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Check out the writings of Joseph Schillinger for ideas in using natural sequences like the Fibonacci series for rhythmic, harmonic, and melodic ideas. Also, Bartok's music is full of Fibonacci examples. In fact, if I remember correctly, the final phrase of the first movement of his Music for Strings, Percussion, and Celesta is made up exclusively of intervals in the Fibonacci series (if counting half-steps). One of my current works in progress uses the Fibonacci series both in large-scale formal organization (recursive, actually, down to the phrase level) as well as pitch organization. Here's a glimpse at one way I use Fibonacci for pitch: 1) Take an interval of 13 half-steps (say C-->Db) 2) Divide it into it's Fib. components: 8+5. C-->Ab-->Db 3) Rotate the 8+5 interval sequence to 5+8: C-->F-->Db 4) Combine the sets in steps 2 and 3: C-->F-->Ab-->Db (interval sequence: 5+3+5) 5) Rotate the 5+3+5 interval sequence to 3+5+5: C-->Eb-->Ab-->Db 6) Rotate to 5+5+3: C-->F-->Bb-->Db 7) Combine 4-6: C-->Eb-->F-->Ab-->Bb-->Db (3+2+3+2+3) 8) Rotate (2+3+2+3+3): C-->D-->F-->G-->Bb-->Db 9) Rotate (3+2+3+3+2): C-->Eb-->F-->Ab-->B-->Db 10) Rotate (2+3+3+2+3): C-->D-->F-->Ab-->Bb-->Db 11) Rotate (3+3+2+3+2): C-->Eb-->Gb-->Ab-->B-->Db 12) Combine: C-->D-->Eb-->F-->Gb-->G-->Ab-->Bb-->B-->Db (2+1+2+1+1+1+2+1+2) If you repeat the steps again, you end up with the chromatic scale, so I stopped there. I'm particularly fond of using the Fibonacci series for formal organization, but this is the first time I've tried building any pitch material with it. I'm also quite fond of the prime numbers. I've got a song cycle where the piano part in one of the movements is isorhythmic using 5 chords and 7 rhythms (I think--it's been 8 years since I've looked at the score). The rhythms themselves were also derived from the resultant polyrhythm of 3 prime numbers. This is a technique that I cheerfully stole from a combination of Schillinger and Messiaen. Using the prime sequence or Fibonacci sequence as frequency ratios can yield either very 'normal' stuff or very wild stuff, depending on how you would implement it. I wrote a piece for guitar and 'tape' (called "Cthulhu") while in grad school where the tape part opens with a bell-like instrument created in Kyma using FM synthesis where the carrier and modulator were at 'golden-section' ratio to one another (the ratio to which the Fibonacci sequence increasingly approaches). It was a wild sound. On the other hand, I've played with prime number frequency ratios with Csound and Audiomulch tone generators and the result was a very cohesive timbre. Melodically, you'd probably want to reduce the ratios to within an octave or at least within a couple octaves. This is similar to a technique used by any number of composers working in Just Intonation: 7:1 becomes 7:4 so that it falls between 1:1 and 2:1 (or 1/1 and 2/1). It'd take me a lot of practice on my fretless guitar to be able to reliably play intervals of 13/11 or 11/7 or (gulp) 89/47. This is where Csound or other computer music programs become invaluable. Cheers, Jon Southwood On 6/21/05, Todd Pafford <calenlas@gmail.com> wrote: > Love this discussion. What I wonder, though, is would it be possible > to weave a melody using the prime sequence (or, ooh, the Fibonacci > sequence) as note intervals? And, what would be better, using the > sequence numbers as scale intervals or as frequency ratios? Then > combine that with the rythmical divisions. > > I don't know how it'd sound, but it'd be an interesting exercise. :) > > Todd > >