenden Harmonien über die von einem Ton des Cantus firmus zum andern konstruierten einzelnen Zusammenklänge gestellt zu haben, gebührt Hugo Riemann (‚Lehrbuch des einfachen, doppelten und imitierenden Kontrapunkts,’ 1. Aufl. 1888).” Kurth, Linearer Kontrapunkt , 133–34. 96 Kurth, Linearer Kontrapunkt , 137–41. 97 An earlier famous instance of this opposition occurred in the “Querelle des Bouffons” of the 1750s between Jean-Jacques Rousseau and Jean-Philippe Rameau. Both theorists infused the issue with politically charged contentions, such as nationalist claims over the supremacy of Italian or French opera. See, for example, Thomas Christensen, Rameau and Musical Thought in the Enlightenment (Cambridge, UK: Cambridge University Press, 1993), chap. 8. Traditionally, scholars have construed Rameau as the precursor to the various branches of German harmonic theory in the nineteenth century, with a similar potential for political stakes; e.g. David W. Bernstein, “Nineteenth-Century Harmonic Theory: The Austro-German Legacy,” in The Cambridge History of Western Music Theory , ed. Thomas Christensen, (Cambridge, UK: Cambridge University Press, 2002), 778–811. 98 Kurth dedicated a full chapter of his treatise to discussing the shortcomings of Fux’s approach. Kurth, Linearer Kontrapunkt , 103–16. See also Rothfarb, Ernst Kurth as Theorist and Analyst , 84. 203 approach propagated a moment-by-moment vertical slicing of contrapuntal textures into harmonic sonorities. Such a focus on the music’s vertical organization construed counterpoint literally as a texture built by juxtaposing “punctus contra punctum”—or, in musical terms, “note against note.” 99 Kurth’s designation “linear counterpoint” wittily countered this conception already on a semiotic level, by mediating the “point” in “counterpoint” through the “line.” Kurth further proposed the term “ paralinear ” to describe the polyphonic texture, by substituting both

“contra” and “point” of “counterpoint” to emphasize the concurrence of multiple lines that develop simultaneously and as independently as possible:

Liegt daher im Namen “Kontrapunkt” schon das Abirren vom mehrstimmigen Linienprinzip ausgedrückt, so wäre bei der Wahl eines den horizontal durchgeführten Satzentwurf deutlicher ausprägenden Ausdrucks davon auszugehen, dass nicht Note gegen Note, sondern Linie gegen Linie gesetzt wird und statt von kontrapunktischer eher von kontralinearer Schreibart zu sprechen, oder besser noch, da die melodischen Züge nicht eigentlich gegen einander gesetzt werden, sondern neben einander verlaufend , durch die Gleichzeitigkeit möglichst ungehindert, von paralinearer Schreibart.... 100 The term “counterpoint” thus already expresses the straying away from the polyphonic linear principle. Therefore, in choosing an expression that captures better a horizontally oriented approach to the musical texture, one has to start by recognizing that rather than note against note, one puts line against line. One should talk not of contrapuntal, but rather of contralinear composition, or, better still, of paralinear writing, since the melodic progressions are not set against one another, but rather develop next to one another , as uninhibited by their simultaneity as possible.

In order to appreciate polyphony as a “paralinear” texture, Kurth concluded, with emphasis, that an entirely new plan of action was needed:

Der Ursprung des kontrapunktlichen [sic ] Satzes liegt nicht im Akkord, sondern in der Linie. Bei dieser hat darum auch die Theorie und Technik einzusetzen. … Die erste

99 Kurth, Linearer Kontrapunkt , 99–100. Kurth consistently referred to “punctum contra punctum” (rather than the more common form “punctus contra punctum,”), embracing perhaps a compositional perspective in which both tones (“points”) were deployed as (dative) objects. 100 Kurth, Linearer Kontrapunkt , 100. The emphasis is original. A similar, previous passage on the same page reads: “Der Name “Kontrapunkt” bedeutet so genau das Gegenteil von dem, was er sagen soll; denn die melodisch-polyphone Schreibweise ist der Gegensatz zu einer solchen, die jeden Ton einer Stimme mit einem Einzelton einer andern verbindet, Note gegen Note setzt; sie zielt dahin, dass Linienzüge sich nebeneinander entwickeln .” The emphasis is original. 204

Bedingung für die Durchführung einer linearen Kontrapunktlehre ist daher die Loslösung von dem Prinzip “Punctum [sic ] contra punctum ,” welches nicht nur den Begriff der Linieneinheit, des geschlossenen melodischen Verlaufs zersetzt, sondern sogleich den Grundwillen mehrstimmig-linearer Struktur umstürzt. 101 The origin of contrapuntal composition lies not in the chord but in the line. The theory and technique of counterpoint must therefore begin with the line. … The first condition for carrying out a theory of counterpoint is thus the abandonment of the principle “punctum contra punctum,” which not only undermines the idea of linear unity, of a continuous melodic process, but simultaneously destroys the fundamental will of polyphonic-linear structure. 102

Moreover, Kurth expanded that the lines in “paralinear” textures should develop as freely and unbound by concerns of vertical coordination as possible: “Die Kunst der kontrapunktischen

Technik ist um so grösser, je losgelöster von allen Zusammenklangsrücksichten sich die

Linienentwicklungen auswirken können” (“The art of contrapuntal technique is the higher, the more freely and detached from all considerations of harmonic sonorities the development of lines can unfold”).103 Moreover,

Der Kern der Kontrapunkt-Theorie liegt darin, wie zwei oder mehrere Linien sich gleichzeitig in möglichst unbehinderter melodischer Entwicklung entfalten können ; nicht durch die Zusammenklänge, sondern trotz der Zusammenklänge. 104 The crux of contrapuntal theory is how two or more lines can unfold simultaneously in the most unhampered melodic development —not by means of the harmonies but despite the harmonies. 105

The extent to which Kurth saw these stipulations fulfilled in Bach’s music can be gleaned roughly from the second half of the treatise, starting with the large third section, “Bach’s

Melodic Style” (“Bachs melodischer Stil”). 106 In these final sections of Linear Counterpoint ,

101 Kurth, Linearer Kontrapunkt , 143. The emphasis is original. 102 Rothfarb, Ernst Kurth: Selected Writings , 46. 103 Kurth, Linearer Kontrapunkt , 102. 104 Kurth, Linearer Kontrapunkt , 144. The emphasis is original. 105 Rothfarb, Ernst Kurth: Selected Writings , 47. 106 Kurth, Linearer Kontrapunkt . While that section commences on page. 147, it only turns to Bach’s style in the fourth chapter “Zur Rhythmik der Bachschen Linie,” 186. 205

Kurth explored his theoretical postulates in practical application through examples of the polyphonic repertoire.

The Linear Forms in Apparent Polyphony (“Scheinpolyphonie”)

Turning from his general aesthetic-theoretical propositions to actual musical examples,

Kurth proceeded gradually from observations about the linear essence of Bach’s melodies

(“Bachs Melodik”) to polyphony within the single line (“Polyphonie der einstimmigen Linie”), and eventually to “real” polyphonic textures that interweave two or more melodic lines. 107 Only that last step in Kurth’s scaffolding, in the fourth and final large section of the treatise on “The

Polyphonic Texture” (“Die polyphone Satzanlage,” starting on page 349), was devoted to Bach’s polyphonic repertoire for keyboard instruments. Here, Kurth confronted, in the practical realm, ideas about the relation among the various polyphonic parts, the creation of consonant and dissonant harmonies from their confluence, and, more generally, the interaction of melodic and harmonic concerns. In the pertinent repertoire to these studies, the different parts of the polyphonic texture are commonly well defined. In compositions of the single instrumental line, as found in Bach’s Sonatas and Partitas for Solo Violin and the Suites for Solo Cello, by contrast, yet more foundational analytical observations pertain to essential structuring principles within each melodic line. They reveal facets about Kurth’s understanding of linear coherence in music, including what a line might even be. Precisely this repertoire and these insights form the focus of my following discussion.

Kurth commented that the idiom of the single line (“einstimmige Linie”) offered the most profound proof of the energetic tension that carried across long spans of Bach’s music, without

107 See Kurth, Linearer Kontrapunkt , 145, Rothfarb, Ernst Kurth: Selected Writings , 48–49. 206 needing harmonic support from an accompaniment. Indeed, in such “uni-linear” textures, the tensioning forces of melody exerted their most concentrated impact, as Kurth put it:

Hier sind ganz besonders die Werke von Bach für Violine und Cello ohne Begleitung als Vorbilder und Studiengrundlagen zu werten: die Technik, die hier in den einstimmigen Linien, wo naturgemäß die Spannkräfte der Melodik am konzentriertesten wirken, in ihrer reinsten Form erscheinen, beherrscht aber auch alle melodischen Entwicklung innerhalb der mehrstimmigen Sätze des polyphonen Stils.108 Here in particular Bach’s works for unaccompanied violin and cello are valuable models and objects for study: The technique prevailing in the one-part lines, where the tensioning forces of melody exert their most concentrated effect and appear in their purest form, [this technique ] governs as well all melodic development in the multi-part movements of the polyphonic style.

Moreover, these compositions exposed the greatest freedom of linear-horizontal development (“Fortspinnung”), in which the melodic line could evolve unbound from both harmonic considerations and rhythmic-metric periodicity. Over about fifty pages, Kurth elaborated on how significantly this capacity of free “Fortspinnung” set Bach’s music apart from compositions specifically of the Classical era, citing examples of works by Wolfgang Amadeus

Mozart and Ludwig van Beethoven. In lieu of regular rhythmic and harmonic schemes that predominated the Classical idiom, Kurth observed that other musical devices structured larger forms in Bach’s music, and in particular in the repertoire for unaccompanied violin and cello.

These structuring principles, which centered on motivic developments and their horizontal trajectories, assured formal coherence within the seemingly unconstrained freedom of this music, and at once established typical patterns of melodic development in Bach’s music more generally.

As the most potent feature in the organization of Bach’s music, Kurth highlighted processes of intensification (“Steigerung”) in the development of the melodic curve

108 Kurth, Linearer Kontrapunkt , 224. 207

(“melodische Kurvenbildung”) and their culmination in highpoints in pitch (“Gipfeltöne”). 109

Kurth defined such climactic processes as trajectories of ascending pitch, and noted that the ascent via scalar patterns was particularly common. In the example of Figure IV.2, for instance,

Kurth signaled the tones participating in this process through “+”. These tones are exposed in pitch within their immediate surroundings, making them “highpoints within the melodic curve”

(“Kurvenhöhepunkte”). 110

Figure IV.2 : Ernst Kurth, Linear Counterpoint , Example 70 (J. S. Bach, Suite for Solo Cello in G major (BWV 1007), Prelude, mm. 22–24)111

Kurth classified such ascents by step-wise motion as progressing via a “straight line”

(“geradlinige Steigung”). 112 Though he noted that climactic moments did not necessarily have to be reached via such “straight” trajectories, the absolute majority of the examples that he cited exhibit exactly that profile. 113

109 See for instance Kurth, Linearer Kontrapunkt , 226 and 252. 110 Kurth described this with respect to his Example 44, an excerpt from the Presto-movement of Bach’s Sonata for Solo Violin in G minor: “Die Fortsetzung der geradlinigen Steigung vom 4. Takt liegt also in den Kurvenhöhepunkten; diese Technik von Wellenbewegungen, deren Gipfel untereinander eine hinansteigende Reihe, oder auch umgekehrt hinabsinkende Entwicklung zeigen, ist für Bachs einstimmige Fortspinnungstechnik besonders kennzeichnend.” Kurth, Linearer Kontrapunkt , 228. 111 Kurth, Linearer Kontrapunkt , 251. 112 Kurth, Linearer Kontrapunkt , 226 and 251. 113 See Kurth, Linearer Kontrapunkt , 251. 208

Both the allusion to the line as well as its characterization as a scalar progression already conjure up clear resemblances between Kurth’s ideas and Ernst Toch’s Melodielehre , as discussed in Chapter III. Like Toch, Kurth also defined culmination points, and, concomitantly, points of condensation in the musical form, primarily through their exposition in pitch. As we saw, this fixation on effects of pitch annoyed Arnold Schoenberg, who countered that other musical parameters could equally promote the sensation of formal culmination points. Toch and

Kurth, by contrast, ascribed structuring effects in the organization of form primarily to pitch- related events. Moreover, like Toch, who derived general principles for the aesthetically successful construction of the Tonhöhenlinie , Kurth formulated similar rules about the distribution and scope of highpoints in the melodic development, including the recommendation that the same highpoint should never be reached twice. Unlike Toch, however, who focused his inquiries on melodic excerpts on a very small scale, Kurth extended his considerations to more expansive musical contexts. Indeed, he argued that linear trajectories, such as “straight” progressions, had to be perceived even across passages of chordal figuration, or arpeggiating patterns, which he called “curves” (“Rundungen,” “akkordlich gerundete Formen”):

Der Begriff der Linie ist auch durch akkordlich [sic ] gerundete Formen hindurch aufrecht zu erhalten. … Niemals versandet aber Bach’s Linie, auch bei aller Rundung über akkordliche Konturen, in matter Umspielung von Harmonien. 114 The concept of line has to be sustained also across chordally rounded forms. … Despite its pliability around chordal contours, Bach’s lines never lapse into mere ornamental noodling of harmonies.

In the excerpt from the opening of Bach’s Cello Suite in E-flat major (BWV 1010) in Figure

IV.3, for instance, Kurth demonstrated this stipulation in a texture that on the surface consists merely of arpeggiated chords.

114 Kurth, Linearer Kontrapunkt , 259–60. 209

Figure IV.3 : J. S. Bach, Suite for Solo Cello in E-flat major (BWV 1010), Prelude, mm. 1–16, with added annotations (following Kurth’s analysis of Linear Counterpoint , Example 86) 115

As Kurth commented, a polyphonic multiplicity lies latent in the exposed pitches of this arpeggiated texture, meaning that both the re-articulated bass tone E-flat as well as the upper- most tones of the half-measure patterns incite their own linear-horizontal trajectories. The top voice that Kurth heard as an independent horizontal stream thus progressed, after an initial falling fourth e-flat’–b-flat , in falling thirds d-flat’–b-flat, c’–a-flat, etc. (as annotated by the circles) . In measure 10 of the excerpt, meanwhile, the bass line starts to move as well (as highlighted by the squares). In the subsequent examples of the treatise, Kurth illustrated that such perceptions were not confined to pitches exposed at the outer fringes of the musical texture, but could also occur in inner voices. In that way, an alternative interpretation of Figure IV.3 could isolate two separate top voices, each descending by (predominantly) step-wise motion, one starting from the e-flat’ , the other from b-flat .

115 Figure IV.3 is reproduced from a different source, and the annotations added to highlight Kurth’s analysis. Kurth himself did not annotate his Example 86 in the treatise. See Kurth, Linearer Kontrapunkt , 264–65. 210

The above example also illustrates the commonality of sequential patterns in this repertoire, a feature that Kurth discussed across multiple further examples. But also in the absence of such sequential structures, linear trajectories permeate Bach’s music. As Kurth emphasized, they could even tie across tones of varying metrical placement. In the excerpt of

Figure IV.4, for instance, Kurth heard the descending bass-line from f-sharp to B, of which almost all participating tones fall on a different position within the measure, as I have highlighted through the annotations.

Figure IV.4 : Ernst Kurth, Linear Counterpoint , Example 114 (J. S. Bach, Suite for Solo Cello in D minor (BWV 1008), Menuett II, mm. 12–16), annotations added 116

Examples such as the ones quoted above demonstrate how Bach’s music, and in particular the repertoire for unaccompanied string instruments, was saturated with a technique that created the illusion of polyphony within the single instrumental line.

In Bach’s Linien ist eine Technik herausgebildet, nach welcher in der einstimmigen Linienentwicklung eine Mehrstimmigkeit latent liegt und welche das Erfassen und Ergänzen von reicherer und vielfältigerer musikalischer Verarbeitung im Hören anregt, als sie in der einen Stimme zu wirklichem Erklingen gelangt. 117 A specific technique has evolved in Bach’s lines, through which polyphony lies latent in the individual linear development. This animates the listener to grasp and interpolate richer and more diverse musical processes than are actually being sounded in the single voice.

As Kurth described, the listener had to interpolate and discern this phenomenon from what was actually sounding. The term “Scheinpolyphonie,” with which this technique is commonly

116 See Kurth, Linearer Kontrapunkt , 277. 117 Kurth, Linearer Kontrapunkt , 263. 211 designated, and usually translated as “apparent polyphony,” thus appears fitting. As a phenomenon, it arises from the mechanical constraints of the violin and cello with regards to performing multiple parts in simultaneity. In comparison to a keyboardist’s capacities in playing multiple parts at once, the violinist or cellist is confined in their respective agility. Often, indeed,

Bach’s compositions for these unaccompanied instruments feature only a single tone at a time, commonly in a steady rhythmic motion of regular eighth notes. When the listener is tasked with discerning multiple “apparent” voices evolving simultaneously from such a stream of single tones, the simulation of polyphony relies on both the listener’s abilities, and certain structuring principles in the music. Even though Kurth did not explain these principles at play, they can be deduced from his analytical observations. With respect to the illusion of polyphony in the single instrumental part, Kurth classified a number of common patterns that signal the concurrence of multiple voices and, in turn, provide analytical guidance to the listener. At the same time, these conditions specify the parameters that promote the linear coherence of each individual melodic voice, and they thus reveal a refined understanding of the mechanisms of “paralinearity,” as

Kurth conceived it.

With “apparent polyphony” lying latent in the music itself, but having to be brought to life by the listener, Kurth concluded that the performer did not need to put any particular emphasis on specific pitches to bring out the apparent voices, but merely support their natural emergence from the texture through sensitive phrasing. 118 Kurth claimed that the listener performed the necessary imagination to hear the polyphonic interweaving of multiple parts, involving much detail:

118 Kurth, Linearer Kontrapunkt , 283. 212

Wenn hierbei zwei Stimmen aus der Scheinpolyphonie, oder eine Scheinstimme und die Realstimme in ein und denselben Ton einmünden oder durch denselben Ton kreuzen, so hören wir diese gemeinsamen Berührungspunkte der Stimmen wie doppelt angetönt.119 When thereby two voices of apparent polyphony, or one apparent voice and one real voice merge in one and the same tone, we hear these shared points of intersection between the voices as if doubly strung.

Moreover, Kurth suggested that the listener would mentally retain the constitutive tones of linear progressions in their inner ears so as to connect them into a mental image. 120

Neben diesen beiden Arten der melodischen Spannungsverdichtung, den in Schwebe bleibenden Vorhalten und verhaltenen Leittonwirkungen sind noch rein melodische Spannkraftserhöhungen dadurch erzielt, dass plötzliche und im melodischen Hören auffallende Unterbrechung der Bewegungsrichtung eintritt und diese erst nach einer Zwischenstrecke wieder aufgenommen und fortgeführt wird, so dass sich im Hören der Ton, mit welchem der Linienzug zuerst abgerissen wurde, erhält und dann mit den späteren Tönen in Verbindung gebracht wird. 121 Besides these two ways of intensifying melodic tension, by holding suspension tones and leading tones in suspension, the tension-giving forces of melody can furthermore be heightened by the sudden, noticeable interruption of the direction of motion, which is resumed and continued only after an intermediary passage. When listening, the tone, with which the linear progression first broke off, is retained and then connected with the later tones.

This logic is noteworthy for its resonance with both phenomenological and Gestalt-psychological thinking, as I laid out in Chapter I, as well as with Heinrich Schenker’s later invocation of

“fernhören.” I shall return to these comparisons below.

