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Comma pump scales

🔗Gene Ward Smith <gwsmith@svpal.org>

9/5/2004 2:40:32 AM

It occurred to me that all of the notes of a comma pump, tempered by
the comma in question, could make an interesting scale. I found ten
scales, each of twelve notes, which support a 225/224 comma pump of
tetrads such that each tetrad in the chord progression shares an
interval with adjoining tetrads. Some of these scales are epimorphic
and some are not, but generally they seem similar either way. I've
uploaded them to

/tuning-math/files/pumpscale/

The tuning is 5-limit, but normally one would probably want to use
something with a lower error, such as 1/4-kleismic. The 5-limit tuning
is theoretically convenient and allowed me to discover that one of
these scales, pump9, is diadie2. This means I have something
interesting to report about both diadie scales, as diadie1 is lumm5r.

In this case at least it seems this method of scale construction does
lead to an interesting result; we have in each case a twelve note
scale with six tetrads, which can be arranged in a circle to form a
comma pump. Moreover, we also have pentads; diadie2=pump9 gives us
four pentads, two of each kind. More than the fact that it is a Fokker
block, this leads me to regard it as the most interesting of these ten
scales. Despite Carl's advocacy of diadie1, I think this also gives it
the nod as the most interesting of the diadie blocks as well.