DOCSLIB.ORG

Frank Lehman Schubert's Slides: Tonal (Non-)Integration of A

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Frank Lehman Schubert's Slides: Tonal (Non-)Integration of A Frank Lehman Schubert’s SLIDEs: Tonal (Non-)Integration of a Paradoxical Transformation Abstract SLIDE, the transformation that exchanges triads sharing the same third, is a pervasive feature of Schubert’s mature works. Blending indicators of distance and proximity, com- plexity and direct intelligibility, SLIDE is the chromatic progression par excellence for evoking liminal states. Schubert’s use of the transformation poses a challenge to our abil- ity to reconcile prolongational and transformational modes of tonal hearing. Following an evaluation of historical and group-theoretical conceptions of SLIDE, this article pro- poses a set of functional paradigms through which the relation may be understood in Romantic harmony. Extrapolating patterns of SLIDE usage from Schubert’s oeuvre illu- minates the procedures through which the progression may be integrated into tonal fabrics. Special attention is given to the four-hand piano duets, D. 812, 940, and 947 in particular; in these works, the presence of sonata form forces SLIDE’s incorporation into exposition structures. The D. 812 Grand Duo is used as a concluding case study. To fully appreciate its complex game of semitonal relations, the Duo requires overlapping trans- formational narratives and a revival of Karg-Elert’s idiosyncratic Terzgleicher function. In studying Schubert’s SLIDing chromaticism, we stand to understand how compos- ers ensconced within the tonal common practice nevertheless found ways to selectively incorporate tonally paradoxical materials into diatonic forms. Keywords nineteenth century, Neo-Riemannian theory, Franz Schubert music theory & analysis International Journal of the Dutch-Flemish Society for Music Theory volume 1, # i & ii, october 2014, 61–100 research article © Frank Lehman and Leuven University Press http://dx.doi.org/10.11116/MTA.1.4 Schubert’s SLIDEs: Tonal (Non-)Integration of a Paradoxical Transformation Frank Lehman The push and pull between diatonic and chromatic harmony is a hallmark of nine- teenth-century tonal practice. As a consequence, the question of integration forms a central concern for theorists of this repertoire: how ought the increasingly bold infu- sion of chromaticism be reconciled with the putative diatonic understructure that still girds much extended common-practice music? Answers, unsurprisingly, range widely. Up until a certain point, Schenkerian theory can rationalize chromaticism as a product of linear processes that do not fundamentally tamper with diatonic prolongation.1 The strategy of expanding and revising what is meant by harmonic functionality may also be used to grant chromatic relations similar capabilities to diatonic ones.2 Some theorists invoke interpretive qualities such as ambiguity, paradox, and multiplicity—notions that still rely on the assumption of underlying diatonic expectations.3 This idea of tonal Thanks to Suzannah Clark, Richard Cohn, Noam Elkies, Alexander Rehding, and the anonymous reviewers of Music Theory & Analysis for suggesting examples and contributing insightful feedback. 1 For just a few examples in Schubert analysis, see Heinrich Schenker, ed., Oktaven und Quinten u.a., (Vienna: Universal Edition, 1933), 4; and Felix Salzer, Structural Hearing: Tonal Coherence in Music (New York: Dover Publications, 1962), 180. For an effort to bring harmonic thinking more into play with linear analyses of Schubert, see David Beach, “Harmo- ny and Linear Progression in Schubert’s Music,” Journal of Music Theory 38/1 (1994), 1–20. 2 Despite their differences, Daniel Harrison’s dualistic and David Kopp’s chromatic-mediant theories of nine- teenth-century tonality are both committed to the expansion of functionality beyond simple diatonicity: Harrison, Harmonic Function in Chromatic Music: A Renewed Dualist Theory and an Account of Its Precedents (Chicago: University of Chi- cago Press, 1994); Kopp, Chromatic Transformations in the Nineteenth Century (Cambridge: Cambridge University Press, 2002). A similar widening of function to incorporate ambiguous or chromatic chords is endorsed by Charles Smith, who refers some romantic-era chromaticism ultimately back to diatonic models: Smith, “The Functional Extrava- gance of Chromatic Chords,” Music Theory Spectrum 8 (1986), 94–139. A pertinent strategy is found in Richard Cohn’s merger of hexatonic and diatonic spaces in his analysis of Schubert’s Piano Sonata in BH major, D. 960: Cohn, “As Wonderful as Star Clusters: Instruments for Gazing at Tonality in Schubert,” 19th-Century Music 22/3 (1999), 213–32. 