To corroborate his analytical views, Kurth also cited the composer Bach himself, who had arranged his Sonata for Violin Solo in A minor for keyboard (BWV 1003), transposing it to

D minor in the process. 122 In his Examples 171–76, Kurth juxtaposed the two versions as Bach

119 Kurth, Linearer Kontrapunkt , 302. 120 Kurth, Linearer Kontrapunkt , 278. Referring to the excerpt of Figure IV.4 quoted below, Kurth explained that across measures 5 through 7, the g is reiterated so as to retain it in the ear: “während in den zwischenliegenden Takten 6 und 7 das mit der Bassteigerung … erreichte g durch wiederholtes Antönen im Laufe der melodischen Bewegung im Gehör festgehalten bleibt.” 121 Kurth, Linearer Kontrapunkt , 272. 122 See Kurth, Linearer Kontrapunkt , 307–10. 213 notated them for violin and keyboard. In the latter, the different polyphonic voices that Kurth had earlier isolated from the “single line” appear separated on the two staves of the piano transcription. Somewhat oxymoronically, this visual display served Kurth to prove a phenomenon that he ascribed to the psychoacoustic realm, involving the auditory capacities of the listener. Also with respect to the mental retention of constitutive tones in the listener’s mind,

Kurth drew on notation to illustrate his observations. In his Examples 182 and 183, he re-notated select musical passages to show how the re-articulation of the same pitches effectively extended their rhythmic-metrical value in pseudo-acoustic terms (see also Figure IV.11 below).123 Apart from these instances, however, Kurth used graphical annotations of his musical examples scarcely, indicating linear coherence across tones merely through punctual symbols (such as the

“+” sign added above and below specific notes in the above Figure). Again, the listener discerned apparent polyphony aurally, as a phenomenon inherent in the music, without having to rely on visual guidance from a piano transcription or other forms of notation.

From Kurth’s analyses, the decisive parameter to emerge for determining the separation of apparent polyphonic voices is closeness in pitch and register. By the same token, registral disparity can serve—almost forcefully—to tease different voices apart: “In solchen Fällen ist weniger von einer Scheinstimmen-Technik als geradezu von Spaltung der Stimme zu sprechen”

(“In instances like that, we should speak of a separation of the part rather than of a technique of apparent voices”).124

In the example of Figure IV.5 (like in those of Figures IV.3 and IV.4), the linear trajectory that Kurth isolated across the passage connected tones that were exposed as “boundary points” of the musical texture (“Randpunkte der Linienphasen”). Notably, in this example, the

123 See Kurth, Linearer Kontrapunkt , 315–16. 124 Kurth, Linearer Kontrapunkt , 279. The emphasis is original. 214 bass line, which ascends from the opening F-sharp over more than an octave to g in measure 5, transforms into the top voice, progressing to g-sharp on the downbeat of measure 8 and finally to a in the middle of measure 9.

Figure IV.5 : J. S. Bach, Suite for Solo Cello in D minor (BWV 1008), Prelude, mm. 25–33, with added annotations (following Kurth’s analysis of Linear Counterpoint , Example 115) 125

The excerpt of Figure IV.6 illustrates the separation by register yet more plastically.

Based on their registral span and disparity, Kurth discerned three different voices in this passage from Bach’s Partita for Solo Violin in B minor (BWV 1002), as he indicated through the square brackets above and below the staff. In this specific instance, the different voices appear in groups of four notes at a time, without any intervening activity in other voices.

125 Kurth did not annotate this example to reflect his analysis. See Kurth, Linearer Kontrapunkt , 278, Example 115. 215

Figure IV.6 : Ernst Kurth, Linear Counterpoint , Example 119 (J. S. Bach, Partita for Solo Violin in B minor (BWV 1002), Double No. 2, mm. 65–69)126

Overall, Kurth observed that apparent voices usually progressed in a consistent direction, such that a change in direction was perceived as a disruption, as he expressed in the passages quoted earlier. The only exception to this rule occurred in the context of utmost stability in the other voices, such as in his Example 120 (Figure IV.7). In this scenario, the steady reiteration of the pitch a forms a pedal point, against which the other tones are separated out as a different voice, which circulates around the a.127

126 Kurth, Linearer Kontrapunkt , 280. 127 This phenomenon was also possible, Kurth observed, with re-iterated sequential patterns, which similarly created a stable frame of reference. See Kurth, Linearer Kontrapunkt , 303, Example 165. 216

Figure IV.7 : Ernst Kurth, Linear Counterpoint , Example 120 (J. S. Bach, Suite for Solo Cello in G major (BWV 1007), Prelude, mm. 33–37)128

Already the above examples and the typical formations of apparent polyphonic voices that Kurth derived from them demonstrate how this musical phenomenon restricted the freedom of musical development, in order to make the implied polyphony recognizable to the listener. As we saw, the coherence and separation of voices was determined primarily through closeness and distance in pitch. Utmost closeness in pitch is achieved through the re-articulation of the same pitch, as in Figures IV.3 and IV.7. Kurth described such formations as the allusion of a “pedal point” (“Andeutung von Orgelpunktstimmen”). 129 The next closest increment in pitch after the repetition of the same tone was a progression by step-wise motion. A predilection that we also encountered in Chapter III in the theories of Friedrich August Kanne and Ernst Toch, this form of melodic trajectory similarly dominated the passages that Kurth chose to highlight in his

128 Kurth, Linearer Kontrapunkt , 280. 129 Kurth, Linearer Kontrapunkt , 294–302. Considering that the phenomenon entails the extension of the same tone across longer passages of music, the use of “point” in the designation “Orgelpunkt” is somewhat ironic. 217 musical examples. As mentioned earlier, most apparent voices in the examples that Kurth considered as “Scheinpolyphonie” either proceed by step-wise motion, or propagate in a step- wise sequential pattern. Kurth called such apparent voices “diatonic” (“diatonisch”), in distinction from “chordal” (“akkordisch”), and “cadential” (“kadenzartig”) progressions. For

Kurth, chordal patterns arpeggiated across tones of the same harmony (as we saw earlier in

Figure IV.3, in what Kurth also described as “chordal curvatures”). Of course, such patterns could be combined with step-wise progressions, as the upper-voice of that example illustrated. 130

More specifically, Kurth discussed how sequences of broken thirds or sixths could be understood as parallel simultaneous intervals, thereby separating them out into the super-imposition of two parallel scalar runs. 131

Cadential lines, meanwhile, imitated the voice leading typical of bass parts (“Andeutung von Harmonie-Basstimmen”). 132 In Kurth’s understanding, this involved mostly leaps of fourths and fifths. Indeed, the horizontal trajectory that Kurth visualized for such bass lines led him to identify matching progressions even when they lacked the harmonic support that is usually associated with them. In his Example 139 (not reproduced), for instance, from the Courante of the Cello-Suite in C major (BWV 1009), Kurth singled out what he called a “cadential voice” and annotated how it progressed by fifths in alternation with thirds ( E – a – F – b-flat – G – F).

However, harmonically, the passage merely oscillates between the arpeggiation of an F major triad and its applied half-diminished seventh chord on e. The constitutive tones of the linear progression that Kurth isolated from the musical texture thus vary with respect to their harmonic

130 More examples of such interlocking patterns are provided in Kurth, Linearer Kontrapunkt , 289–90, Examples 133–36. 131 See Kurth, Linearer Kontrapunkt , 266, Example 88. 132 “Besondere Wirkung erzielt aber Bach durch Andeutung von Basstimmen nach Art von Harmoniebässen; vorspringende tiefe Töne lassen eine kadenzierende Basstimme in den linearen Zusammenhang hineinklingen, meist in den typischen Quart- und Quintsprüngen, die eine Bassführung kennzeichnen.” Kurth, Linearer Kontrapunkt , 289. 218 weight and function. 133 In other instances, however, Kurth proved more sensitive to harmonic considerations, for instance, when he analyzed how the effect of melodic dissonances (such as leading-tone relations) could be heightened by delaying their expected resolution through the interpolation of further melodic material. 134

Notably, within this classification of observed patterns, Kurth reserved the designations

“line” and “linear” mostly (though not exclusively) for step-wise progressions, while other patterns arise as “formations,” “contours,” “voices” (“Bildungen,” “Umrisse,” “Stimmen”), and the like. 135 These terminological decisions solidify the commonalities of Kurth’s theory with those of his contemporaries such as Schenker and Toch. The perspectives of all three theorists once again find a strong epistemic foundation in contemporaneous advancements in Gestalt- psychological research.

The Gestalt Theory of Apparent Polyphony

As mentioned above, Luitgard Schader has drawn a connection between Kurth’s thought and the work of Gestalt theorist Max Wertheimer. In addition to Wertheimer’s study on the perception of motion, which I discussed above, Schader points to his Untersuchungen zur Lehre von der Gestalt (1922–23). In this publication, commonly considered a cornerstone in Gestalt- theoretical research, Wertheimer put forward a number of situational laws to explain propensities

133 Especially since Kurth picked out the tones of the line from within the middle of the texture and from varying metrical positions, this analytical example is amongst his least convincing. Such examples fuelled the critical reception of Kurth’s treatise, which, as I discussed in earlier chapters, focused a lot of attention on the question of harmonic support to Kurth’s linear thinking. 134 Kurth, Linearer Kontrapunkt , 268–71. 135 “Rundungen von Scheinstimmen über akkordliche Umrisse ,” “In allen diesen Fällen nahmen die geschlossenen melodischen Zusammenhänge zwischen den vorspringenden Punkten die Form diatonisch steigender oder fallender Linien an. Indessen verbindet Bach oft die Wirkung einer angedeuteten zweiten Linie mit einer Füllwirkung in harmonischen Sinne, indem die vorspringenden Punkte unter sich akkordlichen Bildungen angehören.” Kurth, Linearer Kontrapunkt , 286. The emphasis is mine. 219 in the perception of Gestalt entities. 136 Recall that Wertheimer, like other theorists of the Berlin school of Gestalt theory, assumed the coherence of Gestalt perception as an a priori condition to his inquiries. This premise distinguished these theorists from earlier thinkers such as Ehrenfels.

Rather than justifying that we draw together multiple stimuli into larger entities, Wertheimer addressed the internal logic of these entities.

Wertheimer explained that in his studies, which draw on experiments conducted in 1911–

14, he sought to illuminate the principles that accounted for the internal cohesion or separation of

Gestalt perceptions: “Gibt es Prinzipien für die Art so resultierender ‘Zusammengefasstheit’ und

‘Geteiltheit’? Welche?” (“Are there principles [to account for ] such resulting ‘cohesion’ and

‘separateness’? Which ones?”). 137

While he demonstrated his insights primarily through visual illustrations, Wertheimer expressed this leading question of his essay in musical terms:

Ich höre eine Melodie (17 Töne!) mit ihrer Begleitung (32 Töne!). Ich höre Melodie und Begleitung, nicht einfach “49” oder wenigstens gewiß nicht normaliter oder ganz nach Belieben 20 plus 29. 138 I hear a melody (17 tones!) with its accompaniment (32 tones!). I hear melody and accompaniment, not just “49” [tones ], or certainly not normally, or just at will 20 plus 29.

This way of presenting the problem mirrors precisely the task that Kurth faced in trying to explain the ways by which a listener might be able to appreciate the apparent polyphony in

Bach’s repertoire for unaccompanied string instruments. Much like Wertheimer, Kurth

136 Wertheimer himself positioned his studies as the summary and continuation of earlier scholarship on similar issues, as he indicated in a footnote. Wertheimer, “Untersuchungen zur Lehre von der Gestalt, II”: 302–3n3. 137 Wertheimer, “Untersuchungen zur Lehre von der Gestalt, II”: 302. In addition to his use of the term “Zusammengefasstheit,” Wertheimer referred to Georg Elias Müller’s research on the “Kohärenzgrad” in sensory perception, as presented in Müller, “Die Gesichtspunkte und die Tatsachen der psychophysischen Methodik,” Ergebnisse der Physiologie 2, no. 2 (1903): 267–516. This use of “coherence” offers an additional backdrop to the metaphors in Kurth’s language, besides the chemical and physical allusions that scholars like Krebs have pointed out. 138 Wertheimer, “Untersuchungen zur Lehre von der Gestalt, II”: 301. 220 confronted the compositions as holistic entities and isolated from them their constitutive polyphonic voices.

Based on this foundational correspondence, I propose to further concretize the resonances between Wertheimer’s and Kurth’s ideas that Schader has started to describe. This will moreover underscore my reading of the functionality of the line in Kurth’s thought. Among Wertheimer’s

Gestalt-theoretical principles, Schader has highlighted in particular two for their congruence with

Kurth’s theory: the “factor of proximity” (“Faktor der Nähe”), and the “factor of common fate”

(“Faktor des gemeinsamen Schicksals”). In the accompanying illustrations, Wertheimer depicted these principles through different graphical arrangements of dots. For the “factor of proximity,” a row of dots with alternating distances between them demonstrates that we prioritize elements close to one another over those more distantly dispersed when drawing multiple stimuli together into larger, holistic perceptions (see Figure IV.8)

Figure IV.8 : Max Wertheimer, illustration of the “factor of proximity,” from “Untersuchungen zur Lehre von der Gestalt” 139

The “factor of common fate,” meanwhile, proclaims that points in similarly exposed positions on a plane are perceived as connected, as well as when they are organized along an imaginary straight line, which might deviate from the normative horizontal or vertical orientation

(see Figure IV.9).

139 Wertheimer, “Untersuchungen zur Lehre von der Gestalt, II”: 304. 221

Figure IV.9 : Max Wertheimer, illustration of the “factor of common fate,” from “Untersuchungen zur Lehre von der Gestalt”140

With respect to the latter, Schader proposes succinctly how Kurth’s isolation of apparent polyphonic voices from Bach’s music enacted the logic of Wertheimer’s conclusion in multiple ways: not only by connecting tones that were exposed in pitch from across the musical texture, but also in proposing that their coherence extended as long as they progressed in a uniform direction of melodic motion.

Die Töne, oder Motive, solcher Scheinstimmen müssen eine markante Übereinstimmung besitzen, um als separate Stimme gehört zu werden. Dies kann die extreme Lage sein, eine Tonwiederholung, es können auch rhythmische Figuren sein, wesentlich ist lediglich, daß der Hörer ihr typisches Merkmal erkennt, dann werden solche physikalisch separaten Töne als geschlossenes Ganzes wahrgenommen.141 The tones, or motives, of such apparent voices have to exhibit a distinctive correlation in order to be heard as a separate voice. This can be achieved through their extreme position, through a repetition of tones, it could be through rhythmical figures. It is only essential that the listener recognize their typical quality. Then such physically separate tones are perceived as a coherent whole.

Schader’s reading is geared at the holistic perception of such apparent voices, across the spans of music from which the participant tones are isolated. That same concern also drives

Schader’s interpretation of the ways in which she conceives the “factor of proximity” to play out in Kurth’s thinking. Here, she refers to Kurth’s earlier essay on the “Motivbildung Bachs”

140 Wertheimer, “Untersuchungen zur Lehre von der Gestalt, II”: 305. See also the illustrations on the following pages of Wertheimer’s text, esp. 304–13. 141 Luitgard Schader, “Ernst Kurth und die Gestaltpsychologie,” 180. The emphasis is original. 222

(1917), in which he argued that motives in Bach’s music appear as coherent units rather than the sum of its component tones. 142 This understanding certainly reflects Gestalt-theoretical thinking, but not necessarily Wertheimer’s theory, let alone the specific “factor of proximity.” It seems rather more reminiscent of Ehrenfels’s pioneering approach.

Where Schader’s interpretation is indebted to Ehrenfels, it is my contention that

Wertheimer’s formative principle of proximity finds a much closer correlation in Kurth’s theory of apparent polyphony, and here in particular in the precedence given to step-wise melodic progressions, as highlighted above. We have seen how the primacy assigned to scalar trajectories in melody was shared among the music theorists considered, including Kanne, Toch, and

Schenker. These music theorists thus intuited in their linear-melodic conceptions a principle that

Wertheimer formulated in psychological terms. Conversely, the factors that Wertheimer codified for the perception of cognitive entities can illuminate critical aspects of these music-theoretical approaches. To start, as Schader rightly emphasizes, the melodic structures featured in these theories had to be distinctively defined so as to be readily discernable by the listener. The linear melodic trajectories featured in these three theories, specifically their step-wise internal organization, can all be classified—in different ways—as precisely such recognizable formations. Such a taxonomical limitation to a set of predefined patterns thus arises as a common cognitive condition to all these music theories alike.

This constraint is all the more decisive the further removed from the surface of the music the respective theorist is operating from. To explicate that point, let us return to the two dimensions of music—horizontal and vertical—that I addressed in Chapter I and that Kurth referred to in his historical narrative. Wertheimer’s principle of proximity could be enacted along

142 Schader, “Ernst Kurth und die Gestaltpsychologie,” 179, referring to Ernst Kurth, “Zur Motivbildung Bachs. Ein Beitrag zur Stilpsychologie,” Bach-Jahrbuch 14 (1917): 92. 223 both axes: in the vertical dimension to denote closeness in pitch, as proposed above, and in the horizontal dimension, relating to closeness in the temporal order. In the three theories of Toch,

Kurth, and Schenker, this latter dimension is treated at different scales. As we saw in Chapter III,

Toch derived his Tonhöhenlinie from the immediate succession of tones as they occurred on the musical surface. Here, Wertheimer’s principle could unfold equally in both dimensions. By comparison, Kurth assumed a more removed perspective in his analysis of apparent polyphony, when parsing the musical texture into its constitutive polyphonic voices. Schenker expanded the scope of this approach yet further, with the Urlinie connecting temporally remote tones into a coherent unit.

The long timespan between two consecutive tones of the Urlinie indeed provoked suspicion even among contemporary readers of Schenker’s theory, who wondered how one could possibly perceive a strain of coherence across these dispersed moments in the musical work.

After all, especially the span between an initial scale degree ^3 and the ensuing descent to ^2 in the background Ursatz could extend across virtually the entire duration of a symphonic or sonata movement. Schenker countered these concerns through the concept of “fernhören,” conjuring a mental capacity of the listener to draw on memory and anticipation in order to perceive a connection between these tones. 143 Through the invocation of “fernhören,” Schenker thus accounted for the holistic analytical structures that the Urlinie uncovered across entire

143 For a commentary on the possible origins of Schenker’s term, see Ian Bent’s note in Heinrich Schenker, Der Tonwille. Pamphlets in Witness of the Immutable Laws of Music: Offered to a New Generation of Youth , ed. William Drabkin, trans. William Drabkin and Ian Bent, 2 vols. (Oxford; New York: Oxford University Press, 2004), 1: 164. Steve Larson relates the term to Felix Salzer’s notion of “structural hearing.” Steve Larson, Musical Forces: Motion, Metaphor, and Meaning in Music (Bloomington: Indiana University Press, 2012), 326. See also Felix Salzer, Structural Hearing: Tonal Coherence in Music (1952; repr., New York: Dover, 1982). 224 compositions, presenting a “total hearing” of the work. 144 The idea is similar to what Kurth articulated in the quotation earlier about the listener’s ability to retain tones of a linear progression and connect them across moments of interruption with the resumption of the melodic trajectory. The Gestalt-theoretical foundations of these conceptions are hard to overlook. In particular, Wertheimer’s factor of proximity informs the melodic schemes through which both music theorists defined the specific pitches that the listener had to expect to continue the respective linear trajectories.

