I think I’ve come up with a way of generating pitch, rhythmic, and textural rotation in the brass fanfare I’m working on while repressing my own intuition (which can’t always be trusted!). I started with the harmonic series–like I’ve been doing a lot lately. I created a chord that looks kind of like the harmonic series, although it is crammed into equal temperament (at least for now) to make it more manageable for a microtonal novice like me. So, this chord begins with wide intervals in the lower range and proceeds, as one would expect, to smaller intervals as the pitches get higher. (Without looking at my notes, I think the pitches are C2, C3, G3, C4, E4, G4, B-flat4, C5, E-flat5, F-sharp5, G5, A5, and D6).
I decided to go a little Messiaen and assign each pitch in this chord to a certain rhythm. Initially, I simply made the harmonic’s ordinal number the denominator of a fraction of the lowest note’s duration. In other words, C3 would be half the duration of the bottom note C2, G3 would be 1/3 of C2, C4 1/4, etc. This presented the practical problem of dealing with 13 against 12 against 11 against 10 against 9, etc. Of course it wouldn’t phase a composer like Ferneyhough, but with a deadline looming I just didn’t have the stomach for it today. I adjusted the rhythms to a simpler (think Ligeti) model of native subdivisions with a triplet and quintuplet thrown in for good measure (no pun intended). So now each pitch in the chord is assigned a value that corresponds to it’s place in pitch space (the lowest note being the longest, the highest note being the shortest). That seemed intuitive to me, but intuition often leads to dull and monotonous, so I devised a system of rotation.
I collapsed the chord into a stepwise 8-pitch (not octatonic) C scale (C, D, E-flat, E, F-sharp, G, A, B-flat). I then rotated the first pitch to the end of the scale (D, E-flat, E, F-sharp, G, A, B-flat, C) eight times and transposed each rotation to begin on C (C, D-flat, D, E, F, G, A-flat, B-flat). Thus I had eight C scales that each have a different pitch content. If you look at each of these scales, they are out-of-order transpositions of the first scale. For example the first rotation above is tonally analogous to the original scale, but transposed to B-flat. In other words, all the pitches in the first rotation correspond to the pitch B-flat in the same way that the pitches in the original scale correspond to the pitch C. So I’m thinking tonally here–the original scale is “in C” and the first rotation is “in B-flat”.
In the original, the tonal relationships are root, 9th, sharp 9th, 3rd, sharp 11th, 5th, 6th, 7th. This is important because durations are attached to the note’s relationship with the active root. The root (bottom note in the original scale) is the longest duration, etc. In the first rotation (in B-flat), the tonal relationships are 9th, sharp 9th, 3rd, sharp 11th, 5th, 6th, 7th, root. The root is now at the top and the 9th is on the bottom.
Don’t forget that these scales are only pitch collections which will be ordered differently in the actual music.
So, here’s the important outcome of today’s work. As one chord morphs into another in the music, individual voices will move to the closest pitch in the new collection. That means that the bottom voices will probably stay on C throughout. The tenor voices might change to a D-flat or D occasionally and so on. But, the durations will change according to the operative collection at any given moment. So if C is the “key,” the B-flats, for example, will be about 1/7 the duration of C–fast notes. But, later, when B-flat collection takes over, the B-flats will be longer and the C (now functioning as a 9th) will be much shorter. But, the actually pitches won’t move much. The C’s will still be in the low voices and the B-flats in the high.
The basic result will be a texture that has the fast-moving lines slowing rotating through the ensemble. This system will force the tubas to play fast and the trumpets to play slow, or in other words, counter to my intuition of duration related to position in pitch space. Rather, now duration is attached to harmonic relationships which will constantly change.
OK–now gotta write this sucker.
