Manuel Op de Coul's list

I was away from home for 2 1/2 weeks and then had to spend a lot of time
going through a mountain of accumulated e-mail, so it's only now that I am
able to remark about this list, which appeared Dec. 29. I think that it,
perhaps expanded to include any more anyone can come up with, is something
I've eagerly hoped to see. But a question arises.

Many of the scales he described are actually defined by just intervals, or as I
would prefer to say (since the term "just intonation" frequently means a
specific 5-limit scale) rational frequency ratios. I know that Indian and Greek
scales are.

So, since all of Manuel's modes are selections from ET scales, my question is
how precisely the given ET scale had to match the interval. While for example
an interval of 7/12 of an octave (700 cents or 583.333... moc) is a pretty
good fit to a Pythagorean fifth (~702 cents or ~585 moc) we know that an
interval of 1/3 of an octave (400 cents or 333.333... moc) is not nearly as
good a fit to a just third (~386 cents or ~322 moc). Yet both are often
considered as equivalent to the given ratios.

Obviously they don't match exactly. I know I can't hear a difference of 5 moc,
but I am sure I could hear a difference of 20 moc. So it is imoortant to
know how close his ET modes are to the named scales.

Bruce R. Gilson
brg@netcom.com

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