Schenker’s approach balanced out the limits of these principles. While he maximally extended the temporal span of the involved mental faculties, he narrowed down the predefined patterns of the Ursatz to highly circumscribed structures. The equilibrium achieved between these provisions indeed offers another plausible explanation as to why Schenker eventually limited the possible forms of the Ursatz in his last monograph Free Composition to encompass only three different descending Urlinien , starting variably from scale degrees ^8, ^5, or ^3. 145

Compared to the balance achieved between these two extremes, Kurth took a medial, and at once more diversified approach. In addition to the linear-melodic patterns that Kurth classified as typical formations of apparent polyphony, he analyzed how Bach’s compositions for

144 Within the extensive scholarship on Schenker’s thought, see for instance Bojan Bujic, “Delicate Metaphors,” Musical Times 138, no. 1852 (1997): 18, for some ideological considerations around Schenker’s concept, and the invocation of “total hearing.” Leslie Blasius discusses resonances with psychological research from the turn of the century in Schenker’s approach in Blasius, Schenker’s Argument and the Claims of Music Theory (Cambridge, UK: Cambridge University Press, 1996). Larson adopts some of the psychological implications of Schenker’s thought into a more presentist outlook on musical experience and discourse. Larson, Musical Forces: Motion, Metaphor, and Meaning in Music . 145 Unlike his earlier publications on the Urlinie , Schenker’s highly influential monograph Free Composition includes only these three descending forms. Heinrich Schenker, Der freie Satz: das erste Lehrbuch der Musik , 2 vols., Neue musikalische Theorien und Phantasien 3 (Vienna: Universal-Edition, 1935). From the vast literature on the evolution of Schenker’s theory, see for instance Suzannah Clark, “Schenker’s Mysterious Five,” 19th-Century Music 23, no. 1 (July 1999): 84–102, Matthew Brown, Explaining Tonality: Schenkerian Theory and Beyond (Rochester, NY: University of Rochester Press, 2005), and Robert P. Morgan, Becoming Heinrich Schenker: Music Theory and Ideology (Cambridge: Cambridge University Press, 2014). 225 unaccompanied violin equally comprised the full array of contrapuntal compositional techniques.

These included the presentation of fugal subjects and countersubjects, the derivation of motives from the subject, and invertible counterpoint. The fugue movement of Bach’s Sonata for Solo

Violin in C major (BWV 1005), of which he included two full episodes as excerpts in his treatise

(Kurth’s Examples 181 and 186), served as Kurth’s primary example to showcase these possibilities. 146

In these examples, yet different Gestalt-theoretical principles are at play. Especially with regards to recognizing the fugue subject when it is embedded in a stream of eighth-note figurations, Ehrenfels’s theory as presented in his “On ‘Gestalt Qualities’” (1890) appears most pertinent. As discussed in Chapter I, in this pioneering article, Ehrenfels tackled precisely the question as to how a melody could be recognized in different musical contexts. While Ehrenfels considered specifically the possibility of transposition to a different key or register, other theorists soon explored the application of these insights to other musical circumstances, such as timbre and performance style. 147 The musical contexts of Bach’s fugue movement for solo violin might be yet more diverse than the situations that Ehrenfels considered in his work. But his theory still offers a powerful lens to understand the recognizability of the fugue subject in its varied appearances. In his Examples 182 and 183 (Figures IV.10–11), for instance, Kurth first reproduced the fugue subject as a point of reference, identifying it as the choral theme “Komm, heiliger Geist, Herre Gott.” He then demonstrated how this theme is hidden within the chain of eighth notes in a later passage of the movement (Figure IV.11).

146 For Kurth’s analysis of this movement, see Kurth, Linearer Kontrapunkt , 313–22. The pagination and numbering of these examples deviate from the first edition of the treatise. For the edition of 1922, Kurth inserted an extra example (the new Nr. 180, on p. 312–3), before he turned to the discussion of the C major fugue. 147 See Schader, Ernst Kurths “Grundlagen des linearen Kontrapunkts,” 58–59, referring to Wilhelm Jerusalem’s adaptation of Ehrenfels’s theory in Jerusalem, Einleitung in die Philosophie (Vienna: W. Braumüller, 1903). 226

Figure IV.10 : Ernst Kurth, Linear Counterpoint , Example 182 (J.S. Bach, Sonata for Solo Violin in C major (BWV 1005), fugue subject) 148

Figure IV.11 : Ernst Kurth, Linear Counterpoint , Example 183 (J.S. Bach, Sonata for Solo Violin in C major (BWV 1005), fugue subject within eighth-note figurations, mm. 171–74)149

As explained earlier, through the notational differentiation in his Example 182, Kurth also sought to illustrate the rhythmical extension of select tones through their re-articulation, and thereby to highlight the horizontal coherence of the theme as a single linear thought.

Perhaps it is just a coincidence that this fugue subject and its countersubject (which enters in the lower voice in measure 4 of Figure IV.10), too, progress primarily by step-wise motion.

Their compositional enactment is certainly more diverse than the motives in the examples of apparent polyphony that we encountered earlier. But from a Gestalt-theoretical perspective, all

148 Kurth, Linearer Kontrapunkt , 315. 149 Kurth, Linearer Kontrapunkt , 316. 227 these musical excerpts evoke similar techniques of the listener to appreciate their polyphonic essence, whether real or apparent.

Indeed, the same cognitive abilities are also needed when listening to “real” polyphonic textures, such as in Bach’s contrapuntal repertoire for keyboard instruments. Similarly with this repertoire, the listener is tasked with discerning the different polyphonic voices as they develop simultaneously. Notably, the Gestalt-psychological and cognitive theories through which I framed the discussion of Kurth’s ideas offer further guidance for such a listening experience as

Kurth envisioned it. They at once direct the listener’s attention to the linear-horizontal trajectories in music, just as Kurth argued that Bach’s music should be heard and understood.

With the exception of such examples as shown in Figures IV.10 and IV.11 above, Kurth conveyed his theory for the most part through words rather than graphical illustrations. As I have argued, the line constituted a central metaphor and imagery for Kurth’s rich theoretical framework of Linear Counterpoint , encapsulating the profusion of aesthetic connotations that he described about the perception of melody. While harnessing qualities of the line that are associated with its visual appearance, Kurth employed the line as an essentially invisible image across the treatise, to capture sensations and cognitive processes.

In the next chapter, I turn to visual artistic renderings of Bach’s music that transfer

Kurth’s framework and its analytical perspective on Bach’s polyphony into a profoundly graphical realm.

228

V. PERFORMING MUSIC (A NALYSIS ) WITH PEN , PAPER , AND STEEL :

ARTISTIC RENDITIONS OF MUSIC AT THE BAUHAUS

To “visualize” implies more than simply seeing, it implies “making” something that can be seen—a bringing to visibility. As such it implies a certain kind of comprehension through conceptualization and it affords a kind of “sharability.” Practically, visualizing allows us to point—literally or figuratively—to the thing and share thought about that thing with others. And, in the case of music, it means engaging the object in a way different from the way it is primarily apprehended––a visible thing is used to take account of a heard thing.1

In Chapter I, I portrayed how the scientific and philosophical conditions of the early twentieth century stimulated the convergence of aesthetic ideas across art forms and media. I introduced the Bauhaus as Germany’s highly influential hub of such aspirations in the 1920s, and one of the defining schools of European Modernism. 2 Artists at the Bauhaus pursued an inter- medial aesthetic agenda, which was founded on the belief that every artistic idea could be expressed in any kind of format or medium. As prominent artists and teachers, Bauhaus- members Wassily Kandinsky and Paul Klee, for instance, explored in their lectures and treatises the ways in which the foundational graphical elements—point, line, plane, and color—could function not only across all forms of visual expression, but also encompassing music and dance. 3

As I indicated, these efforts grew out of the perception that the visual arts were lagging behind music and dance in variety and efficiency of expressive means. The experiments, in which the

1 Judy Lochhead, “Visualizing the Musical Object,” in Postphenomenology: A Critical Companion to Ihde , ed. Evan Selinger (Albany: State University of New York Press, 2006), 68. 2 The Bauhaus school existed from 1919–33 and during that time span moved between three locations. The school was first established in Weimar (1919–25), moved to Dessau (1925–32), and finally relocated to Berlin (1932–33) before being closed, giving in to pressure from the Nazi-regime. 3 Paul Klee, Pädagogisches Skizzenbuch , Bauhausbücher 2 (Munich: Albert Langen, 1925), Wassily Kandinsky, Punkt und Linie zu Fläche: Beitrag zur Analyse der malerischen Elemente , Bauhausbücher 9 (Munich: Albert Langen, 1926). Both treatises were published as part of the book series edited at the Bauhaus. 229 artists explored the connotations and functions that these basic graphical elements could assume in artistic contexts such as music and dance, were therefore ultimately geared at enriching the expressive vocabulary of specifically visual artistic modes. Kandinsky’s visualization of Ludwig van Beethoven’s Fifth Symphony, discussed in Chapter I, exemplified such an applied examination. I return to that example in the present chapter, and consider two further diagrammatic renderings of specific musical compositions: one by Klee, and one by a lesser- known artist affiliated with the Bauhaus, Henrik Neugeboren.

Art historians have discussed these examples in the capacity described above—as artistic studies with a pedagogical orientation, and with the purpose of deriving and enhancing creative potential from the translation between artistic media on the one hand and from observing the compositional organization of the musical works in question on the other.4 These insights tend to feed back into a narrative centered on the visual arts, while their value for musical discourse goes overlooked. Indeed, since these visualizations manifest a specific analytical and interpretative lens onto the music they depict, I propose that they prove equally relevant and enlightening for examination by music scholars as they have for studies by art historians. In that sense, I read these artistic renderings as musical visualizations, to mean not only “visualizations of music,” but also a “visual lens onto musical culture.” This approach follows from Judy Lochhead’s observation quoted in the epigraph of this chapter—that visualizing (a musical object) always involves a process of “comprehension through conceptualization, [which ] … affords a kind of

‘sharability.’” My analyses of these artistic renditions examine what Kandinsky, Klee, and

Neugeboren had to “share” about the music, founded on the understanding that their engagement with the music was driven by an analytical agenda and an attendant inquisitive rigor. The guiding

4 An illuminating analysis of these examples is Peter Vergo, The Music of Painting: Music, Modernism and the Visual Arts from the Romantics to John Cage (London; New York: Phaidon, 2010), 230–50. 230 questions of my approach are 1) what qualities and organizational principles of the music are captured or highlighted in these displays, 2) in which ways are graphical means employed, and

3) to what ends?

In their visually oriented narratives, art historians have also highlighted the important role that music played at the Bauhaus, not only as part of the theoretical goal of infusing all art forms with a modernist aesthetic, but also in praxis, in the concerts organized at the school, as well as in many of the artists’ private lives. 5 As I review in more detail throughout the chapter, many of the artists active at the Bauhaus were professionally trained as musicians and some maintained a vivid interest in performance throughout their lives. I ask to what extent this performative lens might in fact have influenced their graphical renderings of musical compositions. Ultimately, I argue that these visualizations showcase an intrinsic relation between musical visualization, analysis, and interpretation from an as yet unconsidered perspective.

While each of the three artists developed their own notational system, they all adhered to the graphical vocabulary of conventional staff notation, namely the two elements of the point and the line. 6 This restriction in graphical symbols allows for a thorough comparison, not only among these alternative notational approaches, but also in relation to staff notation. In two out of the three cases, the artists even printed their renderings side by side with the respective excerpts

5 Among the many sources dedicated to the musical activities at the Bauhaus, the following give a good overview: Clement Jewitt, “Music at the Bauhaus, 1919–1933,” Tempo , New Series, no. 213 (July 2000): 5–11; Karin von Maur, The Sound of Painting (Munich: Prestel, 1999); and Peter Vergo, The Music of Painting: Music, Modernism and the Visual Arts from the Romantics to John Cage (New York: Phaidon, 2010). With special attention to Paul Klee, the following monographs discuss his work at the intersection of music and painting: Hajo Düchting, Paul Klee: Painting and Music (Munich: Prestel, 1997); Andrew Kagan, Paul Klee/Art & Music (Ithaca, NY: Cornell University Press, 1983); Christoph Vitali, ed., Paul Klee und die Musik: Schirn-Kusthalle Frankfurt, 14. Juni bis 17. August 1986 (Berlin: Nicolaische Verlagsbuchhandlung, 1986); Régine Bonnefoit, Die Linientheorien von Paul Klee (Petersberg: Michael Imhof, 2009), esp. chap. 8, “Linien im Melos.” 6 Kandinsky analyzed this repertoire of graphical elements used in staff notation in his treatise. “Besonders interessant und bezeichnend ist, daß die heute übliche musikalisch-graphische Darstellung— die Notenschrift—nicht anderes als verschiedene Kombination von Punkt und Linie ist.” Kandinsky, Punkt und Linie zu Fläche , 93. 231 from the musical score. This juxtaposition affords insights into the iconic function assigned to the graphical elements as well as to the musical aspects and parameters emphasized by the different systems. Already on that level, the examples featured below demonstrate how tightly notation is linked to conceptualization.

In relation to the reluctance towards graphical representations of music and music- theoretical conceptions that the previous chapter documented in the work of Ernst Kurth, the artistic visualizations of the present chapter offer a complementary view on the potential and shortcomings of music notation. For the artists, drawing and graphing was the operative mode to gaining insight and knowledge—or “comprehension through conceptualization,” as Lochhead puts it. The “operative” potential of drawing in this context aligns with one of the central functions that Sybille Krämer has cogently theorized for writing, and in particular for drawing lines. 7 Krämer demonstrates how line drawing as a technique of visualization is employed to organize ideas and generate knowledge across various disciplines, for instance in mathematical graphs and multiplication charts. As we shall see from the case studies below, such conceptual processes incidentally led some of the artists to music-analytical insights that correspond closely with Kurth’s theory of Linear Counterpoint . Due to this fortuitous conceptual correlation, these artistic renditions thus illustrate how some of the music-theoretical ideas encountered in previous chapters might be reflected in our imagination.

7 Sybille Krämer, “Punkt, Strich, Fläche: Von der Schriftbildlichkeit zur Diagrammatik,” in Schriftbildlichkeit: Wahrnehmbarkeit, Materialität und Operativität von Notationen , ed. Sybille Krämer, Eva Cancik-Kirschbaum, and Rainer Totzke (Berlin: Akademie Verlag, 2012), 88–96 (esp. “Operativität durch Sichtbarmachung,” 90). Art historian Horst Bredekamp has captured this potential as the “Erkenntniskraft der Linie.” Bredekamp, “Die Erkenntniskraft der Linie bei Galilei, Hobbes und Hooke,” in RE-VISIONEN. Zur Aktualität von Kunstgeschichte , ed. Barbara Hüttel, Richard Hüttel, and Jeanette Kohl (Berlin: Akademie Verlag, 2002), 145–60. 232

From Dots to the Line: Listening through Kandinsky’s Ears

Kandinsky published his treatise Point and Line to Plane in 1926 as part of the book series edited at the Bauhaus. 8 A concise survey of the basic graphical elements across all art forms, the treatise also examines the functionality of these elements with regards to music. It is in this context that Kandinsky declared, “everyone knows what a musical line is,” that auspicious proposition that I probed in the introduction. 9 In that discussion, I also proposed to read the graphical example that Kandinsky conjured in support of his claim (his Figure 11, of which two parts are reproduced as Figures I.2 and I.3) through the lens of Gestalt theory. From that viewpoint, Kandinsky’s visualization could be construed as depicting the listener’s experience of the music. I now return to this example to substantiate my reading in more detail, and to excavate another interpretive layer of it.

Dedicated to four brief excerpts from the first movement of Beethoven’s Fifth

Symphony, op. 67, Kandinsky’s Figure 11 constitutes the primary musical example across Point and Line to Plane . Kandinsky used the process of graphical translation to explore which of the musical parameters he could render most effectively through the point and the line. As I observed in Chapter I, the predilection for the point in the Figure’s first three parts was predicated by a property of the musical excerpts, namely the repetition in pitch. The last part finally featured a graphical line, to depict the symphony’s second theme.

These graphical explorations are paired—albeit in a different part of Kandinsky’s treatise—with reflections about the conventional system of music notation, and ideas for

8 Wassily Kandinsky, Punkt und Linie zu Fläche . 9 “Es ist bekannt, was eine musikalische Linie ist (siehe Bild 11).” Kandinsky, Punkt und Linie zu Fläche , 107: The emphasis is original. 233 alternative models. 10 For instance, Kandinsky proposed to use colors to denote differences in timbre, and, more unconventionally, to apply different degrees of thickness in the line to suggest register:

Die Tonhöhe der verschiedenen Instrumente entspricht der Breite der Linie: eine sehr dünne wird von der Geige, Flöte, Pikkolo hervorgebracht; eine etwas dickere — von der Altgeige, Klarinette; und man gelangt über die tiefen Instrumente zu immer breiteren Linien, bis zu den tiefsten Tönen der Baßgeige oder Tuba. Außer in ihrer Breite wird die Linie auch in ihren farbigen Arten von der mannigfaltigen Farbigkeit verschiedener Instrumente erzeugt. 11 The register of the various instruments corresponds to the width of the line: a very fine line represents the sound produced by the violin, flute, piccolo; a somewhat thicker line represents the tone of the viola, clarinet; and the lines become thicker via the deepest instruments, finally culmunating in the thickest line representing the deepest tones produced by the double bass or the tuba. Aside from its width, the line is produced in its colour variations by the diversified timbral character of different instruments. 12

For obvious reasons, Kandinsky enacted neither of these propositions in his Figure 11. For one, the treatise was printed in black and white only, thwarting the representation of (tone-)color. And rather than showing register through thickness, Kandinsky resorted to the much more common orientation by the metaphor of “height” in “pitch space” as he observed as the operative principle in staff notation for the representation of pitch. 13

Kandinsky’s commentary and his observations regarding staff notation illuminate his critical awareness of notational practices, his analytical approach, and his will to find genuine alternatives. He framed these visions with an admiration for the efficiency and efficacy of staff

10 As I explain in Chapter I, the dissociation between these two aspects in the layout of the treatise is due to the organization by graphical elements of increasing size. While Figure 11 is printed in the section dedicated to the point, Kandinsky’s theoretical reflections are part of the section on the line. 11 Kandinsky, Punkt und Linie zu Fläche , 92. 12 Translation adopted and amended from Wassily Kandinsky, Point and Line to Plane: Contribution to the Analysis of the Pictorial Elements , trans. Hilla Rebay and Howard Dearstyne (New York: Solomon R. Guggenheim Foundation, 1947), 98. 13 “Ebenso wird die Höhe linear gemessen, wobei fünf Horizontale die Grundbasis bilden.” Kandinsky, Punkt und Linie zu Fläche , 93. (“The pitch is likewise measured in lines, and five horizontals form the basis of this.” Kandinsky, Point and Line to Plane , 99.) 234 notation, which is able to convey even the most complex sonic phenomena unequivocally to the trained reader:

Lehrreich ist die erschöpfende Knappheit der Übersetzungsmittel und ihre Einfachheit, welche die kompliziertesten Klangerscheinungen in deutlicher Sprache dem kundigen Auge (indirekt dem Ohr) vermittelt. Diese beiden Eigenschaften sind für die anderen Künste sehr verlockend.... Aber auch hier gibt es nur einen Weg—analytische Teilung auf Grundelemente, um schließlich zu eigenem graphischen Ausdruck zu gelangen. 14 Particularly instructive is the exhaustive concision of the means of translation and the simplicity [of staff notation ], which convey the most complex sound phenomena in clear language to the experienced eye (indirectly to the ear). Both of these characteristics are very alluring for the other forms of art…. There is, however, only one way to arrive finally at their own graphic expression—analytic separation into fundamental elements. 15

As Kandinsky concluded, the formation of new systems of graphical expression had to start with the “analytical separation into fundamental elements,” like the point and the line. These two elements could then be defined anew in their notational capacities, as Kandinsky did in his depictions of Beethoven’s Fifth Symphony.