3 Candace Brower, in “Paradoxes of Pitch Space,” Music Analysis 27/1 (2008), 51–106, views paradox as a compositional resource made possible by listeners’ tendency to hear tonal relationships vis-à-vis spatial schemas, schemas that are subject to Escher-like tiling illusions. On the collision and fusion of subdominant and dominant functions in Ro- mantic chords, see Kevin Swinden, “When Functions Collide: Aspects of Plural Function in Chromatic Music,” Music Theory Spectrum 27/2 (2005), 249–82. For the Voglerian idea of Mehrdeutigkeit and multiple interpretability, see David Damschroder, Thinking About Harmony: Historical Essays on Analysis (Cambridge: Cambridge University Press, 2008). music theory & analysis | volume 1, # i & ii, october 2014 | 61–100 61 © Frank Lehman and Leuven University Press | http://dx.doi.org/10.11116/MTA.1.4 Frank Lehman schubert’s slides multiple determination may lead to a more radical outlook of under- or non-determina- tion: “triadic atonality,” to use a provocative term.4 If chromaticism poses a genuinely independent mode of composition and tonal perception in the nineteenth century, it ought to garner its own categories and methods; this attitude informs attempts to artic- ulate a parallel but distinct tonal “Second Practice.” It has also contributed to the rise of neo-Riemannian theories, which shift attention from function to voice leading, trans- formation, and absolute progression.5 With so many options at the analyst’s disposal, one must not only ask how chromatic elements it into Romantic music, but also how one’s theoretical apparatuses should interact in analysis—and whether these apparatuses relect non-coextensive ways of hearing. Suzannah Clark compares the act of choosing an analytic system to the selec- tion of a speciic visual “lens.”6 Though lenses focus perception of certain musical fea- tures, Clark cautions that they may also distort some objects and be blind to others. Of the theoretical systems available to study chromaticism, triadic transformation the- ory (or neo-Riemannian theory/NRT) is perhaps the most suitably wide-angled. NRT’s advantage lies not solely in the symmetrical pitch spaces or algebraic groups it offers. Of special value is its interest in the dynamic ways in which listeners perceive harmonic relationships, not as ixed properties of an a priori tonal system, but as subjective and mutable qualities of a particular listening experience. This means, among other things, that NRT can intersect and even integrate with diatonic theories. My choice to employ this lens (with some Schenkerian and Roman numeral ilters here and there) is therefore 4 Cohn considers, and ultimately dismisses, this phrase (from Edward Lowinsky) for describing this repertoire: Cohn, “Introduction to Neo-Riemannian Theory: A Survey and Historical Perspective,” Journal of Music Theory 42/2 (1998), 167 –80, http://dx.doi.org/10.2307/843871. Though more recent applications of neo-Riemannian the- ory have taken steps towards accommodating tonality (see Steven Rings, Tonality and Transformation, [New York: Oxford University Press, 2011], http://dx.doi.org/10.1093/acprof:oso/9780195384277.001.0001), early applications frequently pointed towards symmetrical processes as governing triadic chromaticism in the place of prolongational processes. This can be observed in David Lewin’s claim regarding non-isomorphism between diatonic-Stufen and Riemannian-transformational space. See Lewin, “Amfortas’s Prayer to Titurel and the Role of D in ‘Parsifal’: The Tonal Spaces of the Drama and the Enharmonic CH/B,” 19th-Century Music 7/3 (1984), 336–49. It also manifests in Bri- an Hyer’s attribution of harmonic intelligibility of Die Walküre’s magic sleep chords purely to “algebraic structure.” See Hyer, “Reimag(in)ing Riemann,” Journal of Music Theory 39/1 (1995), 101–38, http://dx.doi.org/10.2307/843900. 