RE: non-octave scales and octave equival

Brian wrote-

>Paul Erlich goes on to write that "In the case
>of inharmonic partials, octave equivalence may
>play less of a role, but still exists, and is less
>demanding as to intonation." Both [...] experiments
>[...] strongly contradict this
>statement. In particular William Sethares has
>a set of instrument timbres resynthesized with
>all harmonics stretched so that the octave is a
>ratio of 2.1 instead of 2.0, etc.
>Playing a vertical octave dyad with such timbres
>produces unbearable dissonance; but playing a
>vertical octave whose ratio is 2.1 rather than 2.0
>produces the familiar sensation of octave
>equivalence. So the evidence *strongly* indicates
>that 2:1 octave equivalence goes away when the
>timbre becomes inharmonic, and this is confirmed
>by William Sethares' mathematical procedure for
>finding scale pitches from an inharmonic timbre.

What's contradictory?

>2, 3, 4, 5, 6 are highly consonant.
>7 is less so, intermediate in fact between consonance
>and dissonance; 8, 9, 10 are highly consonant, 11
>is much less consonant...

Whatever that means, I don't think 10:9 is more consonant than 8:7!


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