By printing his own visualizations of the music below a reproduction of the excerpts from the score (reduced to a single staff), Kandinsky created the conditions for a direct comparison between notational systems (see Figures I.2 and I.3). While the juxtaposition of visual renderings might at first glance appear redundant, this format only facilitates the analytical ambitions that

Kandinsky announced, exposing how the graphical elements were used in the different notational contexts, and perhaps even to what extent the two systems might be complementary. Notably,

Kandinsky did not “translate” from one form of visual representation of the music directly to another, as his annotation might suggest, reading “the same, translated into points.” Rather, the object of Kandinsky’s translation was music as sound. This becomes clear very quickly upon closer analysis. Already the vertical misalignment between the note-heads in the score and the

14 Kandinsky, Punkt und Linie zu Fläche , 93. 15 Kandinsky, Point and Line to Plane , 99, translation amended. 235 dots on the white background in Figure I.3 speaks to Kandinsky’s approach: He focused only on what is indeed sounding, unlike Beethoven who notated an eighth-note rest to open the symphony. Moreover, Kandinsky distributed the graphical elements quite freely across the paper.

This is particularly conspicuous with respect to the two groups of eighth notes in measures 1 and

3. In staff notation, the spacing of these eighth notes is identical in both instances. But in

Kandinsky’s image, the three dots of the second group are placed further apart from one another than are those in the first group. This suggests that Kandinsky heard the second group at a broader tempo.

Instances like this expose Kandinsky as an interpreter, with his own very specific hearing of the symphony. Indeed, in a footnote printed underneath the Figure in his treatise, he acknowledged that his interpretation of the symphony was informed not only by his own musical experience, but also through the consultation with conductor Franz v. Hoesslin.16 Hoesslin conducted the orchestra at the theater in Dessau from 1923–26, and thus overlapped with

Kandinsky in the same city for a year when the Bauhaus relocated to Dessau in 1925. Further aspects that specify Kandinsky and Hoesslin’s interpretation pertain to details that the score leaves open. With regards to the fermata tones in measures 2 and 4–5, for example, a conductor interpreting the symphony has to decide about their duration and relation to one another, as well as their dynamic profile. Already in these facets, interpretations of the symphony take infinite nuances, while sharing as their common backdrop the information relayed by the score.

Across the performance history of the symphony, conductors, music theorists and critics have attempted to circumscribe these interpretative possibilities by proposing normative—yet, of

16 “Bei diesen Übersetzungen ist mir Herr Generalmusikdirektor Franz v. Hoesslin mit seiner wertvollen Hilfe beigestanden, wofür ich ihm meinen herzlichen Dank ausspreche.” Kandinsky, Punkt und Linie zu Fläche , 39: (“In making these translations, I received the valuable aid of Music Superintendant Franz v. Hoesslin and for this I extend him my heartfelt gratitude.” Kandinsky, Point and Line to Plane , 45.) 236 course, historically fluctuating—guidelines for these and the many other questions that the symphony poses to its interpreters (much as any other composition). In close historical proximity to Kandinsky’s rendition, Felix Weingartner’s monograph On the Performance of Beethoven’s

Symphonies serves as an authoritative source of reference for the performance aesthetics of the time. 17 From a historically removed vantage point, Gunther Schuller’s comprehensive essay

“Beethoven: Fifth Symphony” reviews a vast spectrum of interpretive possibilities and recorded renditions, while presenting his own performance suggestions. 18 Both Schuller and Weingartner based their judgment on their own structural analyses of the score. While both conductors advocated a rendering in which the second fermata of the symphony’s opening motto is held longer than the first—but not necessarily twice as long—their interpretative preferences depart from one another in many other regards.

In comparison to the interpretative flexibility that the score affords, Kandinsky’s visualization conveys a possible interpretation of the music. Through the spacing of the graphical elements and the extension of the triangular shapes, formed by the dotted lines that extend from the larger dots and merge on their right, Kandinsky specified the duration of the fermata tones in relation to the groups of eighth notes and in relation to one another. Conforming to Schuller’s and Weingartner’s advice, the second fermata in Kandinsky’s interpretation is about twice as long as the first one. Apart from indicating the duration of the fermata-tones, the triangular shapes also imply a gradual fading of these sounds, much like the hairpin signs commonly used to denote diminuendos. But since the score does not give any indication regarding the dynamic

17 Felix Weingartner, Ratschläge zur Aufführung der Symphonien Beethovens (Leipzig: Breitkopf & Härtel, 1906). A translation of the essay on the Fifth Symphony can be found in Weingartner, On the Performance of Beethoven's Symphonies trans. Jessie Crosland (New York: Kalmus, 1906), 60–85. See also Weingartner, Über das Dirigieren (Leipzig: Breitkopf & Härtel, 1905). 18 Gunther Schuller, “Beethoven: Fifth Symphony,” in The Compleat Conductor (New York: Oxford University Press, 1997), 109–229. 237 shape of these tones, Kandinsky’s interpretation is again only one out of many. Some recorded performances document renditions that shape these tones with diminuendos, as Kandinsky suggested, and others that sustain them at a fairly constant volume.

Among the instances of interpretive license that Kandinsky and Hoesslin took over the information imparted by the symphony’s score, one detail in particular situates their hearing within the performance aesthetics of their time. Weingartner’s monograph reveals that he perceived the particular case of dragging the tempo in measure 3 as ill-advised tackiness of his time. Weingartner used the example of this musical passage to reprimand a group of contemporaneous conductors for their misguided urge to imitate Hans von Bülow’s idiosyncratic conducting style through an excessive and overly free use of rubato. He observed that dragging the tempo in measure 3 diverted from the phrasing and expressive potential already inherent in the composition. 19 A number of historical recordings demonstrate that in the early twentieth century, such an interpretation of the symphony was not uncommon, such as Franz Schalk with the Vienna Philharmonic Orchestra (1929), Wilhelm Furtwängler with the Berlin Philharmonic

Orchestra (1926), and the recording by Arthur Nikisch with the Berlin Philharmonic (1913).20

Therefore, while Kandinsky’s interpretation would not have found Weingartner’s approval, at least the painter was in illustrious company with some of the leading conductors of his time.

Kandinsky’s image thus inscribes a trace of performance practice. Not unlike the visual artifact of a reproducing piano roll, which encodes a specific musical performance, the understanding of Kandinsky’s visualization relies on being already familiar with the music.

19 Weingartner, Über das Dirigieren , 28 and 38–39. 20 Frank Schalk, cond., Symphony No. 5 in C minor, Op. 67 by Ludwig van Beethoven, Vienna Philharmonic Orchestra, 1929, HMV C2022, 78 rpm disc. Wilhelm Furtwängler, cond., Symphony No. 5 by Beethoven, Berlin Philharmonic Orchestra, 1926, Polydor 69855/9, 78 rpm disc. Arthur Nikisch, cond. Symphony No. 5 by Beethoven, Berlin Philharmonic Orchestra, 1913, HMV 040786/87, 78 rpm disc. Many more historical recordings are catalogued through the CHARM project at http://www.charm.rhul.ac.uk/discography/search/disco_intro.html . 238

Since Kandinsky did not provide any indication as to an absolute reference in pitch, register, tempo, or dynamics, his visualization cannot stand on its own, but only as an interpretive supplement to the score. The reader’s familiarity with the music—or her ability to familiarize herself with it through the score—is thus a crucial presupposition to the efficacy of Kandinsky’s visualization. With Beethoven’s Fifth Symphony, Kandinsky could of course hardly have chosen a better-known piece. The work sustained a continued reception and performance history throughout the nineteenth century and constitutes a staple in the repertoire of Western music to the present day. 21

This precondition of familiarity with the composition becomes even more pertinent in the last part of Kandinsky’s visualization, which depicts the entrance of the second theme, as it emerges in the wake of the symphony’s opening motto (see Figure I.2). Here, Kandinsky’s method of inscription deviated further still from conventional music notation. In comparison to the regularly incremented note heads on the staff, Kandinsky’s visualization takes on a quite autonomous shape. Even though the excerpt is still unfittingly labeled as “das 2. Thema in

Punkte übersetzt,” (“the second theme translated into points,” like the previous parts of

Kandinsky’s figure that pertained to manifestations of the opening motto), the theme here is conspicuously rendered as a line.

21 David Dennis has discussed many of the interpretations and political appropriations of this composition and the attendant associations that the symphony assumed. Occurring after Kandinsky’s rendition, but relevant to the sonic heritage of readers today, is the example of the call signal that the BBC introduced during the Second World War “for wartime transmissions into the continent.” Its sequence of three short and a long tone became associated variably with the Morse code for the letter “V” (as in “victory”), and with the rhythm of the opening motto of Beethoven’s Symphony. David B. Dennis, Beethoven in German Politics, 1870–1989 (Yale University Press, New Haven, CT, 1996), 170–71. 239

Considering the line as providing “the greatest means of expression in music,”22

Kandinsky exploited this full array—such as variations in curvature, thickness, and acuity—to capture the musical character of Beethoven’s melody, and its contrast to the trenchantly articulated opening motto and its separated dots. In addition to the suggestions quoted above about employing the line’s color and thickness, Kandinsky specified some musical qualities that he envisioned to represent through other variations of the line, such as “the degrees of intensity from pianissimo to fortissimo [which ] can be expressed in an increasing or decreasing sharpness of the line, or in its degree of brilliance.” 23

Examining Kandinsky’s line with an eye to these parameters, we should note first of all that its overall shape delineates the melodic contour within the common two-dimensional notational plane, with the passing of time and pitch height as its two axes. The line does not change color or noticeably vary in degree of brilliance. The most distinct feature that Kandinsky employed to an idiosyncratically expressive effect are variations in the thickness of the line. The line is at its thickest during the opening ascent of a fourth (b-flat’ to e-flat’’ ), which assumes its musical expressivity from being the first upwards leap of the passage and from counteracting the general emphasis on downward motion, which characterized the movement so far. The thickness of Kandinsky’s line relaxes when moving down to the consonant d’’ , only to swell again a little on the way upwards to the melodic climax f’’ , which in itself is phrased without any further emphasis by Kandinsky. The dissonant passing tone e-flat’’ is thus expressed as a moment of higher tension than the melodic highpoint of f’’ , which is harmonically consonant. Notably, the

22 “Es darf behauptet werden, daß in der Musik die Linie den größten Vorrat an Ausdrucksmitteln liefert.” Kandinsky, Punkt und Linie zu Fläche , 92. (“It can be asserted that in music the line supplies the greatest means of expression.” ) Kandinsky, Point and Line to Plane , 99), 23 “Die Stärkegrade vom Pianissimo bis zum Fortissimo können in der zu- oder abnehmenden Schärfe der Linie, bzw. in ihrem Grade von Helligkeit, Ausdruck finden.” Kandinsky, Punkt und Linie zu Fläche , 93. The English translation is adapted from Kandinsky, Point and Line to Plane , 99. 240 expressive variation in thickness, or intensity, occurs along the line, often in moments that lie between the tones. More specifically, because the swelling of the line occurs between the first two tones of the melody ( b-flat’ to e-flat’’ ), and therefore between the articulation of these notes by the performer, the line renders not an acoustic realization of the melody but rather the sort of mental conceptualization a performer (such as Franz v. Hoesslin) would have to envision when playing, by listening ahead.

Viewed as such, the illustration of Figure I.2 documents well the “expressivity” that

Kandinsky ascribed to the line as a notational element. Shaping the moments between the tones as crucial for the expression and coherence of the whole phrase is a quality of the line that exceeds a representation through a row of dots. But not under all circumstances do lines necessarily assume that function. In staff notation, for instance, the slur above the staff indicates the coherence of the theme and in that respect fulfills one of the functions of Kandinsky’s line.

But the slur is conventionally not variable in thickness or shape. The representational function of the point and line are thus conditioned by the notational system in which they are employed. As my analysis showed, Kandinsky similarly used the dots in Figure I.3 to very different effect than the graphical dots symbolizing note heads on the staff. He expressed temporal order through their flexible spacing, whereas he observed how, in staff notation, time was encoded through the combination of dots and lines:

Die Zeit wird dabei ausschließlich an Hand der Farbe des Punktes (allerdings nur weiß und schwarz, was aber auch zur Beschränkung der Mittel führt) und der Zahl der Fähnchenstriche (Linien) erkennbar. 24 The time is recognizable therein only by means of the colour of the point (white and black only, which also leads to the restriction of the means) and the number of flags (lines). 25

24 Kandinsky, Punkt und Linie zu Fläche , 93. 25 Kandinsky, Point and Line to Plane , 99, translation amended. 241

Kandinsky’s visualization of Beethoven’s music illustrates well how points and lines lend themselves to communicating different aspects of nuance when representing music graphically.

While the dots are variable especially in size and placement—marking volume and temporal or rhythmic grouping—the line affords the possibility to communicate nuance with respect to other musical parameters, such as an expressive tonal trajectory across larger intervallic leaps or harmonic tension. As I discussed in Chapter I, both graphical symbols furthermore carry aesthetic and expressive associations, such as coherence and smoothness, which Kandinsky and

Hoesslin employed effectively as well to capture the difference in musical character between the symphony’s two themes.

In terms of showing coherence across the phases of the opening motto, the Gestalt- psychological principles postulated by Christian von Ehrenfels and Max Wertheimer—discussed in Chapters III and IV with regards to Ernst Toch and Ernst Kurth’s theories respectively—come to life again. Indeed, with the motto, the repetition in pitch facilitates a grouping of these tones as a larger entity, following the Gestalt principles that Wertheimer codified. 26 The spacing of the dots along the horizontal axis further assists the patterning of the eight notes into two similar groups of four notes each, as does the variation added by depicting the longer fermata tones as larger dots. Further, Kandinsky’s illustrations enact Ehrenfels’s two fundamental principles defining Gestalt qualities—supra-summativity and transposibility—which highlight the internal coherence of the musical passages and make them recognizable as characteristic entities. As interpretive gestures, these visual marks of an imaginary performance remain contingent on

Beethoven’s actual score in conventional notation.

26 Max Wertheimer, “Untersuchungen zur Lehre von der Gestalt. II,” Psychologische Forschung: Zeitschrift für Psychologie und ihre Grenzwissenschaften 4 (1923): 304. 242

Against the Point in Counterpoint: Lines in J. S. Bach’s Polyphonic Style

The capacity to recognize melodies as holistic entities, as Ehrenfels’s theory of Gestalt quality captured, becomes even more pertinent in musical contexts that feature the superimposition of the same theme upon itself—like the stretto passages of a fugue. Most emblematically, such instances of combinatorial mastery occur in the polyphonic music of

Johann Sebastian Bach. This repertoire, which was at the center of Kurth’s attention, as we saw in the previous chapter, also formed the core of an artistic project published by Henrik

Neugeboren in the Bauhaus-journal in 1929. 27

Neugeboren (1901, Kronstadt–1959, Paris) was a composer and visual artist, who studied briefly at the Bauhaus after having received extensive musical training in Berlin (1921–24) from

Ferruccio Busoni.28 Neugeboren’s other teachers in Berlin included composer Paul Juon and pianist Egon Petri, who assisted Busoni with the edition of Bach’s piano music. In the following two years, Neugeboren was a student in the master class of Nadja Boulanger in Paris. After his studies at the Bauhaus, Neugeboren settled in Paris where he was known—but never really well known—by the name of Henry Nouveau. Neugeboren’s project documents his veneration for

Bach’s musial legacy, a source of inspiration that he shared with his teacher Busoni, as well as with a number of other artists at the Bauhaus. The reverence for Bach’s music upheld by artists, especially at the Bauhaus, has indeed been widely acknowledged. 29 Besides Klee, whom I

27 Henrik Neugeboren, “Eine Bach-Fuge im Bild,” bauhaus: vierteljahr-zeitschrift für gestaltung , 3, no. 1 (January 1929): 16–19. 28 Peter Vergo notes that Neugeboren visited the Bauhaus in 1928 and on that occasion met both Kandinsky and Klee. Vergo, The Music of Painting , 233. 29 The particular attention to the music of Bach among artists at the Bauhaus is the topic of scholarly studies including, Christoph Metzger, “Die künstlerische Bach-Rezeption bei Paul Klee und Lyonel Feininger,” in Musikwissenschaft zwischen Kunst, Ästhetik und Experiment: Festschrift Helga de la Motte-Haber zum 60. Geburtstag , ed. Reinhard Kopiez (Würzburg: Königshausen & Neumann, 1998), 371–85; Karin von Maur, “Feininger und die Kunst der Fuge,” in Kopiez, Musikwissenschaft zwischen 243

discuss later in this chapter, the painter Lyonel Feininger deserves particular mention, who even

took to composing fugues for piano and for organ in a Bachian style. 30 While Feininger expressed his admiration for Bach in musical terms, and professed a general spiritual alliance with the composer that animated his pictorial work, artists across Europe such as František

Kupka, George Braque, and Klee paid homage to the composer in abstract paintings, which often declared the allusion in their titles. 31

Neugeboren expressed the motivation for his project as rendering visible the

“construction” of Bach’s music, in an “instructive” way that was “free of fictions”:

das graphikon hat in der hauptsache den instruktiven zweck, die konstruktion des bachschen werkes unabhängig von fiktionen zu zeigen. 32 primarily, the graphicon has the instructive purpose to show the construction of Bach’s work independently from fictions.

This announcement sounds reminiscent of the call to action that Neugeboren’s teacher Busoni

voiced in his analytical annotations of the The Well-Tempered Clavier , which he had edited for

Schirmer: “Special attention should be paid to the masterly construction of the Fugue.” 33 The

Kunst , 343–58; Vergo, The Music of Painting , esp. chap. 5, “The Art of Fugue;” Peter Vergo, “How to Paint a Fugue,” in Music and Modernism, ca. 1849–1950 , ed. Charlotte De Mille (Newcastle, UK: Cambridge Scholars, 2011), 8–23; Susanne Fontaine, “Ausdruck und Konstruktion: Die Bachrezeption von Kandinsky, Itten, Klee und Feininger,” in Bach und die Nachwelt , ed. Michael Heinemann and Joachim Lüdtke, vol. 3, 1900–1950 (Laaber: Laaber, 2000), 396–426. 30 Sketches and a collected edition of these compositions are hosted at Harvard University’s Houghton Library. Feininger is also reported to have known all of Bach’s The Well-Tempered Clavier from heart. See also Vergo, The Music of Painting , 226–30. 31 Kupka’s famous painting that secured his place within the community of Bach admirers was Amorpha: Fugue in Two Colors (1912). Among Braque’s paintings are Hommage à J. S. Bach (1911–12) and Aria de Bach (1912). See also Vergo, The Music of Painting , 219–26. 32 “Das graphikon hat in der hauptsache den instruktiven zweck, die konstruktion des bachschen werkes unabhängig von fiktionen zu zeigen.” Neugeboren, “Eine Bach-Fuge im Bild,” 16. In the manner typical of the Bauhaus, the entire text is printed in lower-case letters. 33 Ferruccio Busoni, ed., The Well-Tempered Clavichord [Book 1] by Johann Sebastian Bach: Revised, Annotated, and Provided with Parallel Examples and Suggestions for the Study of Modern Pianoforte- Technique (New York: Schirmer, 1894), 51n2. The emphasis is original. Busoni had edited the entire Well-Tempered Clavier between 1894–1915, annotating them with analytical insights and performance instructions. The edition was first published in English by Schirmer in New York (Book 1 [1894], Book 2 [1915]), and later reissued by Breitkopf & Härtel in German in 1915–16. 244 resonances with Busoni’s edition extend to the selection of the two fugues that Neugeboren included in his project: the C major Fugue (BWV 846) and the E-flat minor Fugue (BWV 853) from the First Book. Busoni considered both of these fugues important for their “architectural style” and “architectonic perfection.” 34 While Neugeboren produced a two-dimensional graph of the entire C major Fugue, for the E-Flat minor Fugue, he focused on rendering the fugue’s three stretto passages. The article published in the Bauhaus journal only concerns these latter three excerpts. Because of the extra analytical intervention that went into parsing these stretto passages and the related commentary that Neugeboren provided in his article, they will also be the focus of my discussion. 35 Neugeboren mapped these three passages into two-dimensional graphs, such as the one reproduced as Figure V.1.

