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Posted by caleb "middlebrow" morgan >”I studied a lot of music theory at Berklee, although my major was composition, and while I found the theory applied in such books as Introduction to Post-Tonal Theory, by Joseph N. Straus, to be interesting in the course of study, I often have trouble HEARING the relationships that are presented post-composition to the listener. I understand how many find this sort of mathematical study interesting, and even useful for compositional creativity from time to time, but I do have trouble hearing the relationships that theorists often come up with, as do most listeners (including many top-notch composers and musicians).” You make an excellent point, one that I’ve grappled with a lot and that is much debated. How much can people HEAR this stuff? First, short answer: In the music I tend to enjoy the most, the material is presented as themes, melodies and motifs, in the good old-fashioned sense. Think Bartok, some Schoenberg, and Berg, for example. For another example, think about any fugal or imitative texture—the “theme” is present all over the place. It’s quite possible to write 21st century music with motifs, themes, or rows that makes the subject clear through sheer assertion—I mean, the music just repeats the subject in different ways over and over; you can’t miss it. But we can also enjoy music that we can’t understand so explicitly. More on this below. Now, can the mathematical (or other) derivation of a theme be directly perceived? Well yes, and no. Supposing I give this to a solo oboe. She plays, C-Db. Pause. Db-Eb. Pause. Eb-G. Pause. And so on. You mention Straus’ Intro to Post-Tonal Theory. A competent book. I’m simply not sure there is a separate “non-tonal” kind of hearing. My own cognitive process resembles a Rube Goldberg machine. People with absolute pitch and a certain kind of mind have a much simpler process of hearing. I’m not one of them. When it comes to the music of Babbitt or Boulez, I’ve met only a few people who “really” hear the stuff. One violinist I knew (David Fulmer by name) had absolute pitch and a flair for math. So he could listen to a string quartet by Babbitt without the score, track the pitches in his head, and perform a more or less instant mental analysis of the serial relationships. If I had never met him, I would be dubious. I would be sitting there, enjoying the music, and I’d say: “David, I just heard an octave! What was that?” “Oh”, he’d say, that was a weighted aggregate. He’s emphasizing the C# here because it has an important role in the tri-chordal array”. Um, Ooookaaay…. The annoying thing was that David wasn’t b.s.ing. He could really hear the stuff. However, maybe 9 out of 10 music students who claim to like Babbitt either like his music for other reasons, or they are full of it, or they have issues that should be discussed with a mental health professional. Many people have made the point that you can enjoy the music of Babbitt without really getting it. One thing is certain. It does NOT sound random. Try alternating a texture made with some kind of random process with a texture made by a serial process and I guarantee you will hear a difference. Now, at the opposite extreme, there are minimalist composers where there is nothing to hear BUT the basic process and the material. In the work of a composer like Tom Johnson, you can definitely hear the melodies looping at different speeds. You may not realize that the loop is derived from some permutation involving 13 and 2, but you hear what he wants you to hear. A really oblique example is the choreography of Mark Morris. He clearly repeats gestural motifs as a kind of thread that you can follow. I mention him not only to drop names but also to show that motifs can apply outside of music—in dance or painting, for example. Consider the self-similar series: C#, E, B, G, F#, D, C, Bb, F, A, Eb, Ab. It has both tonal associations and a fairly audible structure. Starting on the second note, and skipping every other note: e, g, d, bb, a is an exact transposition of the first 5 notes. Starting on the third note and skipping every 3rd note, with one exception: b,d,a. Looking at all the versions (transpositions, rotations, inversions, retrogrades, 5m expansions, etc.) you find many, many places where the c#,e,b,g,f# motif is repeated. It’s actually pretty straightforward to bring this out by dividing the series into strands in separate registers. Even a middle-brow like me can hear it! Tonally, there’s a Neopolitan function going to a V chord. There’s even a 2-5 at the end! Once again, too tonal for school! Once you get past writing stuff for assignments in school, obviously you can do whatever you want. And I DO think the test of your honesty as a composer is whether you can hear it yourself. And whether you like it. More later. Including response to second part. I definitely would like to read any theory papers you’ve written. I enjoy discussing this stuff, especially when we stay close to specific examples.
on 10/4/2006, 3:28 am, in reply to "Re: mallalieu & self-sim series"
24.63.115.63
PSM113 said:
My response:
Supposing my “theme” is the 12-tone row based (not on the indices) directly on the formula: “2 to the nth power in a modulus of 13”. (Or 2 ^ n mod 13, for short.) In pitches: C, Db, Eb, G, D, F, B, Bb, Ab, E, A, F#. The intervals BETWEEN the notes are: 1,2,4,7,3,6,11,10,8,5,9,6.
Given a simple texture, and an explicit presentation with pauses so the listener has time to “chunk” and process, yes, you can hear that the intervals are getting wider in a more-or-less 2:1 rate of growth.
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