Macroharmony and Centricity in Music of Paul Hindemith by Andrew Eason B.M. A Thesis In Music Theory Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of Master of Music Approved by Peter Martens Committee Chair Matthew Santa David Forrest Mark Sheridan Dean of the Graduate School May, 2014 Copyright 2014, Andrew Eason Texas Tech University, Andrew Eason, May 2014 TABLE OF CONTENTS Abstract iii List of Tables iv List of Figures v I. Introduction 1 II. Methodology 8 III. Consistent Macroharmonies and 7-Note Collections: “Pastorale Interlude” from 16 Ludus Tonalis IV. Inconsistent Macroharmonies and 8-Note Collections: “Geburt Mariä” from Das 29 Marienleben V. Hierarchical Centricities within a 9-Pitch Collection: Sonate für Basstuba und 43 Klavier VI. Concluding Remarks 52 Bibliography 57 ii Texas Tech University, Andrew Eason, May 2014 ABSTRACT Through the work in his book and dissertation, David Neumeyer has established an authoritative methodology specifically intended for rigorous analysis of the music of Paul Hindemith. His work, however, explicitly proscribes the search for “tonal cognates” as they make “too many assumptions about the music.” And while this may have been the case in the literature preceding Neumeyer, such as Hans Redlich claiming a melody is in “D minor”, the abstract concepts surrounding the tonal cognates are no longer considered inextricably linked to the pitch material. This recent development is most evident in Tymoczko’s book A Geometry of Music in which he distinguishes scale, macroharmony, and centricity as wholly independent concepts. Most importantly, this approach flips the issue on its head by considering the diatonic scale as an abstract collection of pitches that forms an independent musical object, rather than a fundamentally tonal cognate. With that said, it is challenging to account for the specific pitch level of collections with traditional set-class analysis which is more focused on comparisons of prime forms. In this presentation, I will show how accounting for the specific pitch level of collections and relating them to centricity can descriptively inform analysis of Paul Hindemith through select works. iii Texas Tech University, Andrew Eason, May 2014 LIST OF TABLES 3.1, “Pastorale Interlude” pitch and voice leading content 18 3.2, Diatonic collections as they relate to Neumeyer’s Stage I graph 22 3.3, Abstract structural pitches derived from a strict “Dorian” interpretation 23 4.1, “Geburt Mariä” B section, pitch and voice leading content 33 4.2, Relationships of structural pitch and macroharmony 37 4.3, “Geburt Mariä” summary of collections in piano right hand mm. 21-32 41 iv Texas Tech University, Andrew Eason, May 2014 LIST OF FIGURES 2.1, Craft Series 1, strength of relationship to tonic C, decreasing left to right 11 2.2, Craft Series 2, harmonic force of vertical intervals, decreasing left to right 11 2.3, Scale and macroharmony are the same in the first line, but not in the second 13 3.1, Succession of diatonic collections in “Pastorale Interlude” 19 3.2, “Pastorale Interlude” mm. 5-9 20 3.3, Neumeyer’s Stage I analysis 22 3.4, Abstract structural pitches derived through macroharmonic analysis 23 3.5, Neumeyer’s Stage II Analysis of the “Pastorale Interlude” 25 3.6, Revised Stage II Analysis of the “Pastorale Interlude” 26 3.7, “Pastorale Interlude” full score 28 4.1, “Geburt Mariä” mm. 7-20; G-major collection 31 4.2, “Geburt Mariä” mm. 78-95; G-major collection 32 4.3, “Geburt Mariä” mm. 44-49 Ab collection (8-23) 34 4.4, “Geburt Mariä” mm. 50-55; tertian chords in contrast with preceding music 35 4.5, Subject of “Fuga undecima in B” 36 4.6, Stage IV reduction of “Geburt Maria” B section 37 4.7, Voice-leading models between sets of differing cardinalities 38 4.8, “Geburt Mariä” Soprano mm. 21-36 39 4.9, “Geburt Mariä” piano left hand mm. 21-33; Octatonic bassline with vertical 40 tertian sonorities 4.10, “Geburt Mariä” Piano right hand mm. 21-32 41 v Texas Tech University, Andrew Eason, May 2014 5.1, Sonate für Basstuba und Klavier, Tuba mm. 1-4, P1 44 5.2, Sonate für Basstuba und Klavier, Piano mm. 18-21, P2 44 5.3, Sonate für Basstuba und Klavier, Piano mm. 24-28, P3 44 5.4, Sonate für Basstuba und Klavier, Piano mm. 28-30, S1 45 5.5, Sonate für Basstuba und Klavier, Piano mm. 32-34, S2 45 5.6, Sonate für Basstuba und Klavier, Piano mm. 39-41, S3 45 5.7, P1 with accompaniment mm. 1-4, demonstrating full sounding macroharmony 47 5.8, Sonate für Basstuba und Klavier, Stage I analysis 50 vi Texas Tech University, Andrew Eason, May 2014 CHAPTER I INTRODUCTION The present research project is a collection of analyses of Hindemith’s music drawn from the later portion of the composer’s career: 1942-1955. While there is currently a well-established theoretical body of works regarding analysis of Hindemith’s music in David Neumeyer’s writings—which will be covered in detail below—it is