34 “Stated briefly, this Fugue is the most important in the Book—perhaps in the whole First Part [of the Well-tempered Clavier ].” Busoni, ed., The Well-Tempered Clavichord [Book 1], 50. Also in the remarks on the C major fugue, Busoni redirected attention to the “architectural style” of the “notable” E-flat minor fugue: “A fugue so architectonically perfect in construction as this will be met with, in the course of Part I, in possibly one other case—that of the notable Eb-minor fugue, whose ‘architectural style’ is, to be sure, entirely different.” Busoni, ed., The Well-Tempered Clavichord [Book 1], 7. 35 The graph of the C major fugue is held at the Bauhaus archives in Berlin. A brief reference to it is made in Metzger, “Die künstlerische Bach-Rezeption bei Paul Klee und Lyonel Feininger,” 374. 245

Figure V.1 : Henrik Neugeboren, visualization of J.S. Bach, Fugue in E-flat minor (BWV 853), mm. 61 ½–66

While the biographical connections that I pointed out above suggest Busoni’s influence on Neugeboren’s project, in his selection of the Fugue’s three stretto passages, Neugeboren evidently relied on his own analysis of the score. Neugeboren’s numbering of thematic entries deviates from those marked in Busoni’s edition. In the description of the graphs in the article,

Neugeboren specified them as comprising the 26 th to 28 th and the 33 rd to 36 th thematic entries respectively. In Busoni’s edition, which annotates the entrances of the subject, its answer, inversion and augmentation—without however numbering them—these entries would have to be numbered as one less in each instance. Thus, Neugeboren must have counted an extra entry somewhere earlier in the fugue that Busoni had disregarded. The most likely candidate for this missing entry (that is accounted for in Neugeboren’s numbering but not in Busoni’s) is the

246 variation of the theme in the alto part in measures 39½–42, which resembles the variation of the theme with dotted quarter notes as it occurs in the soprano in measure 48 with pickup. 36

Neugeboren’s meticulous preparation of the score was part of his declared aspiration to render a “scientifically precise translation [of the music ] into another system,” rather than an

“emotionally charged individualistic reinterpretation.” 37 In his evocation of the scientific allure of Bach’s music and the methodological commitment of his approach, Neugeboren also referred to the work of Wilhelm Werker and Wolfgang Graeser, both of whom had portrayed what they called the “mathematical” qualities of Bach’s music: its combinatorial construction and aspects of symmetry. 38 Both Werker and Graeser illustrated their analyses of Bach’s music graphically.

A similar approach also features in Iwan Knorr’s textbook The Fugues from Joh. Seb. Bach’s

Well-Tempered Clavier Graphically Depicted (1912), which Peter Vergo cites as another possible reference to Neugeboren. 39 As the title of that monograph suggests, Knorr used diagrams to analyze and depict structural features of Bach’s polyphonic compositions. 40 As

Vergo correctly emphasizes, the efforts of these scholars were geared towards music analysis, and with scientific aspirations no less. But taken at face value, the distinction between their analytical graphs on the one hand, and diagrammatic renderings of the music that were motivated

36 Another option would be the disguised variant of the theme in the bass part of mm. 56 ½–58 (or, less convincingly, the alto part in mm. 32 ½ –35, where only the rhythm is reminiscent of the theme while the melodic contour takes liberties). 37 “Handelt es sich nicht um stimmungsgemäße persönliche umdeutungen, sondern um wissenschaftlich- exakte übertragungen in ein anderes system.” Neugeboren, “Eine Bach-Fuge im Bild,” 16. 38 Neugeboren mentioned these two scholars in his essay, referring to Wilhelm Werker, Studien über die Symmetrie im Bau der Fugen und die motivische Zusammengehörigkeit der Präludien und Fugen des “Wohltemperierten Klaviers” von Johann Sebastian Bach (Leipzig: Breitkopf and Härtel, 1922), and to Wolfgang Graeser’s ground-breaking editorial work on Bach’s “The Art of Fugue, ” published as “Bachs ‘Kunst der Fuge,’” Bach-Jahrbuch 21 (1924): 1–104. On Graeser’s achievements, see Stephen Tunnicliffe, “Wolfgang Graeser (1906-28): A Forgotten Genius,” Musical Times 141, no. 1870 (Spring 2000): 42–44. 39 Iwan Knorr, Die Fugen des “Wohltemperierten Klaviers” von Joh. Seb. Bach in bildlicher Darstellung (Leipzig: Breitkopf & Härtel, 1912). 40 Vergo, The Music of Painting , 230–35. Vergo also reproduces a diagram each from Knorr’s and Werker’s treatises. 247 by visual-artistic concerns on the other, is hard to discern. While Kandinsky’s visualization of

Beethoven’s symphony quite evidently exemplified the latter category, Neugeboren’s graphs are harder to classify.

The clinical appearance of Neugeboren’s graphs matches the mathematical allure of these treatises. Geometrical precision characterizes both the background of scaled paper and the lines that Neugeboren drew upon it to represent Bach’s music. These lines rigorously adhere to the subdivisions of the underlying grid: the length of the vertical lines renders the duration of the individual tones. Neugeboren commented on this direct correspondence with the music as sounding event, clarifying that he sought to “optically translate the full extension of the acoustic process, rather than to merely indicate it through graphical symbols.” 41 This dissociation from

“mere graphical symbols” that Neugeboren emphasized follows from his earlier comment about depicting Bach’s music “independently from fictions.” With these remarks, Neugeboren referred to such notational illusions as presenting different chromatically altered pitches on the same staff line, or encoding rhythmic values through changing coloring of the note heads. In his approach,

Neugeboren aimed to make the music more immediately graspable to the eye, and to “enable the eye to perceive music in just as varied a way as the ear.” 42

In the exact transfer of durations from the score to the visualization, which leaves no room for any interpretative flexibility, Neugeboren’s approach differs significantly from

Kandinsky’s. The lines that Neugeboren drew to map Bach’s stretto passages onto the scaled paper do not appear to carry any of the expressive variance that Kandinsky applied to the line in

Figure I.2. Yet, in different ways, Neugeboren was no less interpretative of the music in question

41 “Da der akustische vorgang hier nicht durch schriftzeichen lediglich angedeutet, sondern in seiner ganzen ausdehnung optisch übersetzt ist.” Neugeboren, “Eine Bach-Fuge im Bild,” 16. 42 “wird das auge befähigt, musik ebenso vielseitige art zu erkennen, wie das ohr.” Neugeboren, “Eine Bach-Fuge im Bild,” 16. Translation amended from Vergo, The Music of Painting , 234–5. 248 than Kandinsky. Neugeboren himself pointed to the musical qualities that his visual rendering highlighted, in short, his interpretative priorities:

den verlauf jeder stimme als zusammenhängende, steigende und fallende farbige linie zu sehen, wobei allerdings, wie beabsichtigt war, der horizontale verlauf besonders hervortritt. 43 to see the course of every voice as a continuous, rising and falling, colored line; in this [approach ] it was intended for the horizontal process to stand out in particular.

While the graph of Figure V.1 (which shows measures 60 ½–66 of the E-flat minor

Fugue) was printed only in black and white in the Bauhaus-journal, Neugeboren insinuated that he envisioned the different contrapuntal voices to be rendered in different colors. In addition to employing different colors, Neugeboren emphasized their “horizontal process” by tying together the vertical lines that represent the tones into continuous melodic lines. These lines highlight the thematic utterances and isolate them as quasi-independent strata from across the polyphonic texture.

In the graph, these thematic entrances are always represented by the same distinct shape.

On the basis of my discussion in previous chapters, we can also consider it a Gestalt. The uniformity of this Gestalt allows us to recognize the theme every time it returns, even when it is transformed, such as in the inversion in the soprano (entering at measure 64 ½), and the augmentation of the theme in the bass. The graph exposes in visual terms how their shape is essentially the same, even when manipulated through mirroring and magnification. In that way,

Neugeboren’s graphs certainly render the music as immediately appealing to the eye as it might otherwise appear to the ear.

43 Neugeboren, “Eine Bach-Fuge im Bild,” 16. 249

Figure V.2 : Henrik Neugeboren, visualization of J.S. Bach, Fugue in E-flat minor (BWV 853), mm. 77–83

The following stretto depicted by Neugeboren (measures 77–83, reproduced as Figure

V.2) similarly demonstrates the relation in shape between the theme, which enters in the bass part and then again in the alto in measure 80 ½, and its variation with dotted quarter notes as it occurs in the alto entrance in measure 77 ½. Furthermore, this particular visualization brings out the crisscrossing of the lower two parts and the wedge that ensues in the second half of measure

81 when the bass part launches its scalar descent, just to leap up again into the register of the alto part in measure 82. Here in particular, Neugeboren enacted his claim to emphasize the linear coherence of the individual voices and to separate them visually even when they overlap in register. Again, this aspiration is reminiscent of an aesthetic that Busoni emphasized in his

250 edition of The Well-Tempered Clavier . A similar instance in which two parts of the fugue intersect in the same register (measures 45–47) caused Busoni to provide a clarifying transcription in his edition, which isolated the two parts as individual lines on separate staves

(see Figure V.3). Since one of them carries the theme, Busoni advised that it ought to be brought out from the texture in performance. 44

Figure V.3 : Ferruccio Busoni, edited score and annotation of J .S. Bach, Fugue in E-flat minor (BWV 853), mm. 45–47

Apart from the analytical commentary in his editions, Busoni variously publicized his aesthetic visions on music, and especially the music of Johann Sebastian Bach. Taken from an essay of 1912, published in Musikblätter des Anbruch in 1921, the particular expression of

“rücksichtslose Polyphonie” (“reckless, uncompromising polyphony”) became a catchword, not least due to August Halm’s criticism—and misunderstanding—that he propagated in a review of

44 “The leading of the two highest parts, which frequently cross, comes out more clearly in the notation given below. The Soprano (theme) should be emphasized.” Busoni, The Well-Tempered Clavichord [Book 1], 52n3. 251

Busoni’s editions. 45 In the context of his “Selbst-Rezension,” Busoni had expressed his awe over

“die durch rücksichtslose Polyphonie sich selbst neu gestaltende Harmonik” in his compositions, which he modeled after Bach’s contrapuntal style. With this remark, Busoni meant the formation of harmonic constellations that would arise from a primary focus on linear-polyphonic processes.

He considered this seemingly self-governing compositional mechanism an accomplishment of maturity after many years of intensively studying Bach’s contrapuntal music. To Halm, in contrast, such a perspective did not sufficiently account for his own hearing of Bach’s music as fundamentally grounded in tonal harmony, even though Busoni’s anecdote had not actually denied a tonal framework. As I surveyed in the last part of Chapter II, such a heuristic juxtaposition between a harmonic and a linear-melodic understanding of Bach’s polyphony permeated the music theoretical discourse of the time. Halm read into Busoni’s assertion an unwarranted neglect of the harmonic organization of Bach’s music. Neugeboren’s rendition, meanwhile, stands at the other extreme. Because of his focus on the “linear process” of the individual voices, principles of harmonic coherence are difficult to glean from Neugeboren’s visualizations. While the general analytical perspective that Neugeboren’s visualizations expose aligns with the aesthetics propounded by Busoni, his realizations enact these ideas more consistently and rigorously than Busoni expressed in his commentary and annotations.

Concomitantly, Neugeboren’s visualizations portray Bach’s polyphonic texture as a horizontally organized superimposition of melodic lines. As Busoni’s proposition and its reception by Halm suggested, such an understanding of polyphony was by no means the norm in

45 Busoni, “Selbst-Rezension” (1912),” Musikblätter des Anbruch 3 (January 1921): 23. The essay is also included among the essays in Busoni, Von der Einheit der Musik: von Dritteltönen und junger Klassizität, von Bühnen und Bauten und anschliessenden Bezirken (Berlin: M. Hesse, 1922), 174–80; August Halm, “Über Ferruccio Busoni’s Bachausgabe,” Melos 2, nos. 10 and 11–12 (1921): 241–42. See also Hans- Joachim Hinrichsen, “Motorik, Organik, Linearität,” 3:346. Hinrichsen mentions that Busoni’s essay had already been published in 1914 as well, without, however, specifying the source. 252 the early twentieth century. Much more expansively and thoroughly than Busoni, Ernst Kurth promoted a respective theoretical framework in his treatise Foundations of Linear Counterpoint:

Bach’s Melodic Polyphony of 1917. 46 As I discussed in detail in Chapter IV, Kurth positioned his treatise as an intervention against the prevailing doctrine of counterpoint at the time, which he traced back to Johann Joseph Fux’s Gradus ad Parnassum from 1725. Kurth specifically sought to supersede Fux’s vertically oriented understanding of counterpoint, which would slice the music moment-by-moment into harmonic sonorities, as expressed in the motto “punctus contra punctum.” Instead, Kurth proposed to focus on the horizontal trajectory of the individual voices, which develop simultaneously. As scholars such as Lee Rothfarb, Luitgard Schader, and

Daphne Tan have pointed out, Kurth’s notion of the linear coherence of these melodic strands relied heavily on Gestalt-theoretical and cognitive advances of his time. 47

The prominence that Kurth’s treatise gained in the 1920s—especially in musical and artistic circles that were united by a shared admiration for Bach’s musical legacy—well exceeded the reception of Busoni’s views. As I examine again in more depth later in this chapter, the reception of Linear Counterpoint further polarized pre-existing aesthetic camps in German music theory and criticism, especially with regards to the appropriation of Bach’s polyphonic

46 Ernst Kurth, Grundlagen des Linearen Kontrapunkts: Einführung in Stil und Technik von Bach’s melodischer Polyphonie (Bern: Max Drechsel, 1917). 47 Lee Allen Rothfarb, Ernst Kurth as Theorist and Analyst (Philadelphia: University of Pennsylvania Press, 1988), Luitgard Schader, Ernst Kurths “Grundlagen des linearen Kontrapunkts”: Ursprung und Wirkung eines musikpsychologischen Standardwerkes (Stuttgart: J.B. Metzler, 2001), Daphne Tan, “Ernst Kurth at the Boundary of Music Theory and Psychology” (Ph.D. dissertation, Eastman School of Music, University of Rochester, 2013). See also Hans-Peter Rösler, Die Musiktheorie von Ernst Kurth und ihr psychologischer Hintergrund (Hamburg: Verlag an d. Lottbek, 1998). 253 style.48 Within these divergent positions, Neugeboren’s renditions clearly propagate a linear conception of polyphony such as the one advocated by Busoni and Kurth.

Based on extant documents of various Bauhaus artists, such as a notebook of painter

Johannes Itten, art historian Régine Bonnefoit has suggested that the reception of Kurth’s treatise extended to the Bauhaus.49 In addition to the connections that Bonnefoit has chronicled, Lyonel

Feininger’s son Laurence studied at the Freie Schulgemeinde Wickersdorf in the mid 1920s, some fifteen years after Kurth had taught at that reform-pedagogical school. In the 1920s, the musicologist Willi Appelbaum, better known today as Willi Apel, was a teacher there and corresponded with Feininger not only about the educational development of his son, but also about artistic concerns, such as the composition of fugues. 50 Considering the overwhelming interest in Bach’s music, and the many connections among the Bauhaus members with musicologists, it is quite plausible that Kurth’s theory of Linear Counterpoint was a well-known source at the Bauhaus.

As we have seen through the references cited above, Neugeboren autonomously identified musicological and music-theoretical studies as a frame to his approach. While he did not mention Kurth’s work, Neugeboren’s music-analytical lens on Bach’s fugue exposes a close

48 On the reception of Kurth’s treatise see for example Rothfarb, Ernst Kurth as Theorist and Analyst , Schader, Ernst Kurths “Grundlagen des linearen Kontrapunkts ,” and Alexander Rehding, “(Mis)Interpreting Ernst Kurth” (MA thesis, Cambridge University, 1995). 49 Régine Bonnefoit, Die Linientheorien von Paul Klee (Petersberg: Michael Imhof, 2009). Bonnefoit points to evidence that different artists at the Bauhaus must have known Kurth’s work: Johannes Itten scribbled the title of Kurth’s treatise on Linear Counterpoint into his notebook, and Kandinsky quoted the later Bruckner -monograph in his own treatise. There is no evidence, however, that Kandinsky was familiar specifically with Linear Counterpoint . 50 Appelbaum (later Apel) taught at Wickersdorf from 1921 to 1927, received his doctorate in Berlin in 1936, and emigrated to the United States that same year. Pertinent for the present context is a letter from Apel to Feininger from 1926. Feininger’s Nachlass, including this written correspondence, is catalogued and preserved in Houghton Library at Harvard University. For a brief commentary on Apel’s biography and his time in Wickersdorf, see Peter Dudek, “Sie sind und bleiben eben der alte abstrakte Ideologe!”: der Reformpädagoge Gustav Wyneken (1875-1964): eine Biographie (Bad Heilbrunn: Verlag Julius Klinkhardt, 2017), 198n55. 254 resemblance to Kurth’s theory of Linear Counterpoint . Incidentally, in his cultural-political alignment, which propagated the much-debated opposition between Bach and Beethoven as models of musical thought (as I portrayed in Chapter I), Neugeboren shared with Kurth an unconditional partiality for Bach’s polyphony over the “relatively imperfect music” of

Beethoven.51

The main focus of Bonnefoit’s research, meanwhile, is dedicated to artist Paul Klee, who was most explicit among the Bauhaus artists in harnessing aspects of Kurth’s theory in his creative and theoretical work. As Bonnefoit conjectures, Klee might even have known Kurth through his own biographical connections, noting that Klee was avidly involved in the music scene in Berne, where Kurth lived and taught from 1912. In numerous paintings that pay tribute to Bach’s music, Klee explored the possibility of an artistic equivalent to the composer’s polyphonic style. With regard to this approach, which Klee termed “pictorial polyphony,”

Bonnefoit analyzes how Klee adopted a Kurthian perspective on counterpoint, as a texture that interweaves multiple autonomous linear entities. 52 Conversely, as I discussed in Chapter IV,

Kurth’s conception of the line exposed notable affinities with Klee’s ideas. I pick up where

Bonnefoit left off and examine further the performative implications of the ways in which Klee enacted his vision of polyphony in the next and final example of this chapter, which also synthesizes aspects from both Kandinsky’s and Neugeboren’s approaches.

