Music Math: The Pitfalls of Reducing to the Common Denominator

The writings of one Joseph Straus have been taking some serious heat over on the Rock’ Em Sock ‘Em Robot boxing ring that is the comment area of FJO’s “Don’t Call Me Stupid.” Straus is undeniably one of the preeminent theorists working in the field today; his impact as a pedagogue is difficult to overstate, particularly given the curricular prominence of his Introduction to Post-Tonal Theory. It is this volume that John Halle cites in “Serialism and Revisionism: A Response to Straus,” noting its overwhelming emphasis on the harmonic practice of the Second Viennese School.

Halle is right about Introduction to Post-Tonal Theory, of course: Even if we restrict our gaze to include only Western concert music, the book leaves out waaaaaay more music than it includes. Introduction to Systematized Dodecaphonic Pitch Ordering is more like it. Halle notes that Ravel and Sibelius are MIA, but I want to know what happened to Finnissy, Schnebel, Young, and Partch, to name but a few. Don’t these composers employ pitches? Why aren’t they in the book?

The short version is that they’re not in the book because it’s difficult to explain to a 19-year-old music education major how to account for each note in their works. Anyone can put together a tone row and a matrix, but that’s only meaningful because (in the pieces Straus cherry-picks for his text, at least) there’s a very clear, visible correspondence between the generating material and the score. I’ll be teaching 20th-century theory in the fall out of Straus’s tome (a decision made far above my pay grade) and I’m really hoping we can plow through the book quickly. Let’s make a few matrices, put a few sets in prime form, and then get to the messy stuff: 11-limit scales, additive number-cycle tuplet rhythms, spectra, etc.

My biggest problem with Straus’s book is that it trivializes 20th-century music by making the clean, unworldly, relatively simple pitch-math out to be “the thing” of the pieces he examines. This approach might help students in large classes locate the beginnings and ends of row-forms in Webern, but it also reinforces the false notion that the value of modern music (in the specific sense—music written during the 20th century in response to the cultural condition of modernity) is reducible to its conformity to artificial numerical patterns. Hopefully we can avoid this pitfall next semester.

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This week on the ol’ New Music Scrapbook you can find a sax quartet of mine called It Plays You, along with a very frank and hopefully somewhat entertaining interview conducted by my esteemed colleague Brett Wartchow. I hope you enjoy both.

15 thoughts on “Music Math: The Pitfalls of Reducing to the Common Denominator

  1. philmusic

    My problem with Forte and Straus is that the approach seems created for one reason–easy to teach and easy to test.

    The basis for this was the computer revolution and the interest in statistical modeling of music years ago. When computers came onto the stage academics threw everything, that is every kind of music, into the mix to see what computer programs could make of them.

    Needless to say nothing stuck except for atonal/serial music where numbers have a certain presence, even though Schoenberg’s rows are letters, not numbers.

    Math is straightforward to teach and understand and yes test. Fortunately there are many other ways to look at music.

    Phil Fried, who prefers Perle and Slonimsky.

    Phil’s page

    Reply
  2. Kyle Gann

    At the Henry Cowell centennial conference in 1997, I gave a paper on the vast influence that Cowell’s explorations of the harmonic series had had on younger generations of composers. Straus gave the paper just before mine. I disremember its topic, but he said, and I paraphrase from memory, “Unfortunately, Cowell based his theories on the harmonic series, which as we all know is not a very significant musical phenomenon.”

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  3. tubatimberinger

    I have to second Phil’s comment; I learned from the Straus book and found it a great spring board BUT, it is just a textbook in the end. I aced that class, but I still had to ask my composition teacher to explain to me how it really works. In my opinion (uninformed as it probably is), no textbook can teach these subjects as well as a composer; one on one with his/her student.

    In the university setting, it’s all about curriculum and measurement. If I had my druthers, we would just go back to true conservatory model where you have teachers, students and a space with resources. No curriculum.

