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In article
> I once listed to a demonstration of a segment of a piece where
two similar instruments were playing two melodies that intertwined and
were quite nice to listen to. The melodies were than played
individually, and were heard to have quite "unnatural-sounding"
intervals and not be melodic at all, at least as we normally think of
melodies. Upon hearing both together, the brain reassigns the notes
between voices to make a more reasonable-sounding duet.
Insert shameless plug: my own "LCM for 12 Piano Sample" piece off my "Brains" CD is based entirely and extensively on this principle, of resultant melodies emerging from multiple lines of identical timbre, which perhaps might be called "linear melodic construction".
There are 12 pianos, each playing an equal-interval descending scale. They all play notes at the same tempo, but their cycles are all different lengths so their "bar lines" are all spaced differently.
The recording is indeed a "Sample", a particular instance of "moving windows" bringing various individual piano voices into and out of audibility according to a rough performance plan. It is a live performance where the human performer is the mixer who brings the various voices in and out. (I generally hate MIDI sequencer/sampler pieces, and most of the pieces on my CD do NOT use MIDI at all but this is one where I think the tools of MIDI are appropriate, so this piece was implemented in Opcode Vision sequencer files, with Akai S1000 sample playback unit; for the recording, I followed the performance plan and manually muted and unmuted the individual voices)
The listener's mind hears all kinds of melodic and rhythmic ostinatos, but they are "emergent" in that they are generally composed of notes actually played by a number of different piano voices.
Piano #12 plays a 1-note scale i.e. an ostinato. Piano #11 plays a 2-note scale, interval of 11 semitones, i.e. a major seventh between the two notes. Piano #10 plays a 3-note scale, interval of 10 semitones, i.e. a minor seventh between each of the 3 notes. Piano #9 plays a 4-note scale, interval 9 semitones, i.e. major sixth between each of the 4 notes. And so on..... piano #2 plays an 11 note scale, interval 2 semitones, i.e. major seconds between the notes, and finally piano #1 plays a 12-note scale, interval 1 semitone, i.e. a good old chromatic scale.
The highest notes are produced by pianos #6 and 7. A very nice interlocking rhythmic thing happens when these two pianos are brought out in front, as happens at the transition from part 1 to part 2 of the piece.
Also the piano voices are laid out in the sampler so that they are panned to different locations, moving at different rates; piano #1, which has the most notes in its cycle (12-tone chromatic scale), also pans the farthest right and left, also moves the fastest through its panning field. There is a kind of phasing effect, as the notes are produced at the underlying basic tempo rate, but they pan around at a different rate. Also, piano #12 is the quietest, both in loudness and in key velocity.
Piano #2, with 11 notes, pans a little bit less far than #1, and pans a little less rapidly. Also its loudness and key velocity is a little bit higher than #1. And so on, till piano #12, playing its 1-note ostinato, is not panned at all, but is right in the center of the stereo field. Also it is the loudest of the voices, and has the highest key velocity.
So the pianos #6 and 7, which produce the highest pitches, are in the "middle" as far as MIDI loudness and key velocity go; since higher pitches generally sound "louder" even at equal audio intensity level, these highest notes stand out the most, i.e. they pop out in front when they appear. Thus the resultant melodies emerging from the interaction of pianos #6 and 7 (plus their neighbors) are very clear and out in front, at times.
The performance plan goes like this: there are three parts, each following a different "windowing" strategy. The whole piece is 10 minutes long, each part being around 3 minutes and 30 seconds.
In part 1, pianos are introduced one by one, beginning with #1 (the 12-note chromatic) in descending order. But, there are no more than 3 playing at once -- when a fourth piano is introduced, the oldest one is simultaneously dropped out.
Thus there is a gradual rhythmic shift as the cycles grow shorter and shorter. After we get all the way to piano #12's ostinato, we work backwards until we have pianos #5, #6, and #7 playing. #5 and #7 drop out, leaving piano #6 playing solo for a moment.
