A Geometry of Music – Dmitri Tymoczko: Foreword and Introduction

Well, to start this series, I’m just going to say that I can’t ever remember how to type, much less say Tymoczko’s name. In the interest of my sanity and for the sake of brevity, I’m going to abbreviate his name to Dr. T. This is not out of disrespect, this is out of my inability to remember how to spell his name.

As with the Persichetti, I’m dedicating this post to the introduction to the text and let Tymoczko speak for himself through the foreword of the text, as well as to announce the start of the series, and as a warning that this one will be quite a bit more intense than Persichetti in various ways.

When I was about 15 years old, I decided I wanted to be a composer, rather than a physicist or mathematician. I had recently switched from classical piano to electric guitar, and although I exhibited no obvious signs of compositional talent, I was fascinated by the amazing variety of twentieth-century music: the suavely ferocious Rite of Spring, which made tubas sound cool; the encyclopedic Sgt. Pepper, which contained multitudes; the hypnotic repetitions of Philip Glass, whose spirit seemed also to infuse the music of Brian Eno and Robert Fripp; and the geeky sophistication of art rock and new wave. I was aware of but intimidated by jazz, which seemed to be perpetually beyond reach, like the gold at the end of a rainbow. (Told by my guitar teacher that certain chords or scales were jazzy, I would inevitably find that they sounded flat and
lifeless in my hands.) To a kid growing up in a college town in the 1980s, the musical world seemed wide open: you could play The Rite of Spring with your rock band, write symphonies for electric guitars, or do anything else you might imagine.

I was somewhat surprised, therefore, to find that my college teachers—famous
academics and composers—inhabited an entirely different musical universe. They
knew nothing about, and cared little for, the music I had grown up with. Instead, their world revolved around the dissonant, cerebral music of Arnold Schoenberg and his followers. As I quickly learned, in this environment not everything was possible: tonality was considered passe and “unserious”; electric guitars and saxophones were not to be mixed with violins and pianos; and success was judged by criteria I could not immediately fathom. Music, it seemed, was not so much to be composed as constructed—assembled painstakingly, note by note, according to complicated artificial systems. Questions like “does this chord sound good?” or “does this compositional system produce likeable music?” were frowned upon as naive or even incoherent.

I studied many things in college: seventeenth-century masses, eighteenth- century Lutheran chorales, and twentieth-century avant-garde music. I learned about Heinrich Schenker, who purported to reduce all good tonal pieces to a small number of basic templates. I absorbed mathematical tools for constructing and deconstructing atonal compositions. But I did not learn anything whatsoever about jazz, Debussy, Ravel, Shostakovich, Messiaen, or minimalism. In fact, even the music of Wagner and Chopin was treated with a certain embarrassment—acknowledged to be important, but deemed suspiciously illogical in its construction. Looking back, I can see that the music I encountered was the music my teachers knew how to talk about. Unfortunately, this was not the music I had come to college wanting to understand.

Twenty years later, things are different, and a number of the barriers between musical styles have fallen. Many composers have returned to the tonal ideas that my own teachers deemed irrelevant. Electric guitars now mix freely with violins, and everything is indeed permitted. But despite this new freedom, tonality remains poorly understood. We lack even the most rudimentary sense of the musical ingredients that contribute to the sense of “tonalness.” The chromatic music of the late nineteenth century continues to be shrouded in mystery. We have no systematic vocabulary for discussing Debussy’s early 20th-century music or its relation to subsequent styles. Graduate students in music often know nothing about bebop, or about how this language relates backward to classical music and forward to contemporary concert music. As a result, many young musicians are essentially flying by the seat of their pants, rediscovering for
themselves the basic techniques of modern tonal composition.

The goal of this book is to understand tonality afresh—to provide some new theoretical tools for thinking about tonal coherence, and to illuminate some of the hidden roads connecting modern tonality to that of the past. My aim is to retell the history of Western music so that twentieth-century tonality appears not as an aberration, the atavistic remnant of an exhausted tradition, but as a vital continuation of what came before. I hope that this effort will be useful to composers who want new ways to write tonal pieces, as well as to theorists, performers, and analysts who are looking for new ways to think about existing music.

While my primary audience consists of composers and music theorists, I have
tried to write in a way that is accessible to students and dedicated amateurs: technical terms are explained along the way, and only a basic familiarity with elementary music theory (including Roman numeral analysis) is presumed. (Specialists will therefore need to endure the occasional review of music-theoretical basics, particularly in the early chapters.) More than anything else, I have attempted to write the sort of book I wish had existed back when I first began to study music. It would make me happy to think that these ideas will be helpful to some young musician, brimming with excitement over the world of musical possibilities, eager to understand how classical music, jazz, and rock all fit together—and raring to make some new contribution to musical culture.

As a short response to this, it’s unfortunate that the musical landscape in academia is so opposed to furthering the education of music as a whole instead of focusing on the compositional intellect that was exhibited by the Second Viennese School and its followers. While I do enjoy the music and techniques they used, I feel that shutting yourself off from any form of music is ultimately weakening yourself as a musician. While I listen to art music almost exclusively, I tend to pick from a wide range of styles within the genre as a whole, everything from Indeterminacy and Minimalism, to Expressionism and Serialism. These styles all contain their own subtleties and nuances, that put forth their own difficulties in writing, and all of which can be applied to composition in an eclectic style. It’s important to do what’s right for the message you are trying to convey in the music, and if that message ultimately decides that using tone rows against a dense background of Impressionistic progressions, to serve the music to the best of its ability, then the composer should be able to understand the nuances of both parts of the style in order to fully capture their idea. When it gets right down to it, I believe that the best composers don’t limit themselves to a single idea or genre of music, and that the ability to understand and deconstruct a style to the point of being able to write in it. Versatility is a composer’s most powerful tool.

However much of a plug this may be for the school I go to, I’m quite happy that the professors at Snow College have largely avoided the issue Dr. T brings up in his introduction. Yes, there is focus put into the music of the Second Viennese School, but there is just as much focus on styles like Romanticism, Expressionism, and Classicism, as well as the vernacular styles of Jazz, Blues, and Country, so as to give students a truly well-rounded education in music. While there are some things I wish that the school went more in depth with, as well as general disagreements with recent changes in the curriculum of Music History, I have to admit that the education you receive there is truly fantastic, particularly so for the money you pay for attendance.


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