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The 181 proper 7-note 31-et scales

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

6/14/2006 3:11:24 AM

I've been trying to figure out how or if I am going to classify these.
I've computed the generators with the largest "gap" for each of these,
by which I mean the gap when you arrage the 31 pitch classes in a
circle using the given generator. I get, for instance, 30 scales which
are of meantone type, meaning meantone is a largest gap. Of these, 11
are ambiguous, with another generator or generators working equally
well. The biggest class is for semififths temperament. Others which
show up are valentine, miracle, nusecond, hemithirds, orwell, squares
and of course meantone. Others of the temperaments of 31 do not
appear; doubtless being more regular in scale numbers closer to a MOS;
the instances of non-appearance are myna, mothra, slender, wuerschmidt
and tritonic.