## Thursday, January 6, 2011

### Xentimbre: Chowning and Sethares style

Chowning on the use of the Golden Mean in his composition Stria (1977)

Chowning: It was based on an idea that occurred in the early 1970s. Just after I'd finished Turenas I was doing some experiments with FM synthesis using inharmonic spectra. I marveled at the fact that in setting inharmonic ratios between carriers and modulators, that unlike in nature, there was a perceptible order when one moved through the frequency space with a constant spectrum. Even when I changed the envelopes, there seemed to be something remaining that was certainly distinct from the harmonic series but was still ordered.

Then when I was in Berlin in 1974 and had no computer to use, but had lots of time, I thought about all this. I was looking for an inharmonic ratio such that the components would be powers of some basic ratio. It turns out that the Golden Mean (1.608) is such a number. If one has a c:m ratio that is 1 to some power of the Golden Mean, then several of the low-order spectral side components are also powers of the Golden Mean.

What I did was draw an analogy between this inharmonic spectrum -- including a frequency space where the pseudo-octave is at powers of the Golden Mean -- and the harmonic series and tonality, where the low-order components of the harmonic series are also the principal intervals of the tonal system -- the octave, the fifth, and so on. I drew this loose analogy and wrote some programs to help me compose, in particular to help me with the sound synthesis. It was not automatic composition by any means, but there were rules for determining the details of the structure, from the microsound level up to the level of a phrase.

In Stria, all frequency components are based on powers of the Golden Mean in the c:m ratios. Then I divided up the frequency space so there was some degree of complementarity. So it is all very cohesive perceptually, even though it's inharmonic and sounds a little strange. But it doesn't take long, even for a naive listener, to realize that even though it's strange it's cohesive at a deep level. I believe this is because of the unified structure of spectral formation.
John Chowning - Stria (1977)

[Obviously there is a little typo here. Phi is actually 1.618034.]

A nice introduction to Bill's work:

Relating Tuning and Timbre by William A. Sethares