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  4. Mischa Salkind-Pearl

    Am I too late?

    I’d like to say that I have had four wonderful years of private study, and that the institutions supporting me have been exactly that: supportive. Having not earned a BA in composition, I have done all of my academic work in composition at the graduate level- first with Linda Dusman (whom Colin knows well), followed by Marti Epstein and Dalit Warshaw. To respond to Mclaren on FJO’s other post- these teachers have been nothing but encouraging, and their musics all vastly different from mine. It was even the case that I went through nearly two years of study with Dr. Dusman without hearing much more than a minute of her music. So much for agendas…..

    Anyhow, a few points on serialism, style, and Straus. Mclaren grumpily points out what happened to the young tonal composer at USC. Bummer, but dude, I gotta say- isn’t it more than a little disingenuous to be writing something so clearly reminiscent of anyone else’s music from the past? Feldman once said “Doesn’t inheriting a tradition necessitate a certain level of critique?” It smacks of the same insincerity as hipsters dressing in 80’s trash, bars and restaurants that “theme” themselves after a culture (Irish Pubs, for the love of god), and any other referential “throwback” on television. It really begs the question- why are we composing? If the answer is expression, and if we agree that what’s important is not what you express but how you express it, then god help me I’ll take Brahms or Sibelius over some close-minded young punk’s triadic drivel any day.

    That said, serialism is long overdue for close examination as a meaningful and viable methodology. It is so tied to it’s own stacked deck of criticisms (thank Boulez and Stockhausen for that- in their time, the critiques were fresh and meaningful, and maybe it’s time to move on), that it’s function is equally as disingenuous as writing a “tonal” symphonic movement in sonata form. Straus exemplifies the dominance of this mode of thinking several decades ago, but neglects to update its message to be useful as anything but a historical examination. If he wants it to be useful to living composers (and somehow I suspect this is not particularly important to him), he would try to find contemporary analogues to the 1960s’ fascination with structure, procedure, and control. There are a million places to turn if you want to pigeonhole a generation of creativity, and even more if you want to influence it.

    I think it is sad that for some people the issue is either/or: serialism/tonality; serialism/creativity; school/education and so on. It is likewise a little silly to take the “everything all at once” attitude that “as long as you feel it, it’s real and honest.” As much as I don’t want to pretend to know what other composers are feeling, sometimes it’s just pretty clear when a piece has genuine meaning for the creator, and when it doesn’t.

    thoughts?

    Mischa

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  5. GW

    Mischa,

    that McLaren story about a tonal composer at USC just doesn’t make any sense because at the time Kosko was a student, USC had no twelve-tone or serial composers on the faculty. From Ingolf Dahl, Halsey Stevens, Ellis Kohs, and Robert Linn to Morten Lauridsen, the school has been a hotbed of conservatism and a pretty good place to study tonal composition.

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  6. JNarum

    The primary criticisms of Straus’s book seem to be: It focuses almost exclusively on pitch relationships. It omits quite a bit of music (and therefore composers), especially of the second half of the twentieth century.

    At the same time, it’s straightforward. It’s sequential. The index and appendices are actually useful. It includes singing and compositional exercises in addition to a wide range of practice questions ready-made for assignments and many bibliographies for further reading. At a slim 273 pages, it’s portable, which means students may be more inclined to bring it to class or – even better – home to do their homework!

    I’m not attempting to defend this book on the basis of “easy to teach and easy to test” (though if I were teaching four or five courses at a time, that would likely be something I’d consider!). However, given the diversity of approaches to music after the middle of the century and the fact that analysts (composers and theorists alike) are still developing ways to think about and model that music, it seems that one would be “safest” putting the approaches that are generally agreed upon into a textbook. (If anyone has any experience with other twentieth-century theory texts, please share. I’m sure I wouldn’t be the only one interested in hearing about them.)

