RE: Manuel Op de Coul's list

Bruce,

Your presumption that all of the modes in the list are selections from
ET scales is wrong. Many of them can indeed be but for most it is
not a requirement. If I have been vague about it, I apologise.
Messiaen's modes work best in equal temperament. The Indian modes
aren't necessarily used in just intonation, take the popular harmonium
for instance, which is tuned more or less equally.
The Arabic 17-tone modes are to be taken from this scale:
256/243 65536/59049 9/8 32/27 8192/6561 81/64 4/3 1024/729 262144/177147 3/2
128/81 32768/19683 27/16 16/9 4096/2187 1048576/531441 2/1.
The modes of the Indian shruti scale are also not for ET, though the
theory of shrutis is not universally accepted among Indian
musicologists and you see different proposals for the frequency
ratios.

Manuel Op de Coul coul@ezh.nl

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