University of San Diego Digital USD Undergraduate Honors Theses Theses and Dissertations Spring 5-19-2015 Twelve-tone Serialism: Exploring the Works of Anton Webern James P. Kinney University of San Diego Follow this and additional works at: https://digital.sandiego.edu/honors_theses Part of the Music Theory Commons Digital USD Citation Kinney, James P., "Twelve-tone Serialism: Exploring the Works of Anton Webern" (2015). Undergraduate Honors Theses. 1. https://digital.sandiego.edu/honors_theses/1 This Undergraduate Honors Thesis is brought to you for free and open access by the Theses and Dissertations at Digital USD. It has been accepted for inclusion in Undergraduate Honors Theses by an authorized administrator of Digital USD. For more information, please contact [email protected]. Twelve-tone Serialism: Exploring the Works of Anton Webern ______________________ A Thesis Presented to The Faculty and the Honors Program Of the University of San Diego ______________________ By James Patrick Kinney Music 2015 Introduction Whenever I tell people I am double majoring in mathematics and music, I usually get one of two responses: either “I’ve heard those two are very similar” or “Really? Wow, those are total opposites!” The truth is that mathematics and music have much more in common than most people, including me, understand. There have been at least two books written as extensions of lecture notes for university classes about this connection between math and music. One was written by David Wright at Washington University in St. Louis, and he introduces the book by saying “It has been observed that mathematics is the most abstract of the sciences, music the most abstract of the arts” and references both Pythagoras and J.S. Bach as people who noticed a connection between the two long ago.1 David Benson from the University of Georgia wrote the other one, and he dives right into some questions that the book attempts to answer, such as “How is it that a string under tension can vibrate with a number of different frequencies at the same time?” 2 I have not looked at questions this complex, but I first became interested in the mathematical composition of music when I composed a piece based off the Fibonacci sequence for a college music class. It was in a music history class covering music from the 19 th and 20 th centuries that I was first introduced to serialism, and it immediately piqued my interest. My advisor recommended that I read up on twelve-tone serialism particularly, and gave me George Perle’s book on the subject to start. He recommended that I look specifically at Anton Webern because he utilized it the most consistently in his works, which would probably be easiest to analyze. I did all of the above and decided to base my thesis on his composition Variations, Op. 27 . 1 David Wright, Mathematics and Music , vol. 28 (American Mathematical Soc., 2009), ix. 2 David Benson, Mathematics and Music (University of Georgia. Department of Mathematics, 2004), ix. 2 In my thesis, I will provide a background on how twelve-tone serialism came to be, talking about the formation of the Second Viennese School and the origins of atonality. Then I will give an overview of serialism and then dive into the specifics of twelve-tone serialism, with regards to the formation of the row and the placement into music. I will then provide an in-depth analysis of Variations and display the conclusions of my research, and finally conclude with ideas for further research. Background on Atonality Before looking at the birth of atonality, I will first take some time to describe the end of the Late Romantic period and then see how the atonality of the Post-Great War period arose. The Late Romantic period can hardly be brought up without bringing up Wagner’s Der Ring des Nibelungen , The Ring Cycle. The Ring was Wagner’s ideal of gesamtkunstwerk , or “total artwork.” 3 It was his theory that he laid out in a few pamphlets that he believed that gesamtkunstwerk was an artistic ideal that eventually “crumbl[ed]…into the individual arts – that of the dance, of music, of poetry, and of the plastic arts.” 4 He believed that it was his task to reunite the arts, and this realization culminated in the twenty-six year process that brought about Der Ring des Nibelungen .5 Wagner controlled and created every aspect of The Ring , from the music to the text to the costumes, and even had his own stage build to stage the production. The consequence of The Ring is that Wagner had developed tonal music to the extent that composers who came after him were left in his shadow and the shadow of The Ring . Einstein notes that the only operas that come after Wagner are only worthwhile because they do not 3 Alfred Einstein, Music in the Romantic Era (New York: W. W. Norton and Company, Inc., 1947), 235. 