RE: Arabic Tuning

CPS stands for Combination Product Set, an invention of Erv Wilson. For
example
2)3 [1.3.5]
means take every possible product of two out of the three factors 1, 3, and
5. This gives 1*3, 1*5, and 3*5, or 3, 5, and 15. Invoking octave
equivalence, we get 12, 10, and 15: a minor triad!
1)3 [1.3.5]
is of course a major triad . . .


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Paul wrote:

''I wonder, in Brian's scheme of mapping real harmonic series to equal
temperaments in the quest for "better" timbres, what happens when you reach

a harmonic that is inconsistent with the temperament, e.g. the 11th
harmonic
in 12-equal?''

You don't have to go as high as the 11th harmonic to find one example of
what others have tried. The Hammond organ simply skipped the seventh
harmonic in the series of sliders for added diapasons (the 1-2-3-4-5-6-8
diapasons were tuned to match the Hammond approximation of ET).


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