51 “Daß unsere vorwiegend architektonische zeit zu bachs gewollter und gekonnter konstruktion mehr beziehung hat und sie deshalb höher bewertet als jede, aus wesentlich anderen vorstellungen entstandene, relativ-unvollkommenere musik (beethoven) ist klar.” Neugeboren, “Eine Bach-Fuge im Bild,” 16.(“It is obvious that our predominantly architectural era has a closer relation to Bach’s deliberate and skilled construction and that we thus value it higher than any other, relatively imperfect music (Beethoven) that arose from entirely different ideas.”) On Kurth’s parsing of music history according to his aesthetic principles, see Rothfarb, Ernst Kurth as Theorist and Analyst , esp. chap. 5, “Kurth’s Historical View of Harmony.” See also Chapter I of this dissertation. 52 See Régine Bonnefoit, “Paul Klee und die ‘Kunst des Sichtbarmachens’ von Musik,” Archiv für Musikwissenschaft 65, no. 2 (January 2008): 121. The original German term is “bildnerische Polyphonie.” 255

Performing Bach with Pen and Paper

The example is documented in Klee’s teaching materials for the Bauhaus from 1922, collated under the title Beiträge zur bildnerischen Formlehre (Figure V.4).53 In a demonstration for his students, Klee transcribed an excerpt from Johann Sebastian Bach’s G major Sonata for

Violin and Harpsichord (BWV 1019). Klee’s visualization is informed by his own musical experience and expertise, and even more apparently so than in the cases of Kandinsky and

Neugeboren. Though known principally as an artist, Klee was also professionally trained as a violinist and his wife Lily as a pianist. As various sources document, Klee continued to play music throughout his life, including chamber music with his wife and friends. 54 According to his son’s account, Klee’s musical taste centered on the period between Bach and Mozart, with selected works from the nineteenth century. While he made the acquaintance of prominent composers of his day, such as Paul Hindemith and Arnold Schoenberg, and esteemed their music—as well as that of Igor Stravinsky, Bela Bartók, and others—he did not perform it. 55 I will discuss momentarily how Klee’s musical expertise materialized in his diagrammatic depiction of Bach’s music.

53 Paul Klee, “Bildnerische Formlehre,” 1922, Zentrum Paul Klee, Bern, BF/55, http://www.kleegestaltungslehre.zpk.org/ee/ZPK/BF/2012/01/01/055/ . 54 For a useful overview of Klee’s musical training and activities see for example Klee und die Musik: Schirn-Kusthalle Frankfurt, 14. Juni bis 17. August 1986 , ed. Christoph Vitali (Berlin: Nicolaische Verlagsbuchhandlung, 1986), esp. “Biographie,” 237–47. 55 Ole Henrik Moe, “Felix Klee—Protokoll eines Interviews” in Vitali, Paul Klee und die Musik , 209–15.

256

257

The visualization shows the opening two measures of the Sonata’s Adagio , which are composed in an imitative contrapuntal style (see Figure V.5).

Figure V.5 : J.S. Bach, Sonata for Violin and Harpsichord (BWV 1019), Adagio, mm. 1–2

Like Neugeboren, and like Kurth’s theory of Linear Counterpoint , Klee drew attention in particular to the horizontal trajectory of the individual melodic parts. He even highlighted through a dotted line how the harpsichord’s right-hand part continued across the rest in measure

2, thus ensuring that its linear coherence was readily visible. The four vertical wavy brackets, meanwhile, tie the lines together in instances in which two voices cross each other in register or across large melodic leaps. Like a music analyst, Klee also differentiated between a melody and accompaniment through the shape of the respective lines. Overall, the thickness of the lines in the graph indicates the emphasis of the metrical hierarchies that are marked on the bottom of the page through the grey-shaded areas. The straight lines of the accompanimental parts reflect these gradations. But within the line that represents the melody, Klee treated these gradations much more freely. Here in particular, his practice as a violinist manifests itself in the expressive shape that he bestowed on the line. It shows how the music accumulates and releases energy and tension along the way, sometimes even in the swells in the middle of sustained tones. Essentially,

Klee transferred the pressure of the bow on the string to the pressure of the pen on the paper.

258

As Bonnefoit has pointed out, Kandinsky had suggested precisely such a transference as a means of notation in his treatise. In the context of outlining the expressive potential of the line, as discussed above, Kandinsky declared, “Der Druck der Hand auf den Bogen entspricht vollkommen dem Druck der Hand auf den Stift ”56 (“The pressure of the hand on the bow corresponds exactly to the pressure of the hand on the pencil” 57 ). Bonnefoit has also drawn attention to a later, more abstract painting by Klee, in which he enacted the same idea again:

“Heroic Strokes of the Bow” (“Heroische Bogenstriche”) from 1938 (see Figure V.6). 58 In the painting, Klee translated the physical, embodied gestures of bow strokes into brush strokes on the canvas, which materialize as lines of varying curvature and thickness. Through this mapping of movements of the performer’s body, Klee’s lines also resemble the kinesthetic notational figures that Alexander Truslit developed to guide musical performers, as discussed in Chapter

IV.59

56 Kandinsky, Punkt und Linie zu Fläche , 93. 57 Kandinsky, Point and Line to Plane , 99. 58 See Bonnefoit, Die Linientheorien von Paul Klee , 149. The painting is held at the MoMA in New York. Its material specifications are: pigmented paste on newspaper on dyed cloth on board in artist's frame; dimensions: 28 3/4 x 20 7/8" (73 x 53 cm). 59 Alexander Truslit, Gestaltung und Bewegung in der Musik: ein tönendes Buch vom musikalischen Vortrag und seinem bewegungserlebten Gestalten und Hören , ed. Hans Brandner and Michael Haverkamp (Berlin, 1938, repr. Augsburg: Wißner, 2015). 259

Figure V.6 : Paul Klee, “Heroische Bogenstriche“ (1938)

The analogy with painting, however, sheds light on a peculiarity in Klee’s visualization of Bach’s Adagio . In the visualization, Klee bestowed the same expressive line to the melody when it first occurs in the harpsichord, even though the harpsichordist’s—or even a pianist’s— possibilities are ostensibly much more limited when it comes to playing expressive swells in the middle of sustained tones than a violinist’s. This is even more striking considering that the harpsichord introduces the melody first, and thus its line does not just mimic but anticipates the violin’s version of the melody.

Again, Kandinsky had captured such a distinction between the acoustic and mechanical capabilites of different instruments in his treatise, where he differentiated between point-

260 instruments—with the piano as his example—and line-instruments, such as the organ. 60 I want to conjecture, however, that Kandinsky would surrender this distinction in favor of highlighting the continuous melodic contour of Beethoven’s second theme, even if it were played on a piano, for example. As I argue, Kandinsky’s line renders the mental imagination and perception of the melody rather than its acoustic generation. This becomes even more evident in light of the following considerations.

The Beethoven examples that I discuss earlier appear in the section of Kandinsky’s treatise dedicated to the functionality of the point, and they are introduced with a statement about the use-value of points in music, in particular for percussion instruments and the piano:

Außer den bereits erwähnten Pauken- und Triangelschlägen können Punkte in der Musik auf allerhand Instrumenten (besonders auf Schlaginstrumenten) hervorgebracht werden, wobei der Flügel geschlossene Kompositionen ausschließlich durch Zusammenstellungen und durch das Nacheinanderfolgen der Klangpunkte ermöglicht. 61 In addition to the beating of the kettle-drum and striking of the triangle of which we have already spoken, points can be produced in music with all sorts of instruments––especially the percussion instruments. The piano, however, enables the presentation of unified compositions exclusively by means of the combination and the sequence of tonal points. 62

This reference to the piano’s quality as a “point-instrument” thus framed the visual representations of Beethoven’s symphony. As I mentioned earlier, for the most part, the excerpts of the symphony feature the repeated notes of the opening motto in its various manifestations, which necessitate a point-like articulation, regardless of the performing instrument.

In this context, a footnote that Kandinsky added to the above statement undermines the notion that he was predominantly concerned with the acoustic generation of sounds. The footnote contemplates the aesthetic, if not psychological, appeal of the point for composers, perhaps to

60 “Die Orgel ist ebenso typisches Linieninstrument, wie der Flügel ein Punktinstrument ist.” Kandinsky, Punkt und Linie zu Fläche , 92. (“The organ is quite as typical a ‘linear’ instrument as the piano is a ‘point’ instrument.” Kandinsky, Point and Line to Plane , 98). 61 Kandinsky, Punkt und Linie zu Fläche, 37. 62 Kandinsky, Point and Line to Plane , 43, translation amended. 261 counterbalance Kandinsky’s later assertion of the line as having “the most expansive array of expressive means in music.” Intriguingly, the authority that Kandinsky invoked in support of the point is Anton Bruckner, and even more specifically, Ernst Kurth’s reception of Bruckner.

Kandinsky quoted from Kurth’s Bruckner treatise, a passage that construes Bruckner’s manic obsession with points as a psychological compensation for the (linear) expanse of his creative ideas:

Daß der Punkt auch auf einige Musiker eine mehr oder weniger bewußte, aber doch eine anziehende Kraft ausübte, die im inneren Wesen des Punktes sich deutlich erkennen läßt, geht klar aus den “Zwangsvorstellungen” Bruckners hervor. Zwangsvorstellungen, deren inneren Inhalt mancher unter der sichtbaren Oberfläche zu sehen verstand: “War dies (Bewundern von Punkten bei Unterschriften und auf Türtafeln) zwangsartige Verkrampfung, dann scheint es doch kein Irrgeist gewesen zu sein, der sich in die Punkte verbohrte; kennt man Bruckners Wesensart, ganz besonders die Weise, wie er nach Erkenntnissen (auch in seinen musiktheoretischen Studien) suchte, so scheint in der Hingezogenheit zur schwindenden Ureinheit aller räumlicher Ausdehnung eine psychologische Bedeutung zu liegen. Er suchte letzte Innenpunkte im Grunde überall; aus ihnen erflossen ihm die unendlichen Größen, und in ihnen wies es zum ersten Element zurück.” Bruckner v. Dr. Ernst Kurth, B. I, S. 110, Anm. Max Hesses Verlag, Berlin. 63 It is clearly evident that certain musicians also have been more or less consciously attracted by the magnetic power of the point, which can be distinctly recognized through its inner tension as demonstrated by the obsessive-compulsive “hallucination” of Bruckner, whose meaning had been detected and described: “How could this (his interest in the effect of points after signatures or on doorplates) have been a derangement of his spirit, when it seems that it was no wandering mind which investigated these points–– especially if one understands Bruckner’s nature and the manner in which he searched for knowledge as indicated in his studies of the theory of music? It becomes apparent that psychological significance resides in the fact that he was attracted to the reclining proto- unit of all spatial expansion’s origin. He sought everywhere for the ultimate inner points, to reach this final analysis out of which, in his opinion, originates the infinity of vast dimensions, impossible without its originating extension point.” “Bruckner” by Dr. Ernst Kurth, vol. I, p. 110, footnote. Max Hesses Verlag, Berlin. 64

The footnote is curious on at least two levels: Firstly, being the only reference to Kurth’s music theoretical oeuvre in Kandinsky’s treatise, the quoted passage oddly belies Kurth’s

63 Kandinsky, Punkt und Linie zu Fläche , 37n. 64 Kandinsky, Point and Line to Plane , 43n, translation amended. 262 overarching agenda, which was ostensibly more concerned with the linear coherence and horizontal expansion of music than its conception as a condensed metaphorical point. Not only in

Linear Counterpoint (which Kandinsky did not cite), but also in the broader context of Bruckner ,

Kurth’s theory targeted first and foremost the linear qualities of music. In the case of Bruckner’s music, Kurth employed the wave as his principal metaphor to portray these qualities in the music’s melodic and formal organization.

On the level of Kandinsky’s argument, conjuring up Bruckner, the organist, to support claims about the aesthetic value of the point and the acoustic properties of “point-instruments” moreover appears contradictory in its own right, considering that (in a different part of the treatise) Kandinsky adduced the organ as exemplary of “line-instruments.” Rather than corroborating Kandinsky’s concern with the acoustic associations of the point in music,

Bruckner’s appearance thus subverted the categorical differentiation between different types of instruments that Kandinsky proposed. Indeed, the quoted passage likely attracted Kandinsky due of its emphasis on subconscious forces and the “psychological significance” assigned to the point as a graphical and notational element. Rather than marking a sharp acoustic attack, the point arises, in Kurth’s words, as the condensation of processes of expansion, either deliberate or subconscious. This emphasis shifts the focus away from the initially proposed classification, which was based on acoustical mechanisms of tone production, to more metaphorical and psychological associations of notational signs. In these capacities, the point and the line capture musical qualities that are independent of primarily acoustic concerns.

Klee, as well, evidently transcended concerns with the acoustic generation of sounds to render a more idealistic perspective on the music, through an analytical lens that illuminates how it ought to be heard, or at least imagined. Indeed, he reminded us that the performer, too, is a

263 listener, and that the harpsichordist—despite the mechanical limitations of her instrument— ought to hear the expressive shape and linear coherence across the musical phrase in order to convey it in performance. As I argued earlier, the same conditions applied to the line with which

Kandinsky depicted Beethoven’s second theme.

Visions of Tonal Space: Examining the Organization of the Graphs

My analyses so far have focused on the particular functions assigned to the graphical elements, and particularly the line, within the artistic visualizations, as they pertain to the musical compositions that they depict. Sybille Krämer differentiates such an “aisthetic” function of the line with lines defining the underlying notational system, such as the staff, ledger, and bar lines in staff notation. 65 In the comments quoted above, we encountered Kandinsky observing that that notational system provides five horizontal lines to demarcate gradations in pitch, and

Neugeboren criticizing the misleading convergence of different chromatic alterations in pitch on each of these horizontals, what he lamented as “fiction.” 66 The artists certainly studied these features before devising their own notational systems. It thus merits taking a closer look at the layout of their graphs, the backgrounds to their artistic renderings, as it were, including such features as the designation of axes and their gradations. While both Klee and Neugeboren rendered the grid of their graphs visible, such a structuring background is only implied in

Kandinsky’s visualization. 67 Overall, the axes in all three graphs refer to the same parameters,

65 Sybille Krämer, Figuration, Anschauung, Erkenntnis: Grundlinien einer Diagrammatologie (Berlin: Suhrkamp, 2016), esp. chap. 5, “Aisthesis und Erkenntnispotenzial der Linie.” 66 “Ebenso wird die Höhe linear gemessen, wobei fünf Horizontale die Grundbasis bilden.” Kandinsky, Punkt und Linie zu Fläche , 93.(“The pitch is likewise measured in lines, and five horizontals form the basis of this.” Kandinsky, Point and Line to Plane , 99). 67 Claus Pias has pointed to different instances of invisible lines and rasters in Kandinsky’s theory and creative work, and interpreted them as anticipations of the invisible raster of the computer screen. Claude Pias, “Point and Line to Raster: On the Genealogy of Computer Graphics,” in Ornament and Abstraction: 264 and correspond as well to the organization of conventional music notation, as well as with all other graphical examples encountered across this dissertation: the horizontal trajectory marks the passing of time, whereas variation in the vertical orientation denotes changes in pitch. 68 But beyond these similarities, the three diagrammatic representations still host a number of differences.

Both Klee and Neugeboren apportioned the passing of time on the x-axis into metrical units derived from the music: Klee subdivided the quarter-note beats into eighth notes, while

Neugeboren used alternating vertical cross-sections of the scaled paper to denote the quarter-note beats. Neugeboren delineated the measures with thicker lines, similar to bar lines. He also numbered both the measures and beats at the top of his graph, while Klee wrote out the subdivisions of both the eighth notes and the quarter notes on the bottom of his graph.

Additionally, Klee marked the half-measures with numbers at the top of his graph, above the music notation. Moreover, as noted before, Klee specified a hierarchy within each order of metric units at the bottom of his graph: through the thickness of the grey-shaded beams, he indicated the weight of the respective beat in relation to the others—an ordering principle that pertained both to the eighth notes, as well as to the quarter notes. Neugeboren, by contrast, did not differentiate the weight of the metric units.

Within the grid arising from their respective annotated subdivisions, both artists rendered exactly the duration of the individual tones as indicated by the score. There is thus no

The Dialogue between Non-Western, Modern and Contemporary Art , ed. Markus Brüderlin and Ernst Beyeler (Basel; Köln: Fondation Beyeler; DuMont, 2001), 64–68. 68 As mentioned in Chapter I, Lawrence Zbikowski has discussed the common mapping “pitch relationships are relationships in vertical space” as an example of conceptual metaphors, following the classification of Lakoff and Johnson and has observed how it transfers onto the physical space of the two- dimensional sheet of paper on which music is commonly notated. Lawrence M. Zbikowski, Conceptualizing Music: Cognitive Structure, Theory, and Analysis (Oxford: Oxford University Press, 2002), 66–67. 265 interpretative variation in the duration or metrical placement of tones in their visualizations, not even in Klee’s visualization, which otherwise assumes qualities of a musical performance, as we have seen. The expressive variations that Klee depicted occur only within each tone, and within the confines of its metrically allotted duration.

As I demonstrated above, this is different in Kandinsky’s visualization. On the blank background, Kandinsky placed the graphical elements freely along the implied x-axis of his visualization. Rather than mapping exactly the duration of the tones as the score specified, he interpreted this aspect of the music as a performer might. In this regard, Kandinsky’s rendering comes closest to a recording of a musical performance. Not unlike a pianist recording on a reproducing piano and engraving his performance on the paper roll, Kandinsky impressed

Beethoven’s motto onto the page. And like on a piano roll, he encoded timing through the relative placement of the graphical elements on the paper. In both cases, the visual stamps are positioned along an implied horizontal axis, marking exactly the moment at which they are articulated. This implied x-axis thus represents a continuous passing of time, which could be subdivided equally into metrical units or any other more abstract temporal denomination.

Provided that the piano roll plays at a constant speed, equal distances cover equal temporal spans. 69

By relinquishing the structural designations in the background of his visualization,

Kandinsky departed the furthest from the conventions of staff notation among the three artists discussed here. Unlike the other two examples, he factually surrendered the independence of his visualization, since it can only be related to a specific musical context by supplementing the information conveyed in the score. This appears ironic, perhaps, considering that Kandinsky was

69 Krämer has theorized this spatialization of temporal relations. See in particular Sybille Krämer, “Friedrich Kittler - Kulturtechniken der Zeitachsenmanipulation,” in Medientheorien: Eine philosophische Einführung , ed. Alice Lagaay and David Lauer (Frankfurt/Main: Campus, 2004), 201–24. 266 at once the most outspoken in admiring the efficacy and unequivocal encoding of meaning in staff notation.

At the same time, Kandinsky’s rendering bears the closest resemblance with a musical performance since the absence of a restrictive grid afforded maximal expressivity in his aisthetic employment of the point and line. In this respect, as well, the comparison with the mode of inscription on a reproducing piano illuminates affinities with the artistic and intellectual valuation of such artifacts of musical performance. From the very beginning, the pioneers of reproducing piano mechanisms recognized their potential for the study of performance aesthetics. 70 Scholars have contextualized this fascination with the study of individual performances both in the culture of stardom around nineteenth-century virtuosos and in the development of infinitely virtuosic automata, which at once carved out the distinctly expressive qualities of a human performance. Julia Kursell, for instance, has discussed how experimental psychologists of the 1920s employed player pianos as a technology to visualize the touch and timing of pianists’ hands on the keyboard. 71 Based on these visual artifacts, their investigations focused on temporal irregularities and deviations as the mark of a human rendition as opposed to that of a machine. To the present day, methods for analyzing performance commonly rely on technologies of visualization, and entail conclusions about stylistic tendencies and evolutions in performance aesthetics, often based primarily on variations in temporal parameters. 72 In the same

70 Reginald Reynolds, for instance, producer and roll editor for the Aeolian company’s Duo-Art reproducing piano rolls, commented on this potential of these rolls. He even provided a comparative analysis between two distinct recordings and a “neutral” reference. Reginald Reynolds, “On Playing the ‘Pianola’ in Its Various Forms,” in The Appreciation of Music by Means of the ʻPianola’ and ʻDuo-Art,’ ed. Percy A. Scholes (London: Oxford University Press, 1925), 137–55. 71 A pioneer in that regard was pianist and teacher Marie Jaëll. Julia Kursell, “Visualizing Piano Playing, 1890–1930,” Grey Room , no. 43 (Spring 2011): 66–87. 72 For an overview over available software, procedures, and conclusions see Nicholas Cook, “Methods for Analysing Recordings,” in The Cambridge Companion to Recorded Music , ed. Nicholas Cook, Daniel Leech-Wilkinson, and John Rink, Cambridge Companions to Music (Cambridge, UK: Cambridge 267 vein, my analysis of Kandinsky’s visualization construed its stylistic and aesthetic context on the basis of particularities in the inscription, especially those denoting temporal deviations.