5 The idea that non-monotonality and pervasive chromaticism in the nineteenth century constitute a tonal mode of composition (and hearing) that is genuinely distinct from common-practice tonality is explored in The Second Prac- tice of Nineteenth-Century Tonality, ed. William Kinderman and Harald Krebs (Lincoln: University of Nebraska Press, 1996). This notion is critiqued and reined by Dmitri Tymoczko in “Dualism and the Beholder’s Eye,” in The Oxford Handbook of Neo-Riemannian Music Theories, ed. Edward Gollin and Alexander Rehding (New York: Oxford University Press, 2012), 246–67; and by Cohn in Audacious Euphony: Chromaticism and the Triad’s Second Nature (New York: Oxford University Press, 2012). 6 Suzannah Clark, Analyzing Schubert (Cambridge: Cambridge University Press, 2011), 4–5, http://dx.doi.org/10.1017/ CBO9780511842764. music theory & analysis | volume 1, # i & ii, october 2014 62 Frank Lehman schubert’s slides made with the goal of maximizing my analytic ield of view while remaining methodo- logically consistent. I will be turning this transformational lens on only one star in the European Roman- tic sky: the oeuvre
Load more

Recommended publications
  • Chapter 1 Geometric Generalizations of the Tonnetz and Their Relation To
    November 22, 2017 12:45 ws-rv9x6 Book Title yustTonnetzSub page 1 Chapter 1 Geometric Generalizations of the Tonnetz and their Relation to Fourier Phases Spaces Jason Yust Boston University School of Music, 855 Comm. Ave., Boston, MA, 02215 [email protected] Some recent work on generalized Tonnetze has examined the topologies resulting from Richard Cohn's common-tone based formulation, while Tymoczko has reformulated the Tonnetz as a network of voice-leading re- lationships and investigated the resulting geometries. This paper adopts the original common-tone based formulation and takes a geometrical ap- proach, showing that Tonnetze can always be realized in toroidal spaces, and that the resulting spaces always correspond to one of the possible Fourier phase spaces. We can therefore use the DFT to optimize the given Tonnetz to the space (or vice-versa). I interpret two-dimensional Tonnetze as triangulations of the 2-torus into regions associated with the representatives of a single trichord type. The natural generalization to three dimensions is therefore a triangulation of the 3-torus. This means that a three-dimensional Tonnetze is, in the general case, a network of three tetrachord-types related by shared trichordal subsets. Other Ton- netze that have been proposed with bounded or otherwise non-toroidal topologies, including Tymoczko's voice-leading Tonnetze, can be under- stood as the embedding of the toroidal Tonnetze in other spaces, or as foldings of toroidal Tonnetze with duplicated interval types. 1. Formulations of the Tonnetz The Tonnetz originated in nineteenth-century German harmonic theory as a network of pitch classes connected by consonant intervals.
    [Show full text]
  • Riemann's Functional Framework for Extended Jazz Harmony James
    Riemann’s Functional Framework for Extended Jazz Harmony James McGowan The I or tonic chord is the only chord which gives the feeling of complete rest or relaxation. Since the I chord acts as the point of rest there is generated in the other chords a feeling of tension or restlessness. The other chords therefore must 1 eventually return to the tonic chord if a feeling of relaxation is desired. Invoking several musical metaphors, Ricigliano’s comment could apply equally well to the tension and release of any tonal music, not only jazz. Indeed, such metaphors serve as essential points of departure for some extended treatises in music theory.2 Andrew Jaffe further associates “tonic,” “stability,” and “consonance,” when he states: “Two terms used to refer to the extremes of harmonic stability and instability within an individual chord or a chord progression are dissonance and consonance.”3 One should acknowledge, however, that to the non-jazz reader, reference to “tonic chord” implicitly means triad. This is not the case for Ricigliano, Jaffe, or numerous other writers of pedagogical jazz theory.4 Rather, in complete indifference to, ignorance of, or reaction against the common-practice principle that only triads or 1 Ricigliano 1967, 21. 2 A prime example, Berry applies the metaphor of “motion” to explore “Formal processes and element-actions of growth and decline” within different musical domains, in diverse stylistic contexts. Berry 1976, 6 (also see 111–2). An important precedent for Berry’s work in the metaphoric dynamism of harmony and other parameters is found in the writings of Kurth – particularly in his conceptions of “sensuous” and “energetic” harmony.