    Ultimately, it is just a textbook. And unless you’re working with an under-experienced or an apathetic teacher, the textbook is not the class. It’s up to the instructor to bring in other musical examples, design thought-provoking compositional or analytical assignments, demonstrate how the numbers refer to sounds, and try to help students understand why this stuff matters.

    Finally, Colin’s claim that “Straus’s book [...] trivializes 20th-century music by making the clean, unworldly, relatively simple pitch-math out to be “the thing” of the pieces he examines” could be leveled at a lot of music theory more generally. Leaving that aside for another argument discussion… I don’t agree that Straus is making pitch-math out to be “the thing” of these pieces. His text may attempt to explain how pitches are ordered a certain way, but I don’t believe that is conflated with the why of the music. Given the current division between music theory and musicology in American universities, one could argue that the why be covered in a comprehensive and engaging 20th-century history curriculum.

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  7. colin holter

    If he wants it to be useful to living composers (and somehow I suspect this is not particularly important to him)

    I suspect you’re right. I’d be curious to know what Straus’ idea of contemporary music is – are there any composers under 50 he would go to bat for, as an analyst?

    Finally, Colin’s claim that “Straus’s book [...] trivializes 20th-century music by making the clean, unworldly, relatively simple pitch-math out to be “the thing” of the pieces he examines” could be leveled at a lot of music theory more generally. Leaving that aside for another argument discussion… I don’t agree that Straus is making pitch-math out to be “the thing” of these pieces. His text may attempt to explain how pitches are ordered a certain way, but I don’t believe that is conflated with the why of the music. Given the current division between music theory and musicology in American universities, one could argue that the why be covered in a comprehensive and engaging 20th-century history curriculum.

    One sure could, but whether we call it a “theory” class or a “history” class, I think you’d agree that a single analytical survey course slanted heavily toward the first 50 years of the century represents an unacceptably thin portion of the curriculum. Straus’ book for what it is may not be a complete disappointment – but what it is and what it’s cracked up to be by virtue of its curricular dominance are not the same thing.

    Great comments from everybody, by the way – thanks!

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  8. Mischa Salkind-Pearl

    Good point about USC. But since this type of tonal-composer-meets-atonal-institution sob story gets tossed around from time to time, I felt I should mention that my experience was so vastly different.

    What strikes me is that a lot of composers- both students and faculty (read: novice and professionals)- whom I’ve met, still cling to this idea that musical style falls roughly into two large camps: the conservatives, and the atonalists. I have to agree that Straus’ book is indeed well put together for what it is, which is always a benefit when trying to teach reluctant students. But I’ve found that students will often only internalize information that fits their interest. I taught part of a 20th century history course, and what do you know? Horn players were drooling over the Shostakovich, strings were gaga about Bartok, and pianists seemed to think Feldman was a joke. I have had the same experience with students learning about compositional schools and the “isms” of the 20th century. I wonder if students are averse to reading Straus not for his questionable scholarship, but for his stylistic tunnel-vision.

    I think it’s important for teachers to make sure that musicians understand the 12-tone method. More than a system, it represents a huge philosophical rift in compositional thought. Regardless of stylistic attitude, I suspect that students will get into the convictions behind people like Webern, Boulez, et al. Hell, that’s how I got my students into Cage- ideological integrity is undeniable, and if we then step backward, the music begins to make more sense. I think this is the “why” you’re talking about…..

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  9. philmusic

    “..But since this type of tonal-composer-meets-atonal-institution sob story gets tossed around from time to time,..”

    This is all misdirection. The teachers, the ones I knew and know, care not a wit about style. Neither do they care if in their “personal” opinion your music is good or not.

    They only care about one thing; will you be successful.

    Period.

    Phil Fried
    Phil’s very successful page

    Reply
  10. philmusic

    “..His text may attempt to explain how pitches are ordered a certain way, but I don’t believe that is conflated with the why of the music…”

    Hmmmm. Replicating a blueprint is not an analysis. Interesting that in the subject of theory we seem to depend so much on complete certainty.

