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Wilson_17 & co

🔗Gene Ward Smith <gwsmith@svpal.org>

9/1/2004 7:51:55 PM

I've found another already known dwarf--this is another Erv Wilson
scale, wilson_17, which is dwarf(<17 27 39|), the standard val 5-limit
17-note dwarf. However, in some ways dwarf(<17 27 40|) is more
interesting. Wilson_17 has eight major and seven minor triads, but it
also has a schismic minor triad which obviously would work fine even
without tempering. It is also epimorphic. Dwarf(<17 27 40|) is only
permuation epimorphic, but makes up for it with chords. It has ten
major and nine minor triads, all pure. Moreover, it has four otonal
and four utonal marvel pentads, which is quite nice. For wilson_17,
5120/5103 tempers in two tetrads and one pentad of each species. This
is interesting because it does not involve marvel, but obviously we
are not getting so many chords.

Scala tells me that the standard 17-note 11-limit dwarf is a subset of
the standard 41-note 11-limit dwarf; it is perhaps a little surprising
that more of these subset relationships have not turned up.