    [Show full text]
  • Science Fiction in Argentina: Technologies of the Text in A
    Revised Pages Science Fiction in Argentina Revised Pages DIGITALCULTUREBOOKS, an imprint of the University of Michigan Press, is dedicated to publishing work in new media studies and the emerging field of digital humanities. Revised Pages Science Fiction in Argentina Technologies of the Text in a Material Multiverse Joanna Page University of Michigan Press Ann Arbor Revised Pages Copyright © 2016 by Joanna Page Some rights reserved This work is licensed under the Creative Commons Attribution- Noncommercial- No Derivative Works 3.0 United States License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/3.0/ or send a letter to Creative Commons, 171 Second Street, Suite 300, San Francisco, California, 94105, USA. Published in the United States of America by the University of Michigan Press Manufactured in the United States of America c Printed on acid- free paper 2019 2018 2017 2016 4 3 2 1 A CIP catalog record for this book is available from the British Library. Library of Congress Cataloging- in- Publication Data Names: Page, Joanna, 1974– author. Title: Science fiction in Argentina : technologies of the text in a material multiverse / Joanna Page. Description: Ann Arbor : University of Michigan Press, [2016] | Includes bibliographical references and index. Identifiers: LCCN 2015044531| ISBN 9780472073108 (hardback : acid- free paper) | ISBN 9780472053100 (paperback : acid- free paper) | ISBN 9780472121878 (e- book) Subjects: LCSH: Science fiction, Argentine— History and criticism. | Literature and technology— Argentina. | Fantasy fiction, Argentine— History and criticism. | BISAC: LITERARY CRITICISM / Science Fiction & Fantasy. | LITERARY CRITICISM / Caribbean & Latin American. Classification: LCC PQ7707.S34 P34 2016 | DDC 860.9/35882— dc23 LC record available at http://lccn.loc.gov/2015044531 http://dx.doi.org/10.3998/dcbooks.13607062.0001.001 Revised Pages To my brother, who came into this world to disrupt my neat ordering of it, a talent I now admire.
    [Show full text]
  • The Musical Heritage of the Lutheran Church Volume I
    The Musical Heritage of the Lutheran Church Volume I Edited by Theodore Hoelty-Nickel Valparaiso, Indiana The greatest contribution of the Lutheran Church to the culture of Western civilization lies in the field of music. Our Lutheran University is therefore particularly happy over the fact that, under the guidance of Professor Theodore Hoelty-Nickel, head of its Department of Music, it has been able to make a definite contribution to the advancement of musical taste in the Lutheran Church of America. The essays of this volume, originally presented at the Seminar in Church Music during the summer of 1944, are an encouraging evidence of the growing appreciation of our unique musical heritage. O. P. Kretzmann The Musical Heritage of the Lutheran Church Volume I Table of Contents Foreword Opening Address -Prof. Theo. Hoelty-Nickel, Valparaiso, Ind. Benefits Derived from a More Scholarly Approach to the Rich Musical and Liturgical Heritage of the Lutheran Church -Prof. Walter E. Buszin, Concordia College, Fort Wayne, Ind. The Chorale—Artistic Weapon of the Lutheran Church -Dr. Hans Rosenwald, Chicago, Ill. Problems Connected with Editing Lutheran Church Music -Prof. Walter E. Buszin The Radio and Our Musical Heritage -Mr. Gerhard Schroth, University of Chicago, Chicago, Ill. Is the Musical Training at Our Synodical Institutions Adequate for the Preserving of Our Musical Heritage? -Dr. Theo. G. Stelzer, Concordia Teachers College, Seward, Nebr. Problems of the Church Organist -Mr. Herbert D. Bruening, St. Luke’s Lutheran Church, Chicago, Ill. Members of the Seminar, 1944 From The Musical Heritage of the Lutheran Church, Volume I (Valparaiso, Ind.: Valparaiso University, 1945).
    [Show full text]
  • Perceived Triad Distance: Evidence Supporting the Psychological Reality of Neo-Riemannian Transformations Author(S): Carol L
    Yale University Department of Music Perceived Triad Distance: Evidence Supporting the Psychological Reality of Neo-Riemannian Transformations Author(s): Carol L. Krumhansl Source: Journal of Music Theory, Vol. 42, No. 2, Neo-Riemannian Theory (Autumn, 1998), pp. 265-281 Published by: Duke University Press on behalf of the Yale University Department of Music Stable URL: http://www.jstor.org/stable/843878 . Accessed: 03/04/2013 14:34 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Duke University Press and Yale University Department of Music are collaborating with JSTOR to digitize, preserve and extend access to Journal of Music Theory. http://www.jstor.org This content downloaded from 128.84.127.82 on Wed, 3 Apr 2013 14:34:27 PM All use subject to JSTOR Terms and Conditions PERCEIVED TRIAD DISTANCE: EVIDENCE SUPPORTING THE PSYCHOLOGICAL REALITY OF NEO-RIEMANNIAN TRANSFORMATIONS CarolL. Krumhansl This articleexamines two sets of empiricaldata for the psychological reality of neo-Riemanniantransformations. Previous research (summa- rized, for example, in Krumhansl1990) has establishedthe influence of parallel, P, relative, R, and dominant, D, transformationson cognitive representationsof musical pitch. The present article considers whether empirical data also support the psychological reality of the Leitton- weschsel, L, transformation.Lewin (1982, 1987) began workingwith the D P R L family to which were added a few other diatonic operations.