    As to theorists supporting composers young or old outside their purview Colin that might involve risk. That would be a fine thing but I get the distinct impression that high level academics find their niche and stuck to it whether they like their subject or not and expected other academics to do the same.

    Phil’s How to be an outsider in 2 easy lessons page

    Reply
  11. mclaren

    Henry Cowell’s New Musical Resources (1930), Joseph Schillinger’s The Mathematical Basis Of the Arts (ca. 1945, 2 vols.), Harry Partch’s Genesis Of A Music (2nd ed., 1975), Easley Blackwood’s The Structure of Recognizable Diatonic Tunings (1985), Pierre Henry’s Traite des objets Musicaux (1967) and Gerhard Nierhaus’ Algorithmic Composition: Paradigms of Automated Music Generation (2008) offer alternatives to the Straus book.

    All of the music-theoretic approaches to 20th century music championed in these texts have had continuing influence on viable ongoing compositional styles, unlike the obsolete and psychoacoustically futile methods detailed in the Straus book.

    The Cowell text is largely responsible for the development of neorhythmic music (Kyle Gann calls it “totalist”), a vibrant and expanding musical movement that continues to gain adherents and popularity today. As, for instance, in Eve Beglarian’s Machaut In the Machine Age VI or Michael Gordon’s Four Kings Fight Five.

    The Schillinger book, although clogged with a certain amount of numerological twaddle, has had a decisive impact on both algorithmic and neorhythmic composers today, particularly its emphasis on the “interference of the periodicities” and the potential for (non-serial) mathematical organization of musical form. As, for example, in jazz saxophonist Steve Lehman’s use of a rhythm made up of a sequence of prime values of 16th notes in his song Rai (available on the CD Fieldwork (highly recommended).

    Microtonality remains one of the hottest trends among young composers, and Harry Partch’s and Easley Blackwood’s texts continue to inspire younger composers, as Johnny Reinhard’s American Festival of Microtonal Music demonstrates.

    Henry’s Treatise on Sound Objects has had a vast influence: you only need to attend any International Computer Music Conference to hear its ongoing repercussions.

    And algorithmic composition also qualifies as one of the hottest trends among younger composers, with vast amounts of music being done using MAX/MSP and Pure Data and other algorithmic composition programs by the under-35 composers today. The latest development, live coding in algorithmic laptop performance, continues to expand exponentially among younger composers.

    It stands to reason that since these music-theoretic offshoots represent ongoing vibrant styles eagerly being adopted and pushed forward by younger composers, they must be systematically ignored in music classrooms in favor of a century-old exercise in numerological futility that hardly anyone uses in actual music today. The fact that serialism produces results which run directly contrary to current cognitive neuroscience and psychoacoustics offers an added benefit, since it assures that the resulting music will exhibit no audible organization.

    That’s as we would expect. After all:

    “…The music curriculum at most institutions of higher education…is based on a musical culture of which only remnants still exist, and has little relevance to music in the last half of the twentieth century. In short, our approach to teaching the history, theory, performance, and composition of music, at all levels, is reactionary and of little value to either liberal-arts students or young musicians with professional aspirations.” [Appleton, Jon, "The College Music Curriculum Is In Pressing need of Reform," Chronicle For Higher Education, 19 April 1989, pg. B2.]

    Reply
  12. rtanaka

    It’d probably be good to create a distinction between 12-tone music and serialism because from what I understand they are not the same thing. Serialism usually associates itself with the music after the 2nd Viennese School, where composers started “serializing” parameters other than pitch-classes.

    The original intent of 12-tone music was to give each pitch-class equal weight. This is something that you can actually hear, even if you happen to dislike the music itself. Stravinsky used it, Bartok took an interest in it for a while, and even a lot of jazz and improvising musicians were willing to toy with the idea (albeit less structured) because they felt it had some aesthetic significance. I do think that 12-tone music is worth teaching, since it can be taught as an extension of traditional tonal harmony as well.