Note again that pianos #6 and #7 are halfway i.e. they have the "middle" number of notes in their cycles, and the "middle" intervallic size. But they also reach the highest absolute pitches, due to how the equation of "highest pitch = interval x number of notes" reaches its maximum at the center of its curve.
In part 2, higher and lower numbered pianos are re-introduced in pairs, surrounding #6 (i.e. #'s 5 and 7, 4 and 8, 3 and 9, ...) until all are playing again for a brief moment.
Then they are dropped out one by one, first #12 (the 1-note ostinato) drops out, then #11 (the 2-note major seventh), and so on, until only #'s 2 (11-note whole tone scale) and 1 (12-tone chromatic scale) are playing....
Suddenly they are muted and only #12 plays solo, the 1-note ostinato.
For part 3, the pianos are introduced one by one again, in descending numerical order (i.e. in ascending numbers of notes, ascending cycle lengths, and decreasing interval size).
In this part, you can hear "2 against 1", then "3 against 2", then "4 against 3", and so on, till the cacophony begins to build up too much to distinguish the individual voices and their cycles.
At the end you hear a bit of the totality, the "background grid" where all 12 pianos are playing. This is what it would sound like all the way through, if the "windowing" process were not applied to make this particular piece or "Sample".
More info about this piece and the whole "Brains" CD is on my Web pages. Actually I should put up a longer essay about this piece in particular (there are essays there about some other pieces already). I'll try and do that soon, I'll put this essay there as a start.
I also wrote a second piece in the LCM series, "LCM.4567 for 4 Marimbas", which is shorter and is notated. I do hope to write more LCM pieces in the future.
I've been greatly influenced, in my thinking which led up to the LCM series, by the "classic minimalists" who produced additive rhythmic effects in their music, i.e. Philip Glass, Steve Reich, Terry Riley (in fact the piano #12 playing its 1-note ostinato, which just happens to be a "C", is a direct tribute to Terry Riley's "In C"), and John Adams, plus Robert Fripp and Conlon Nancarrow (the whole idea of playing the piece on a bunch of mechanical piano voices is inspired by Nancarrow's player piano music).
So make sure you listen to all of them, too!
I was inspired to do the linear superposition and creation of emergent melodies, by studying music perception and cognition, with David Wessel at UC Berkeley CNMAT. I wrote the very first LCM piece in Alvin Curran's composition seminar, at Mills College. The first LCM piece was for a roomful of people who would count and clap their hands, each on the "1" beat of their cycle.
Also I was inspired to set up the background "grid", the totality of all 12 pianos and their cycles related by the Least Common Multiple principle which governs when they'll all synchronize, in a sort of "democratic" or "total/integral serial" way, after studying the writings of Pierre Boulez, and the Cologne West German Radiofunk "elektronishce muzik" originators, especially Karlheinz Stockhausen, from the 1950's in his journal "Die Reihe". (my essay about his writing, "Karlheinz Stockhausen's New Morphology of Musical Time", is up on my Web pages)
But I took their basic idea, of "democratic" or totally equal parcelling out of all musical parameters, only as the background "grid". Stockhausen's "New Morphology of musical time" was necessary because of the *failure*, of his attempts to produce interesting results from total "democratic", equal-interval control of all musical parameters. So, I reasoned, the way to go is to use his democratic equal-interval structure as the background grid, and then apply the human, emotional processes to make a real *composition* out of it.
Thus the LCM for 12 Pianos is really a "system" which could produce a large number of different individual pieces, from performances that are really selection, or reduction, processes, sculpting an interesting musical piece by eliminating many of the pianos, at different times.
An un-reduced performance of the entire background grid would take a long time, I forget but I think it was around 57 minutes, for all 12 pianos to start together on the tonic note, proceed in the same metronomic tempo, until they would all come together again on the tonic on the same beat again. The time required for this is the LCM (Least Common Multiple) of all their cycles, i.e. "12!" (12 "factorial") times the tempo of the basic beat underneath.
Chris Koenigsberg: ckk@pobox.com
http://www.pobox.com/~ckk