    [Show full text]
  • Further Considerations of the Continuous ^5 with an Introduction and Explanation of Schenker's Five Interruption Models
    Further Considerations of the Continuous ^5 with an Introduction and Explanation of Schenker's Five Interruption Models By: Irna Priore ―Further Considerations about the Continuous ^5 with an Introduction and Explanation of Schenker’s Five Interruption Models.‖ Indiana Theory Review, Volume 25, Spring-Fall 2004 (spring 2007). Made available courtesy of Indiana University School of Music: http://www.music.indiana.edu/ *** Note: Figures may be missing from this format of the document Article: Schenker’s works span about thirty years, from his early performance editions in the first decade of the twentieth century to Free Composition in 1935.1 Nevertheless, the focus of modern scholarship has most often been on the ideas contained in this last work. Although Free Composition is indeed a monumental accomplishment, Schenker's early ideas are insightful and merit further study. Not everything in these early essays was incorporated into Free Composition and some ideas that appear in their final form in Free Composition can be traced back to his previous writings. This is the case with the discussion of interruption, a term coined only in Free Composition. After the idea of the chord of nature and its unfolding, interruption is probably the most important concept in Free Composition. In this work Schenker studied the implications of melodic descent, referring to the momentary pause of this descent prior to the achievement of tonal closure as interruption. In his earlier works he focused more on the continuity of the line itself rather than its tonal closure, and used the notion of melodic line or melodic continuity to address long-range connections.
    [Show full text]
  • An Introduction Via Perspectives on Consonant Triads
    Introduction and Basics The Consonant Triad Geometry of Triads Extension of Neo-Riemannian Theory Symmetries of Triads What is Mathematical Music Theory? An Introduction via Perspectives on Consonant Triads Thomas M. Fiore http://www-personal.umd.umich.edu/~tmfiore/ Introduction and Basics The Consonant Triad Geometry of Triads Extension of Neo-Riemannian Theory Symmetries of Triads What is Mathematical Music Theory? Mathematical music theory uses modern mathematical structures to 1 analyze works of music (describe and explain them), 2 study, characterize, and reconstruct musical objects such as the consonant triad, the diatonic scale, the Ionian mode, the consonance/dissonance dichotomy... 3 compose 4 ... Introduction and Basics The Consonant Triad Geometry of Triads Extension of Neo-Riemannian Theory Symmetries of Triads What is Mathematical Music Theory? Mathematical music theory uses modern mathematical structures to 1 analyze works of music (describe and explain them), 2 study, characterize, and reconstruct musical objects such as the consonant triad, the diatonic scale, the Ionian mode, the consonance/dissonance dichotomy... 3 compose 4 ... Introduction and Basics The Consonant Triad Geometry of Triads Extension of Neo-Riemannian Theory Symmetries of Triads Levels of Musical Reality, Hugo Riemann There is a distinction between three levels of musical reality. Physical level: a tone is a pressure wave moving through a medium, “Ton” Psychological level: a tone is our experience of sound, “Tonempfindung” Intellectual level: a tone is a position in a tonal system, described in a syntactical meta-language, “Tonvorstellung”. Mathematical music theory belongs to this realm. Introduction and Basics The Consonant Triad Geometry of Triads Extension of Neo-Riemannian Theory Symmetries of Triads Work of Mazzola and Collaborators Mazzola, Guerino.