4 Ibid., 236. 5 Ibid., 236-37. 3 attempt to be heroic and philosophical in the way that Wagner’s operas were. 6 Wagner too, in addition to culminating the development of tonal music, also started the turning point towards atonality with the “emancipation of the dissonance” that started to emerge in his opera Tristan und Isolde , with the development of the dissonant Tristan chord. 7 To look at the birth of atonality, however, we cannot look at Wagner, even though he began the process of emancipating the dissonance. We must turn our attention to Arthur Schoenberg. According to Ethan Haimo, “the birth of atonality was not sudden, did not emerge complete in all of its details…Rather, there was an extended period in which the syntax and idioms characteristic of tonal music gradually disappeared and nontonal procedures began to take their place.” 8 Schoenberg, through the process of composing, gradually arrives at a place that is now considered atonality, although he rejected this term.9 This is important, because it is often thought that tonality became so complex (i.e. Wagner) that it was too difficult to “determine contextual definition as described,” and as a result, tonal functions were completely abandoned in favor of atonality. 10 While this is essentially what happened, the shift to atonality was much more gradual than this oversimplified idea implies. To see how atonality arose from tonality, Haimo looks at Schoenberg specifically, because he is undisputedly the leader of the atonal movement and is primarily responsible for bringing about this shift. He looks at one of Schoenberg’s essays, Harmonielehre , and finds that he has a particular conception of tonality that is not quite dissimilar to many others, and Haimo argues that looking at his theories of tonality can shed light on how his conception of atonality comes about. One thing he notices is that when outlining chord progressions, Schoenberg makes 6 Ibid., 257. 7 Ibid., 361. 8 Ethan Haimo, "Schoenberg and the Origins of Atonality," Constructive Dissonance: Arnold Schoenberg and the Transformations of Twentieth-Century Culture (1997): 72. 9 Paul Lansky et al., "Atonality," Grove Music Online . 10 Ibid. 4 no mention of harmonic progression, but only guidelines for moving from one chord to the next. 11 What this means is that he is able to follow his rules of chord progression, but overall, his harmonic progressions aren’t necessarily directed towards the tonic, but seem to wander aimlessly. Haimo notices that if Schoenberg restricted his method in a number of ways, such as beginning and ending a phrase on the tonic, relying primarily on diatonic notes, and using only a small number of chord progressions, his chord progressions could start to resemble more traditionally “tonal” music using the idea of figured bass. 12 However, as Haimo notes, Schoenberg rarely places these restrictions on his music, and as a result, his music is not intrinsically directed towards a tonic, even though he utilizes triads and seventh chords and proper voice leading. 13 Another clue into the idea of atonality from Schoenberg’s theory of tonality comes from his view on non-diatonic notes. It is his opinion that one should be free to utilize the notes of any of the church modes at any time, and the consequence of this is that he regards non-diatonic notes as equally viable as diatonic notes, which makes it nearly impossible to distinguish which notes are diatonic, and thus what the tonic is. 14 It is clear to see how this idea results in a disestablishment of tonal hierarchy and paves the way for atonality. The Second Viennese School I will now move the discussion to the Second Viennese School and how its constituents arrived at twelve-tone serialism. The Second Viennese School, as Auner outlines, is actually 11 Haimo, "Schoenberg and the Origins of Atonality," 74. 12 Ibid., 75. 13 Ibid., 76. 14 Ibid., 78. 5 difficult to define, and it has been defined differently over time. 15 There are various composers whose membership is questionable, but three undisputed members of the school, who I will regard as the sole members, are Arthur Schoenberg, Alban Berg, and Anton Webern, the latter two being Schoenberg’s most prominent students. The name, of course, comes from the First Viennese School of the Classical period, namely Haydn, Mozart, and Beethoven. Unlike the original school, however, named as such retroactively, this school was self-identified by its members. Apart from the fact that these composers were all born and raised in Vienna, the name also implies their belief of what they were doing as revolutionizing music as had not been done since the Golden Age of music that was the First Viennese School.