nearing thirty years since its publication. As impressive and descriptive as these works may be, the scholarly realm has since developed new perspectives and analytic tools in the burgeoning field of neo-Riemannian theory that simply could not have been accounted for at the time of Neumeyer’s writing. In this paper, I will approach selected compositions of Paul Hindemith using a methodology derived from the structural and reductive theories of David Neumeyer, combined with a focus on macroharmony and centricity, as most fully articulated by Dmitri Tymoczko in A Geometry of Music.1,2 The shadow cast by contrasting the analytic results of these two systems will both bring light to specific facets of each theoretical system as well as enable a new frame of reference on the compositions in question. Paul Hindemith’s aversion to the analysis of his work explains in no small part the relative lack of in-depth analysis of his works. The majority of literature on Hindemith’s music approaches it from an almost purely historical tradition by relying on off-hand generalizations about his music or on vague statements borrowed from other writers. Most of this literature then uses this critical approach as substantial evidence in an 1 David Neumeyer, The Music of Paul Hindemith (New Haven: Yale University Press, 1986). 2 Dmitri Tymoczko, A Geometry of Music (Oxford: Oxford University Press, 2011). Texas Tech University, Andrew Eason, May 2014 attempt to force the composer and his works into either camp of the highly polemical tonal-atonal critical dichotomy characteristic of the early to mid twentieth-century. There are two notable exceptions to this trend in this literature: David Neumeyer’s near encyclopedic theory-building and analysis project centered on Hindemith’s compositional style, and Victor Landau’s article “Paul Hindemith, a Case Study in Theory and Practice,” which combines the comparative analyses found in Hindemith’s The Craft of Musical Composition (hereafter Craft) with Hindemith’s own music. To be sure, there has been considerable literature specifically addressing Craft, such as Norman Cazden’s and Otto Ortmann’s works.3,4 However, these works only take into account Hindemith’s theoretical writings without comparison to or analyses of his works. Although the present research is focused on the application of analytical tools developed after Hindemith’s death, it would be ill-advised to undertake analysis of Hindemith’s music without some direct consideration of the composer’s own writings. Hindemith created Craft as a way consolidate his own theories into a pedagogical framework for students and teachers of composition alike. Intended to be a series of four books, only the first three were completed and published; the third has not yet been translated to English, and very little written material exists that was intended for the fourth. The first book is subtitled Theoretical Part while the second and third books are explicitly exercises for two and three part writing respectively. Here, I will focus primarily on the first book as it is significantly richer for the present ontological pursuits while the later books function more as practical workbooks in comparison. 3 Norman Cazden, “Hindemith and Nature,” Music Review 15, no. 4 (Nov. 1954): 288-306. 4 Otto Ortmann, “An Analysis of Paul Hindemith’s ‘Unterweisung im Tonsatz’,” Bulletin of the American Musicological Society, no. 4 (Sep., 1940): 26-28. 2 Texas Tech University, Andrew Eason, May 2014 Even a cursory glance of the table of contents will give the sense of the composer’s strong philosophical rejection of the atonal movement. The inclusion of keywords like “overtones”, “nature” or “natural”, “triad”, “Scale-Formation”, and “Value of the Intervals,”5 and quotes from Johann Joseph Fux to start the introduction show a deliberate preference towards conservative musical values. The book starts with this discussion of the overtone series through practical demonstrations based on the monochord, violin harmonics, trumpet and flute. Then Hindemith creates a tempered tuning system for the chromatic scale derived through insights gleaned from his discussion of the overtone series. Continuing this acoustic investigation, he creates a system of interval and chord root based in combination and difference tones. It is clear from this acoustic derivation of a theoretical system that Hindemith’s concept of dissonance is not merely an abstract notion influencing compositional treatment of specific pitches but is seen as inherent in acoustic relationships between pitches. The primary article of Victor Landau’s on which I will focus, “Paul Hindemith, a Case Study in Theory and Practice,” selects a number of rules from Hindemith’s pedagogy outlined in Craft that can be identified as followed or violated, and that aren’t abandoned as the student progresses, as are first-species counterpoint rules.