    [Show full text]
  • Generalized Tonnetze and Zeitnetz, and the Topology of Music Concepts
    June 25, 2019 Journal of Mathematics and Music tonnetzTopologyRev Submitted exclusively to the Journal of Mathematics and Music Last compiled on June 25, 2019 Generalized Tonnetze and Zeitnetz, and the Topology of Music Concepts Jason Yust∗ School of Music, Boston University () The music-theoretic idea of a Tonnetz can be generalized at different levels: as a network of chords relating by maximal intersection, a simplicial complex in which vertices represent notes and simplices represent chords, and as a triangulation of a manifold or other geomet- rical space. The geometrical construct is of particular interest, in that allows us to represent inherently topological aspects to important musical concepts. Two kinds of music-theoretical geometry have been proposed that can house Tonnetze: geometrical duals of voice-leading spaces, and Fourier phase spaces. Fourier phase spaces are particularly appropriate for Ton- netze in that their objects are pitch-class distributions (real-valued weightings of the twelve pitch classes) and proximity in these space relates to shared pitch-class content. They admit of a particularly general method of constructing a geometrical Tonnetz that allows for interval and chord duplications in a toroidal geometry. The present article examines how these du- plications can relate to important musical concepts such as key or pitch-height, and details a method of removing such redundancies and the resulting changes to the homology the space. The method also transfers to the rhythmic domain, defining Zeitnetze for cyclic rhythms. A number of possible Tonnetze are illustrated: on triads, seventh chords, ninth-chords, scalar tetrachords, scales, etc., as well as Zeitnetze on a common types of cyclic rhythms or time- lines.
    [Show full text]
  • MTO 25.1 Examples: Willis, Comprehensibility and Ben Johnston’S String Quartet No
    MTO 25.1 Examples: Willis, Comprehensibility and Ben Johnston’s String Quartet No. 9 (Note: audio, video, and other interactive examples are only available online) http://mtosmt.org/issues/mto.19.25.1/mto.19.25.1.willis.html Example 1. Partch’s 5-limit tonality diamond, after Partch (1974, 110) also given with pitch names and cent deviations from twelve-tone equal temperament Example 2. Partch’s 11-limit tonality diamond, after Partch (1974, 159) Example 3. The just-intoned diatonic shown in ratios, cents, and on a Tonnetz Example 4. Johnston’s accidentals, the 5-limit ration they inflect, the target ratio they bring about, their ratio and cent value. As an example of how this table works, take row 11. If we multiply 4:3 by 33:32 it sums to 11:8. This is equivalent to raising a perfect fourth by Johnston’s 11 chroma. Example 5. The overtone and undertone series of C notated using Johnston’s method Example 6. A Tonnetz with the syntonic diatonic highlighted in grey. The solid lines connect the two 5-limit pitches that may be inflected to produce a tonal or tonal seventh against the C. This makes clear why the tonal seventh of C is notated as lowered by a syntonic comma in addition to an inverse 7 sign. It is because the pitch is tuned relative to the D- (10:9), which is a syntonic comma lower than the D that appears in the diatonic gamut. Example 7. Johnston, String Quartet No. 9/I, m. 109. A comma pump progression shown with Roman Numerals and a Tonnetz.
    [Show full text]
  • From Schritte and Wechsel to Coxeter Groups 3
    From Schritte and Wechsel to Coxeter Groups Markus Schmidmeier1 Abstract: The PLR-moves of neo-Riemannian theory, when considered as re- flections on the edges of an equilateral triangle, define the Coxeter group S3. The elements are in a natural one-to-one correspondence with the trianglese in the infinite Tonnetz. The left action of S3 on the Tonnetz gives rise to interest- ing chord sequences. We compare the systeme of transformations in S3 with the system of Schritte and Wechsel introduced by Hugo Riemann in 1880e . Finally, we consider the point reflection group as it captures well the transition from Riemann’s infinite Tonnetz to the finite Tonnetz of neo-Riemannian theory. Keywords: Tonnetz, neo-Riemannian theory, Coxeter groups. 1. PLR-moves revisited In neo-Riemannian theory, chord progressions are analyzed in terms of elementary moves in the Tonnetz. For example, the process of going from tonic to dominant (which differs from the tonic chord in two notes) is decomposed as a product of two elementary moves of which each changes only one note. The three elementary moves considered are the PLR-transformations; they map a major or minor triad to the minor or major triad adjacent to one of the edges of the triangle representing the chord in the Tonnetz. See [4] and [5]. C♯ G♯ .. .. .. .. ... ... ... ... ... PR ... ... PL ... A ................E ................ B′ .. .. R.. .. L .. .. ... ... ... ... ... ... ... LR ... ... ∗ ... ... RL ... ( ) ′ F′ ................C ................ G ................ D .. .. P .. .. ... ... ... ... ... LP ... ... RP ... A♭ ................E♭ ................ B♭′ arXiv:1901.05106v3 [math.CO] 4 Apr 2019 Figure 1. Triads in the vicinity of the C-E-G-chord Our paper is motivated by the observation that PLR-moves, while they provide a tool to measure distance between triads, are not continuous as operations on the Tonnetz: Let s be a sequence of PLR-moves.