With regards to the gradations of the y-axis, Klee’s and Neugeboren’s graphs offer an intriguing case for comparison. With both using the vertical axis to denote pitch, they chose to subdivide it with increments of different size: Klee marked a diatonic C major scale, Neugeboren a chromatic scale. C major was an odd choice for Klee, given that the movement that he depicted is in the key of B minor. He therefore squeezed in extra divisions for c-sharp and f-sharp respectively. The choice of C major springs from the pedagogical scaffolding of Klee’s lectures: as his lesson book documents, Klee first devised the schematic organization of the graph with his students, by the example of C major. 73 He then turned to the specific example from Bach’s

Violin Sonata, and perhaps forgot to adjust the increments of his axis. Even if an odd pairing,

Klee’s frame of reference is clearly a diatonic system. Neugeboren, by contrast, placed Bach’s

Fugue into a chromatic space.

The backgrounds in Klee’s and Neugeboren’s graphs thus denote distinctly different tonal spaces. These divergent representations of Bach’s music epitomize the two opposing camps— one conservative, one modernist—in the Bach revival of the 1920s. As I chronicled in Chapters I and II, the appropriation of Bach’s music was fervently debated in German music journals of the

1920s. The stakes were political. The conservative, German nationalist camp sought to install

Bach as a progenitor to the German cultural tradition, while a modernist, internationalist group of

University Press, 2009), 221–45; and Daniel Leech-Wilkinson, The Changing Sound of Music: Approaches to Studying Recorded Musical Performance (London: CHARM, 2009), http://www.charm.rhul.ac.uk/studies/chapters/intro.html (accessed Jan. 24, 2017), both springing from the comprehensive research project CHARMconducted under the directorship of Nicholas Cook (http://www.charm.rhul.ac.uk/index.html ). For a representative study of reproducing piano rolls for research in historical performance practice, see for example Hermann Gottschewski, Die Interpretation als Kunstwerk: musikalische Zeitgestaltung und ihre Analyse am Beispiel von Welte-Mignon- Klavieraufnahmen aus dem Jahre 1905 (Laaber: Laaber 1996). 73 Klee, Beiträge zur bildnerischen Formlehre , BF/54 (his fig. 21). 268 composers and critics explored new stylistic pathways on the basis of Bach’s polyphonic style. 74

As we saw as well, these debates over Bach’s legacy were closely linked to the reception of

Kurth’s treatise on Linear Counterpoint .75 While Kurth had intended his treatise to support conservative ambitions with regards to Bach’s music, the same composers who explored the modernist potential of Bach’s polyphonic style also cited Kurth’s conception of “linear counterpoint” as an important source of inspiration. Alongside composers, critics and proponents of new music like Paul Bekker and Hans Mersmann welcomed Kurth’s theory and terminology for the analysis of contemporary music. The modernist appropriations thus did away with a foundational premise for Kurth’s framework, since, in their approaches, the merging of individual lines did not necessarily create tonal harmony.

In this cultural-historical context, the two artistic renderings of Bach’s compositions from the Bauhaus take on additional meaning, the more so since, as I have argued, both reflect a

Kurthian understanding of counterpoint. The chromatic framework in Neugeboren’s graphs encapsulates the modernist adaptation of Kurth’s theory that Kurth himself repudiated. To Kurth, subsuming Bach’s music in a chromatic framework would have constituted a similar form of misappropriation as applying his own theoretical terminology to the analysis of non-tonal music.

In comparison, Klee’s rendition and its firm foundation in diatonicism aligns with the conservative agenda around Bach’s music that Kurth and critics like Alfred Heuß and Adolf

Diesterweg endorsed.

Neugeboren’s alliance with modernist adaptations of Bach’s legacy was also driven by the musical aesthetics of his teacher Busoni, who was famous for his arrangements

74 Rehding has also summarized these positions. Rehding, “(Mis)Interpreting Ernst Kurth.” 75 Another account of the reception history of Kurth’s treatise is Schader, Ernst Kurths “Grundlagen des Linearen Kontrapunkts.” 269

(“Bearbeitungen”) and transcriptions (“Übertragungen”) of Bach’s music. 76 Busoni defended such “modernizations” of Bach’s music—including those of other composers, such as Liszt,

Tausig, Raff, Bülow—in the introduction to his edition of The Well-Tempered Clavier , and argued that such adaptations “bring [Bach’s music ] to full perfection.” 77

With its modernist allure, moreover, Neugeboren’s diagrammatical rendering can be construed as a precursor to explorations of graphical notation throughout the rest of the twentieth century. Composer and music theorist Joseph Schillinger, for instance, an influential figure in the cultural scene of New York City in the 1930s, presented the compositional method that he developed in the late 1920s in conjunction with its own notational system. 78 Similarly rendered on graph paper, the graphical layout that Schillinger chose for his notational method strongly resembles Neugeboren’s, including the mathematical precision with which he mapped the tones in pitch and duration. The only difference is that Schillinger, who modeled his compositional method after the allegedly all-encompassing logic of mathematics and geometry, labeled the gradations of the vertical axis with the numbers one to twelve instead of chromatic note names. 79

These avant-garde ambitions notwithstanding, Schillinger also saw music from the past as an important model and he analyzed selected compositions by projecting them into his notational

76 Though the two terms connote slight differences in approach and practice, scholars agree that Busoni often used the terms interchangeably. See for example Erinn Elizabeth Knyt, “Ferruccio Busoni and the Ontology of the Musical Work: Permutations and Possibilities” (Ph.D. dissertation, Stanford University, 2010), 153. 77 “The broader arrangement, the ‘modernizing,’ of certain of [Bach’s ] works (by Liszt, Tausig, and others) does not violate the ‘Bach style’—indeed, rather seems to bring it to full perfection.” Busoni, ed., The Well-Tempered Clavichord [Book 1], i. 78 Schillinger’s method, which would merit more in-depth study beyond the frame apposite to the present context, was published posthumously as Joseph Schillinger, The Schillinger System of Musical Composition (New York: C. Fischer, 1946). For a brief discussion of Schillinger’s work, see Nicolas Slonimsky, review of The Schillinger System of Musical Composition , by Joseph Schillinger, The Musical Quarterly 32, no. 3 (1946): 465–70. 79 Schillinger even employed different colors, which he assigned to the twelve chromatic pitch classes. This use of color differs from Neugeboren’s suggestion to highlight the coherence of each melodic part through a consistent color, demarcating it from the other parts. 270 system. An example of these diagrammatic analyses renders Bach’s two-part Invention No. 8 in

F major (BWV 779). 80 The immediate resemblance of this particular graph to Neugeboren’s visualizations attests to the topicality of such diagrammatic renderings of music within the cultural-intellectual preoccupations of their time. Moreover, Schillinger’s dual use of his notational system for both composition and analysis illustrates once again how closely music- analytical and artistic-creative ambitions correlate in diagrammatic renderings of music.

Especially within the ambitions of capturing music as a mathematically structured art form, as

Schillinger professed, the visualization of musical events constitutes an essential step in the process of “comprehension through conceptualization,” as Lochhead described it. In

Schillinger’s and Neugeboren’s renderings, as well as in Klee’s and Kandinsky’s, the visualization brings out certain musical features that inhere in their presentation as geometrically organized patterns.

A Haptic Encounter with Polyphony

In addition to the visible dimension in which Neugeboren rendered his linear understanding of polyphony, he also envisaged a version that would exist in the physically tangible domain. As he commented in his essay, he envisioned his two-dimensional graphs as the foundation for a three-dimensional sculpture that he designed in honor of Bach. Instead of producing a supersized bust of the composer’s physiognomy—or, as he referred to it, “a tawdry figure with sheet music on a pedestal”—Neugeboren strove to commemorate the composer

80 The sketch is preserved at the New York Public Library, and available online at https://en.wikipedia.org/wiki/Joseph_Schillinger#/media/File:Schillinger-Bach.jpg 271 through a representation of his compositional craft, specifically the masterful “construction” of his polyphonic style. 81

The sculpture was posthumously realized in Leverkusen in 1970, using sketches and models that his peers at the Bauhaus crafted under his supervision (see photographs in Figures

V.7–9). The essay that Neugeboren published contains a sketch by Konrad Püschel and a photograph of a three-dimensional model for the sculpture by Gerda Marx.82 Both Püschel and

Marx were students at the Bauhaus in Dessau at the time.

The sculpture’s evocation of organ pipes is an intended reference to Bach as a virtuoso performer on that instrument. This resemblance is remains purely aesthetic, however. In more technical terms, the lengths of the metal bars in Neugeboren’s sculpture are inversionally proportional to those of organ pipes: rather than the highest bars producing the lowest pitches, in the sculpture, the shortest bars represent the lowest pitches. Neugboren recognized the disadvantage of this counter-intuitive mapping:

sie hat in der abgebildeten fassung einen nachteil: die hohe schwingungszahl der soprantöne ist auf der entsprechenden fläche durch eine sinngemäße räumliche höhe dargestellt. die überragende monumentaliät dieses höhenzuges erdrückt den baß, die “grundgewalt des basses.” ein mangel übrigens, der leicht ausgeschaltet werden kann. 83 it has a disadvantage in the depicted version: the high frequency of soprano tones is represented on the respective plane through its corresponding spatial height. The towering monumentality of this high range oppresses the bass, the “foundational force of the bass.” [It is ] incidentally a deficiency that could easily be overcome.

81 “Ob solche darstellung nicht eine würdigere art von bach-monument wäre als die bekannten kitschigen postamentfiguren mit notenrollen.” Neugeboren, “Eine Bach-Fuge im Bild,” 19. 82 The model is also preserved in the Bauhaus archives in Berlin. 83 Neugeboren, “Eine Bach-Fuge im Bild,” 16–19. 272

Figures V.7–9: Photographs of Henrik Neugeboren, sculpture, Leverkusen

That Neugeboren accepted this “deficiency” even though it could, as he acknowledged, easily be fixed, indicates that he saw greater significance in the advantages that he perceived in this form of representation. As he specified, the vertical height of the different metal parts indicates the distance of each tone from the tonic, which serves as common ground—literally and figuratively—to all voices: “vertikal: die entfernung jeden tones von einem für alle drei stimmen

273 gleichen grundton (der tonika).” 84 Against the chromatic framework in his two-dimensional graphs and its implicit modernist appropriation of Bach’s music, this quotation shows

Neugeboren’s preference to account for the music’s grounding in the fundaments of tonality.

The musical excerpt that serves as the model for the sculpture is the most condensed stretto passage of the E-flat minor Fugue, which Neugeboren calls one of the fugue’s

“culmination points” (“Höhepunkt”). In this stretto maestrale of measures 52–55, the theme enters in all voices at only a single beat apart, at first in its orginial form and then in inversion

(see Figure V.10). Accordingly, the three rows of the sculpture outline essentially the same contour in their zig-zagged shapes, apart from taking occasional embellisments into account, such as the sixteenth-note figuration of the soprano part in the third measure of the excerpt, which is rendered in the narrower zig-zags in the middle of the back-row.

Figure V.10 : J .S. Bach, Fugue in E-flat minor (BWV 853), mm. 52–55

The sculpture transcends the realm of two-dimensional inscriptions of music and facilitates a haptic encounter with Bach’s polyphony. 85 I follow the definition of “haptic” proposed by Mark Paterson, and his call to emancipate the sense of touch from the hegemony of

84 Neugeboren, “Eine Bach-Fuge im Bild,” 16. The emphasis is mine. 85 In a sense, the sculpture is more abstract than Neugeboren’s two-dimensional graphs. But it has a much more concrete and specific reference than other, comparable sculptures designed in honor of composers. To mind come for instance Eila Hiltunen’s Sibelius monument in Helsinki (1967), or Wolf D. Prix’s “Alban-Berg-Denkmal” in Vienna (2015). All these sculptures make reference in one way or another to typical musical features in the oeuvre of the respective composers. But only Neugeboren measured with mathematical precision the proportions of a specific composition. 274 the sense of seeing. 86 While the sculpture can certainly also be assessed through the eyes, it affords different sensory modes of engagement than the two-dimensional graphs of Figures V.1–

2. It can be touched, observed from different perspectives, and if you want, you can even position yourself within it. Moreover, since it is founded on a linear analysis of the music, the sculpture brings to life Kurth’s theory of counterpoint, and makes it accessible in every sense of the word. Especially when looking at it from the side (as in Figure V.8), or when going inside, the separation of the different voices becomes even more obvious than in the two-dimensional graphs. In the sculpture, these linear entities transform into rigid, impenetrable boundaries that dictate a single direction in which we can move through the texture—the same trajectory that

Kurth advocated for listening to Bach’s polyphonic music. 87

But the two-dimensional renderings of music that I have discussed also yield insights that extend far beyond those of artistic interest, as they have imprinted historically traceable pathways into the music from a performer’s and listener’s perspective. Precisely because they operate under the same media-specific constraints as a score and, as I have argued, function as interpretative supplements to it, these visualizations showcase the inherent limitations of any form of music notation. They are at once analyses and interpretations of the respective musical compositions, as well as creative explorations of visual-artistic forms of expression.

86 Mark Paterson, The Senses of Touch: Haptics, Affects and Technologies (Oxford: Berg, 2007), 8–9. 87 In an anthropological study, Eric De Bruyn has examined the duality of functionalities that the line inhibits, between that of a guiding principle and of a separating boundary. De Bruyn’s study focuses on political geometry, and the practices of drawing lines on the globe and on maps to delineate territories, and to trace people’s passages of motion. Eric C.H. De Bruyn, “Beyond the Line, or a Political Geometry of Contemporary Art,” Grey Room no. 57 (2014): 24–49. Susan Stewart, meanwhile, discusses the appeal of “gigantic” sculptures. Susan Stewart, On Longing: Narratives of the Miniature, the Gigantic, the Souvenir, the Collection (Baltimore: John Hopkins University Press, 1984). 275

Performing and Listening Engraved

In my analyses, I have proposed that the visualizations by Kandinsky, Klee, and

Neugeboren render a particular way of hearing the music in question, and that they do so in two intertwined ways. They not only engrave an account of a historically situated listener, but by capturing a specific analytical and performative interpretation of the music, they also guide the spectator’s auditive imagination. This double functionality can be ascribed in particular to the graphical potential of the line. As I explored in Chapter I, early twentieth-century artists and psychologists investigated precisely this dual operative potential of the line, as a trace of both its creative emergence on the one hand, and of the viewer’s recreation and reliving of it on the other. Appositely, the mode of engagement that these visualizations demand of the reader-qua- listener is rather unique. Reading a score also entails an inner listening process. But in such instances, the reader would hear her own interpretation. Reading these visualizations, by contrast, means listening to a specific, pre-defined performance, indeed listening through someone else’s ears. As such, these visualizations offer intriguing vantage points in response to the challenges that Peter Szendy has discussed with regards to sharing listening experiences and accessing experiences from the past.88

Yet, these diagrammatic translations of music are limited just as any visual representation of sound and music. When reading them, we necessarily still interpolate aspects of the music that cannot be conveyed graphically, or only at the expense of other parameters. Their complementarity with the score at once defines these artistic renderings as performances. And since they actualize an emotional encounter with the music, these renderings are also congruent with Busoni’s definition of “performance,” as “the audible presentation” and “ emotional

88 Peter Szendy, Listen: A History of Our Ears , trans. Charlotte Mandell (New York: Fordham University Press, 2008). 276 interpretation ” of music, whose role Busoni saw in “restor [ing ] what the composer’s inspiration necessarily loses through notation.” 89 Ironically, the artistic visualizations achieved this expressive enrichment within the very format of notation, which Busoni deplored for its inexpressivity:

Jede Notation ist schon Transkription eines abstrakten Einfalls. Mit dem Augenblick, da die Feder sich seiner bemächtigt, verliert der Gedanke seine Originalgestalt. 90 Every notation is, in itself, the transcription of an abstract idea. The instance the pen seizes it, the idea loses its original form.91

As I explored in Chapter I, in artistic theory of the early twentieth century, the line was celebrated for offering an entryway into its drawer’s psyche by reflecting his impulsive emotional outbursts. Perhaps this connotation of genuine immediacy and the expressive qualities that the above visualizations exposed through the line can reconcile Busoni’s skepticism to some extent.

In their performative and analytical capacities, the examples analyzed in this chapter occupy a unique space between, or even beyond, categories commonly established for graphical forms of representing music, such as prescriptive or descriptive notation, transcription, artistic ekphrasis, interpretative recording, compositional, or analytical sketch. Moreover, they put manual music inscription in dialogue with the history of recorded sound. As my analyses have portrayed, these visualizations document the perspectives of historical listening experiences—an avenue of inspection that has so far garnered little attention in narratives of music inscription.

89 “The audible presentation, the ‘performance,’ of music, its emotional interpretation , derives from those free heights whence descended the Art itself. […] What the composer’s inspiration necessarily loses through notation, his interpreter should restore by his own.” The emphasis is original. Ferruccio Busoni, Sketch of a New Esthetic of Music , trans. Theodore Baker (New York: G. Schirmer, 1911), 15–16. 90 Ferruccio Busoni, Entwurf einer neuen Ästhetik der Tonkunst , 2 nd rev. ed., with annotations by Arnold Schoenberg and an afterword by H.H. Stuckenschmidt (1916, repr. Leipzig: Insel-Verlag, 1974), 29. The original edition was published in 1907. 91 Busoni, Sketch of a New Esthetic of Music , 17. 277

More commonly, such narratives rely on artifacts that are mediated through machines (such as player piano rolls and sound recordings) or that present standardized forms of the music (such as a score).

Since the graphical decisions involved in creating these visualizations entailed both musical and artistic concerns, as well as an emotional and analytical encounter with the music as sounding event, these artistic experiments bring together and encapsulate the many strains of thought that I have traced throughout this dissertation. They materialize a confluence of the preoccupations with melody, perception, emotional, and graphical expression that united all the case studies of the previous chapters. They also demonstrate the suggestive potential of the music-theoretical concepts invoked in each case and, in many ways, develop them further.

Moreover, these artistic visualizations document the fascination with resonances among artistic forms of expression and between art and science that excited so many thinkers in the early twentieth century.

278

CONCLUSION : SOME THREADS

In the psychological paradigm that pervaded the arts and sciences in the early twentieth century, the mapping between melody and line flourished. It helped music theorists and psychologists to theorize melody as a unified structural and cognitive entity, and thereby to counterbalance the definition of melody as a series of discrete stimuli that prevailed in nineteenth-century acoustic research. As a graphical icon and metaphor, the line could mediate between these divergent conceptions of melody as they arose from research in physics, physiology, and psychology. Especially in its new, “genetic” definition that I explored in Chapter

I, the line encapsulated an analogous tension between the gradual process of its creation on the one hand and its holistic manifestation as a distinct shape on the other. Conversely, for investigations into the viewer’s cognitive perception of the line, and visual phenomena more generally, melody served as a favored model, featuring as a primary object of inquiry in pioneering studies on Gestalt theory, such as Christian von Ehrenfels’s article “On ‘Gestalt

Qualities’” from 1890.1 Emerging theories of aural and visual cognition that described the gradual processes of collecting constituent stimuli and re-combining them into a larger perceptual unit addressed principles equally relevant to the appreciation of melody and the graphical line. Paul Souriau gave a particularly succinct account of this analogy in his study on

L’esthétique du mouvement in 1889:

S’il fallait se rendre compte d’un trait vocal en le percevant note par note, cela serait aussi difficile que de se rendre compte de la forme d’une ligne en la regardant point par point;

1 Christian Ehrenfels, “Über ‘Gestaltqualitäten,’” in Das Primzahlengesetz, entwickelt und dargestellt auf Grund der Gestalttheorie (Leipzig: O.R. Reisland, 1922), 7–29, 77–95; English as “On ‘Gestalt Qualities,’” in Foundations of Gestalt Theory , ed. and trans. Barry Smith (Munich: Philosophia Verlag, 1988), 82–116. 279

mais grâce à la permanence des images auditives, nous embrassons d’une seule audition l’ensemble de ces notes successives. 2 If one had to be aware of a vocal line by perceiving it note by note, it would be as difficult as it is to realize the shape of a line by looking at it point by point; but thanks to the permanence of auditory images, we embrace at one hearing the ensemble of the successive notes.