    I’m largely skeptical of the post-Webern serial movement, though, because the more I study it my opinion of it gets worse over time. Its language and presentation are usually unnecessarily complex, you can’t hear the correlation between its theories and result, and I’ve found that the vast majority of literature in support of the movement tends to be disingenous or very poorly written. It would be nice to think that Straus’ article is a bad apple amongst a well-oiled machine, but after slogging through one bad article after another, the only thing I can really conclude is that the movement itself is lackluster and hasn’t really produced much valuable research. Probably the best thing to do at this point would be to put it in music history classes and study the style as a cultural phenomenon rather than trying to teach it as theory. I think it’s been around long enough to make that type of judgment.

    My sentiments aren’t exactly new, nor are they uncommon, but when the style is strongly engrained into the academic system it sort of becomes the elephant in the room that noone really wants to deal with. If you were reading carefully, you probably noticed that Straus’ article has an extremely defensive tone to it, which is pretty typical of scholarship done in that style. Subconsciously, serialists probably know that the style is on its way out but if you’ve spend decades of your life and career on one thing you’re probably not going to abandon it even in the face of overwhelming evidence.

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  13. mclaren

    Ryan Tanaka remarked: It’d probably be good to create a distinction between 12-tone music and serialism because from what I understand they are not the same thing.

    Would it? Do we have any evidence from peer-reviewed scientific journals setting out the listening experiments to show that listeners can reliably hear a difference twixt 12-tone music and serialism at a rate statistically better than a coin-flip?

    I haven’t seen any. No one appears to have done the listening experiments.

    The assertion that there’s necessarily an audible difference twixt 12-tone music and serial music seems shaky. Consider an example of a composition which serializes pitch but not rhythm, Le Marteau san Maitre. Now compare it with a composition which serializes all parameters, pitch included, Kreuzspiel. From your description, we’d expect that Le Marteau has a more regular rhythmic pulse than Kreuzspiel, but in fact the opposite is the case — Kruezspiel exhibits such a regular pulse that it practically qualifies as a proto-minimalist piece.

    It’s by no means clear that using ad hoc methods to generate irregular rhythms without a discernible metrical pulse produces music audibly different than using mathematical permutational methods to generate irregular rhythms without a discernible metrical pulse.

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  14. rtanaka

    I’ve written a few works where I assigned a tone-row to each instrument and it remains static throughout the rest of the piece. Yes, you can hear it, because the process is cyclical and the brain is very good at discerning patterns, especially when it’s reinforced by the orchestration. The recording isn’t of very good quality but you can listen to it here if you’d like to hear the result yourself.

    The problem with serialism lies mostly in its methods of transformation (even the “traditional” ones like transpositions, inversions, retrogrades), which detracts from the idea of hitting every note. The music of early Schoenberg and the quartets of Bartok aren’t using tone rows but you can generally hear the “effect” that it’s attempting to exhaust the possible pitch-classes that exist in equal temperament. Post-Webern serialism doesn’t seem to have any interest in doing this, since its ideas are generated from its preconcieved theories, rather than a desired result.

    Detractions are fine, but the problem is that you can’t hear the correlation between the theory and result so it just sounds like a bunch of notes that’s atonal for its own sake. Schoenberg is reacting against tonality and you can very well hear this in his music — Boulez, on the other hand, I’m not really convinced that he really understands what he’s reacting against because there’s nothing really there to comment on.

    At least Cage’s chance processes were self-aware of the fact that these types of choices were largely arbitrary, but serialism has a pretension that its methods are somehow of scientific or intellectual worth. Well, if we were to be totally honest about it, it’s neither and never has been — it’s about wanting the freedom to write whatever you want without the obligation to pay your dues to every pitch-class. A perfect ideology for neo-conservatism in a lot of ways, right?

    Reply

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