    [Show full text]
  • MTO 15.2: Samarotto, Plays of Opposing Motion
    Volume 15, Number 2, June 2009 Copyright © 2009 Society for Music Theory Frank Samarotto KEYWORDS: Schenker, Kurth, energetics, melodic analysis ABSTRACT: Rameau’s privileging of harmony over melody may be set against the pendulum swing of Kurth’s pure melodic energy. Although Schenker’s theory clearly identifies linear motion as governed by harmony, Schenker could still place great importance on melodic directionality and impulse as independent elements, even when they run counter to the harmonic setting or to the descending trajectory of the Urlinie. Extrapolating from Schenker’s work, this paper will examine what I call contra-structural melodic impulses, characterized by two aspects: directionality and ambitus, and acting as a compositionally significant counter pull to the tonal structure. Received October 2008 [1] Rameau’s seminal treatise of 1722 opens with a powerful declaration: the science of music is divided into melody and harmony, but, he says, . a knowledge of harmony is sufficient for a complete understanding of music (Rameau 1971, 3, editorial fn. 1). Indeed, an annotation in a contemporary copy adds that this makes a “remarkable statement: harmony and melody are inseparable” (Rameau 1971). It is a remarkable statement, especially when understood in light of Rameau’s progression of the fundamental bass, the progenitor of all later theories of harmony. Rameau’s cadence parfaite gathered together the contrapuntal threads of individual melodic lines and made them subordinates of, or at least co-conspirators with the root progression, which is a much more ideal concept.(1) Almost two centuries later, Ernst Kurth tried to detach melody entirely from harmony, hearing in Bach’s melodic lines an unbridled energy, careening about unrestrained by the bounds of harmony (Kurth 1917).
    [Show full text]
  • Lay a 5 2020.Qxp Layout 1
    Jugend musiziert Wettbewerb für das instrumentale und vokale Musizieren der Jugend unter der Schirmherrschaft des Bundespräsidenten 29. Landeswettbewerb 28. bis 29. März 2020 Ludwigslust Veranstalter Landesmusikrat Mecklenburg-Vorpommern e.V. in Zusammenarbeit mit der Stadt Ludwigslust und dem Landkreis Ludwigslust-Parchim Gefördert vom Ministerium für Bildung, Wissenschaft und Kultur des Landes Mecklenburg-Vorpommern Mit freundlicher Unterstützung der Sparkassen in Mecklenburg-Vorpommern und ihres Ostdeutschen Sparkassenverbandes als Hauptsponsor Liebe Schülerinnen und Schüler, liebe Eltern, liebe Lehrerinnen und Lehrer, liebe Freunde der Musik, im Jahr seines 250. Geburtstags fällt Ludwig van Beethoven wohl nicht mehr in die Kategorie »Jugend musiziert«. Von ihm aber stammt ein Satz, den wohl alle unterschrieben, die selber und mit Leidenschaft Musik machen: »Musik ist das Klima meiner Seele.« Diese Wetterlagen verschiedener Gefühle zu transportieren, sie hörbar zu machen: Das ist das Kunst- volle daran, sein Instrument, seine Stimme und das Zusammenspiel mit anderen zu beherrschen. Wer diesen Landeswettbewerb erreicht hat, verfügt nicht nur über Talent, sondern hat auch sein Können unter Beweis gestellt. Hier dabei zu sein, ist ein echter Erfolg, zu dem ich herzlich gratuliere. Hinter diesem Erfolg steckt eine Menge Arbeit, Fleiß und Disziplin. Aber all das Üben, all die inve- stierte Zeit zahlen sich aus. Der Landeswettbewerb ist eine tolle Chance, am Ende sich und seine Fähigkeiten auf Bundesebene zu präsentieren. Ich drücke allen Teilnehmerinnen und Teilnehmer fest die Daumen, dass sie dieses Ziel erreichen. Zuerst aber heißt es, die Bühne des Landeswettbewerbs zu nutzen und die Jury und vor allem das Publikum teilhaben zu lassen, über die Musik zu ihnen zu sprechen und sie zu berühren.
    [Show full text]