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Consistency domain

🔗Gene Ward Smith <genewardsmith@sbcglobal.net>

4/29/2007 2:16:39 AM

One can reverse the idea of the consistency of
an edo relative to a fixed set, and ask, for a
given prime limit, for the largest p-limit set
contained within an octave such that n is consistent
with respect to this set, which might be called the
p-limit consistency domain for n. It consists of
just those p-limit intervals in the octave for
which the patent val gives the best tuning.

These may be larger than one might suppose, and
the growth in size with n not obvious. For example
in the 5-limit, the consistency domain for 12 has
273 notes. But the consistency domain for 3 is
not much smaller, at 207. The 7 domain is smaller,
and 5 smaller yet (just 131.)

What all this is good for, if anything, I'll think
on.