When the line captures the holistic perception of melody through a distinct shape, it represents melody’s recognizability as a coherent musical expression regardless of its context, as

Ehrenfels theorized through the Gestalt principle of transposability. Moreover, this unified appearance can afford certain analytical insights and carry aesthetic connotations. Ernst Toch, for instance, depicted principles of melodic construction through the graphical representation of the

Tonhöhenlinie and its overall shape and trajectory. To Ernst Kurth, the coherence of the melodic line confirmed its primacy as a perceptual entity, and the experiential qualities that he ascribed to it. Thus, the image of the line symbolized the movement that Kurth perceived in melody, and the energetic drive that propagated across the transitions between the tones. The capacity to shape processes of accumulating tension and release through the line’s graphical continuity—and thus across the entire span of melody, including its tones and the moments between them—could be particularly well observed in Wassily Kandinsky’s interpretation of the second theme of

Beethoven’s Fifth Symphony (see Figure I.2).

The principles of Gestalt theory promoted melody as a coherent linear event, which, in turn, subsumed within itself the constituent tones. While Toch considered the line as the

“smallest unit of perception” in his taxonomy of visual and musical parameters, Kurth described

2 Paul Souriau, L’esthétique du mouvement (Paris: F. Alcan, 1889), 320–21; the translation is from The Aesthetics of Movement , trans. Manon Souriau (Amherst: University of Massachusetts Press, 1983), 154. 280 how the meaning of the individual tone dissolved between the various dynamic forces exerting their impact on it:3

Den beiden Grundkräften des musikalischen Empfindens, die nach der Leseweise kurz als vertikal und horizontal bezeichnet werden, ist eines gemeinsam: sie wirken einer Eigenbedeutug des Einzeltones in der Musik entgegen, indem jede in ihrem Sinne diesen in ihre Wirkungsrichtung einzuschließen strebt, akkordlich oder linear. Im musikalischen Geschehen bedeutet der Einzelton nichts, sein Zusammenhang alles, der Einzelton für sich entgeht dem Bewußtwerden, das größere Komplexe zusammenfaßt. 4 One thing is common to the two primary forces of musical sensation, which can be concisely labeled vertical and horizontal according to the direction of reading: they both counteract the meaning of the individual tone in music, since each [force ] strives to subsume the tone within its constitutive direction, whether chordal or linear. In the musical events, the individual tone does not mean anything, but its context everything; by itself, the individual tone slips from attention, which synthesizes larger constellations.

This dynamic subsumption of the individual tones into the larger whole of melody (and the musical texture) pertains as well to graphical renderings of melody through the curvy line.

Especially in Kandinsky’s and Toch’s renderings of melodic excerpts from Beethoven’s

Symphonies in Figures I.2 and III.16, the continuous shape of the line obscured the identity and placement of its constituent tones, in both pitch and rhythmic or temporal organization. As we saw, the repetition in pitch additionally exceeded the representational potential of these lines.

This, indeed, is the flipside of the Gestalt principles that Ehrenfels codified as supra- summativity and transposability: capturing melody’s Gestalt quality through the continuity and coherence of the graphical line comes at the expense of rendering a melody’s internal structure or its placement in absolute measurements. These graphical renderings thus function as interpretative supplements to the information imparted by the score, as I have explained.

3 Ernst Toch, Melodielehre: ein Beitrag zur Musiktheorie (Berlin: Max Hesse, 1923), 1. 4 Ernst Kurth, Grundlagen des Linearen Kontrapunkts: Einführung in Stil und Technik von Bach’s melodischer Polyphonie (Bern: Max Drechsel, 1917), 66. 281

Moreover, they highlight the limitations inherent in any form of visual-graphical representation or notation of music.

Also the graph-like renderings by Paul Klee and Henrik Neugeboren analyzed in Chapter

V were not immune to these limitations, even as they illustrate an alternative to Kandinsky’s and

Toch’s curvy-linear depictions. Within their grids of temporal and pitch gradations, Klee and

Neugeboren could render rhythm and other metrical-temporal aspects of the music with mathematical precision, and make it more immediately graspable than through the encoding in note values in conventional music notation. Yet, their use of straight horizontal lines curtailed the expressive qualities that especially Kandinsky explored in his curvy line of Figure I.2, with its variations in thickness and acuity. In depicting Bach’s Violin Sonata (Figure V.3), Klee’s exploration of the graphical potential of the line was perhaps the most extensive and creative, but even here, the artist combined his interpretation with the representation of the music from the score.

Drawing, Thinking, Composing, and Hearing Lines

In Klee’s rendering, we also saw the use of lines to tie across large intervallic leaps or temporal rests in the individual instrumental parts. These connections betray the concern with melody’s horizontal coherence and expose which moments were perceived as potential disruptions to this ambition. In the graphical realm, the coherence can easily be enacted and ensured, since lines can connect points—or tones—regardless of their distance. Conversely, the graphical line is not bound by the internal structure of melody.

However, as I illustrated, there are conceptual propensities and limits as to how we might draw connections between constituent tones, or parse an agglomeration of tones into component

282 structures. As I discussed in Chapter IV, Max Wertheimer’s study “Untersuchungen zur Lehre von der Gestalt,” especially the second volume of 1923, explored the principles that guide these processes.5 Of Wertheimer’s Gestalt-theoretical propositions, the “factor of proximity”—which suggests that when combining multiple stimuli into larger, holistic perceptions, we prioritize groups of elements close to one another over those more distantly dispersed—proved particularly pertinent as foundation of linear-melodic thinking. In musical terms, the “factor of proximity” can be construed as a propensity for melodic structures that progress by the smallest possible increments, favoring thus repetition in pitch and scalar segments. In my analyses, the predilection for step-wise melodic progressions emerged as a commonality between Toch’s,

Kurth’s, and Heinrich Schenker’s otherwise divergent music-theoretical frameworks. The theorists thus intuited through their musical insight and experience one of Gestalt theory’s essential laws that Wertheimer formalized in psychological terms. In Chapter III, I moreover described Toch’s (and Friedrich August Kanne’s) preference for step-wise progressions as an attempt to approximate to the line’s graphically constituted quality of continuity.

While Toch applied a selective lens to the repertoire to focus on those musical excerpts that cohered with this limitation, Schenker, conversely, reduced entire compositions to the primordial structure of the Urlinie. (Schenker, too, carefully selected the compositions he chose to analyze, but his assortment was politically motivated, believing the Urlinie to underpin only works of the German genius composers from Bach to Bruckner.) In Kurth’s approach, we saw the Gestalt-theoretical “factor of proximity” to play out particularly in his analyses of “apparent polyphony” in Bach’s Sonatas and Partitas for Solo Violin and the Suites for Solo Cello. In this context, Kurth’s observation of common melodic patterns and progressions offer guidance to the

5 Max Wertheimer, “Untersuchungen zur Lehre von der Gestalt, II,” Psychologische Forschung: Zeitschrift für Psychologie und ihre Grenzwissenschaften 4 (1923): 301–50. 283 listener to hear the interweaving and parallel development of multiple linear-horizontal trajectories.

While Kurth conceived these heuristic principles for the listening appreciation of Bach’s music, the graphical realizations of Bach’s music by Klee and Neugeboren made Kurth’s analytical framework readily apparent and graspable to the eyes and ears of their spectators. In that way, their graphical lines inscribed the listening experience that Kurth sought to foster, and at once solidified the conceptual analogies between processes of aural and visual cognition that underpinned explorations of the melodic line in the early twentieth century. In their graphical form, these interpretations could at once exceed the conceptual limitations of Gestalt theory’s

“factor of proximity” and the music-theoretical taxonomies resulting from it, defining thus new ambitions for our hearing.

Also composers of the 1920s explored the limits of linear coherence in melody. In a trend that paralleled the Modernist emancipation of the line in the visual arts, composers put increasing attention to melody and, more generally, horizontal trajectories in their music. Melody became ever more structurally and perceptually salient in compositions of the 1920s, not least due to the dissolution of common-practice tonality and the structuring effects of its harmonic hierarchies.

As I examined in Chapter II, these tendencies went hand in hand with the theoretical efforts of isolating melody as an autonomous compositional structure from the musical texture and in particular from its tonal and harmonic dependencies. The new compositional style, in turn, reinforced the descriptive potential of the line and “linearity” to convey the effect of this music in analyses and journalistic writing of the time.

Hailed by progressive critics for heralding a new “linear style,” Toch’s String Quartet Op.

26 (1919) exemplified this compositional trend. As I analyzed, Toch underscored the linear-

284 horizontal stratification of the musical texture through the graphical annotation of the instrumental parts. These directions guided the musicians in bringing out the linear qualities of the music in performance. But also the continuity of the parts and their saturation with conventional melodic gestures attracted the ascription of “linearity,” not least in the sense of the analytical framework that Toch proposed in his Melodielehre (1923). The Gestalt-theoretical propensities that Wertheimer theorized provide the conceptual anchor to this analytical mindset, describing the principles according to which we isolate and tie together gestures and coherences.

Contemporary composers around Toch, most famously Arnold Schoenberg and his students, tested the limits of these principles further. Schoenberg’s “System of Composing with

Twelve Tones Only Related to One Another,” for instance, promotes a linear ordering of all chromatic pitches to constitute a composition’s primary building block. But the deliberate avoidance of overly scalar patterns within the row, and the various permutations applied to it, counteracted precisely the cognitively founded conception of the line as propounded by music theorists and psychologists. Also the pointillist tendencies especially in the music of Anton

Webern and the exploration of “Klangfarbenmelodien,” thwarted conventional continuities and the consistency in timbre, which were considered essential premises for the perception of a coherent entity. 6

Of course, these experiments were just the beginning of the compositional explorations that ensued over the course of the twentieth century. Across these developments, the line continued to prevail as a conceptual metaphor to account for analytical perspectives and listening

6 Paul Souriau, for instance, argued that the consistency in timbre was essential for the perception of melody as a unit: “It would be almost impossible to recognize a tune in a series of sounds emitted by instruments of very different timbre, which would each give one note in turn.” Souriau, The Aesthetics of Movement , 153. As a famous counterexample, Anton Webern’s orchestration of Bach’s “Ricercar à 6” explores precisely this possibility. 285 experiences, and, indeed increasingly so, it featured as a graphical icon in innovative forms of notation.

Mapping Movement and Interpreting Lines

An essential point of intersection between aesthetic connotations of the line and melody was their capacity to represent movement. While the attribution of motion to music has been and still is a highly common and versatile metaphor, as Steve Larson exemplarily lays out, in the historical context of the early 1900s, the fascination related specifically to the abstraction of movement under the auspices of a Modernist aesthetic, as Cécile Guédon has proposed. 7 Arne

Stollberg has attended to kinesthetic discourses of the early twentieth century that emerged around the discussion of conductors’ movements and the impact of modern dance on music theory.8 Among the music-theoretical sources studied in this dissertation, the association of movement (as a shared quality between melody and line) was particularly pertinent to Kurth, who conceived of the linear-melodic strains in music as evoking the sensation of loco-motion in the listener. 9 In this internalized conception of motion as contained in the listener’s experience,

Kurth targeted mostly those qualities of the genetic line that involve the viewer’s perception.

A complementary example that captured through a line the external, physical movement of a danced interpretation of melody is provided by Kurth’s friend Erich Moritz von

7 Steve Larson, Musical Forces: Motion, Metaphor, and Meaning in Music (Bloomington: Indiana University Press, 2012). Guédon describes the abstraction of movement as a defining idiom of Modernism across artistic and scientific realms. Cécile Guédon, “Abstraction in Motion: A Choreographic Approach to Modernism” (Ph.D. dissertation, University of London, Birkbeck, 2014). 8 Arne Stollberg, “‘Mimische Ausdruckshandlungen.’ Der Dirigentenkörper im anthropologischen Musikdiskurs des 19. und 20. Jahrhunderts,” in DirigentenBilder. Musikalische Gesten – verkörperte Musik , ed. Florian Henri Besthorn, Arne Stollberg, and Jana Weißenfeld (Basel: Schabe, 2015), 15–47. 9 On that idea, see in particular Daphne Tan, “Beyond Energetics: Gestalt Psychology in Ernst Kurth’s ‘Musikpsychologie,’” Theoria 22 (2015): 99–129. 286

Hornbostel.10 As Stollberg relates, modern dance and in particular the iconic pioneer Isadora

Duncan inspired Hornbostel in his essay “Melodischer Tanz. Eine musikpsychologische Studie”

(1904) to speak of “melodic movement” (“Melodiebewegung”). 11 Hornbostel observed how

Duncan’s movements were coordinated not primarily with the music’s metric structure, but instead with the melodic contour. He annotated this in a brief excerpt from Frederic Chopin’s

Waltz Op. 64, No. 1, as reproduced in Figure VI.1.

Figure VI.1 : Erich Moritz von Hornbostel, annotation of “Melodiebewegung,” Chopin, Waltz in D-flat major, Op. 64, No. 1, mm. 5–12, from “Melodischer Tanz”12

With this musical example, Hornbostel picked a passage that demonstrates particularly well the tension that he perceived between the music’s rhythmic-metrical structure, on the one hand, and its organization in pitch on the other. First, in the first three measures of the excerpt, the melodic pitch-patterns create a hemiolic effect that suggests a grouping of four times four notes, as Hornbostel’s line indicates. Next, in the subsequent measures, Hornbostel’s line extends the length of its phases in accordance with the hyper-metrical expansion to units of two

10 Schader has documented the friendship between Hornbostel and Kurth since the 1900s. Luitgard Schader, Ernst Kurths “Grundlagen des linearen Kontrapunkts”: Ursprung und Wirkung eines musikpsychologischen Standardwerkes (Stuttgart: J.B. Metzler, 2001), 72. Among other occasions of a likely encounter between Kurth and Hornbostel, Schader refers to a meeting of the Internationale Musikwissenschaftliche Gesellschaft in Vienna in 1905 that both attended. At the meeting, Hornbostel presented his talk “Das Problem der Vergleichenden Musikwissenschaft.” 11 Erich Moritz von Hornbostel, “Melodischer Tanz. Eine musikpsychologische Studie,” Zeitschrift der Internationalen Musikgesellschaft 5, no. 12 (1904): 482–88. 12 Figure reproduced from Stollberg, “Mimische Ausdruckshandlungen,” 36. 287 measures. Hornbostel’s line thus follows primarily the melody’s organization in pitch, and thereby implicitly highlights the hyper-metrical structure of Chopin’s music. In this way,

Hornbostel sought to “connect the note heads through lines to a curve, which is structured for the eye in the same way as melody for the ear.” 13

Through the emphasis on pitch, Hornbostel’s line bears a striking resemblance to the

Tonhöhenlinien that Toch drew above musical excerpts in his treatise (such as, for example, in

Figure III.16). The chosen excerpt from Chopin’s Waltz even features predominantly step-wise motion. In both Figures III.16 and VI.1, the curvilinear shapes follow the melody’s progression in pitch, its surface contour. This focus on melody’s organization in pitch (rather than its rhythmic structure) arises as a common thread among the theories and applications of the melodic line discussed in this dissertation. Kurth, Toch, and Hornbostel all emphasized the primacy of pitch in melody not only for music-theoretical speculation, but also for its effect on the listener. As Luitgard Schader observes, Kurth and Hornbostel both argued that the experience of intensification (“Steigerung”) in melody relied primarily on an ascending trajectory in pitch. 14

Similarly, Toch theorized the form of a musical composition in analogy to theories of drama, and ascribed processes of accumulating tension and release to the rising and falling of pitch. As I discussed in Chapter III, this limitation to pitch as the primary structuring feature in music irked

Schoenberg who pointed to other compositional means for achieving the same structuring effects.

13 “Die Notenköpfe durch Linien zu einer Kurve verbinden, die sich für das Auge ebenso gliedert, wie die Melodie für das Ohr.” Quoted from Stollberg, “Mimische Ausdruckshandlungen,” 36. 14 Schader, Ernst Kurths “Grundlagen des linearen Kontrapunkts ,” 97–8. Schader compares a passage from Kurth’s Linear Counterpoint (p. 251) to a quotation from Hornbostel, “Melodischer Tanz,” 484: “Die Richtung der Melodie erzeugt hier die Verschiedenheit der Wirkung, und wir können nicht nur metaphorisch in diesem Sinn von Melodiebewegung reden. Ein Aufsteigen der Tonhöhe empfinden wir als Steigerung, ein Absteigen als Absinken.” 288

In the graphical examples that I examined, this commonality provided the grounds for their comparability, such as in Hornbostel’s figure, which evokes similarities with the theories of

Kurth and Toch. But while Hornbostel explained that he conceived his line to capture the

“melodic movement” as an analogy to a dancer’s interpretation of the music, the connotation of movement in the line did not play much of a role in Toch’s theoretical framework. Toch employed the line to derive and model music-theoretical insights inherent to melodies in their own right. Also the difference addressed above between Kurth’s and Hornbostel’s interest in the line’s capacity to represent movement—one internal, the other external—would hardly be manifest in a visual representation.

The example thus showcases how much the interpretation of a linear-melodic rendering can vary depending on the theoretical framework through which it is viewed. With a focus on the cultural-historical context of the 1920s, this dissertation has examined the adaptability of the line through the comparison of examples founded on a shared intellectual backdrop. It thus models a critical approach to graphical depictions of music, by laying out the variability of connotations and functionalities that graphical icons can adopt.

This versatility and variability of the line certainly promoted its popularity in the early twentieth century and beyond as an image for the emerging musical and psychological conceptions of melody. At the same time, the flexibility to re-purpose the line within different theoretical agendas was contingent on the psychological and cognitive paradigm that informed the Modernist tendencies in the arts. Only with the Modernist abstraction and emancipation of the line did it become available to bear the aesthetic connotations of agency, dynamism, coherence, energy, motion, and continuity that underpinned the analogy between melody and line.

289

While from today’s perspective, the analogy between melody and line could be well described through the framework of cross-domain mapping that especially Lawrence Zbikowski and Steve Larson have explored for its music-theoretical import, the ideological frame in the applications that I analyze always leads back to the cultural and intellectual context that I unraveled in this dissertation.15 I argue that it was the convergence of developments in this particular climate, between discourses in the visual arts, music, psychology, and philosophy, that fostered the mapping between melody and line.

As notions of the melodic line—ideas about the linear qualities of melody and the sounds that a line might evoke—continue to animate musical and artistic thought and discussions, it is therefore worthwhile to look back at this critical moment in which their histories intertwined and to scrutinize the conceptual conditions at play then and now.

15 See Larson, Musical Forces: Motion, Metaphor, and Meaning in Music , and Lawrence Zbikowski, Conceptualizing Music: Cognitive Structure, Theory, and Analysis (Oxford: Oxford University Press, 2002). 290

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