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That 13 note modmos from tuning

🔗Gene Ward Smith <gwsmith@svpal.org>

7/13/2004 1:56:34 AM

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> Hemiwuerschmidt (99&130) has a 7-limit Graham complexity of 16, so we
> need to get up at least to the 19-not MOS before having complete tetrads
> in a MOS. Here I give a 13-note modmos, found via more pen & paper
> fiddling, which has three major tetrads and two minor tetrads, which
> is not bad for 13 notes tempered in something more accurate than
> miracle. It JI lattice terms, it has [-2,0,0], [0,0,0] and [1,1,0] for
> major tetrads and [-1,0,0] and [0,1,0] for minor tetrads, so the
> harmony links together nicely.

The trouble with tuning this in hemiwuerschmidt is that you may as
well detemper it to 7-limit JI, in which case valentine (15&31) or
myna (27&31) actually get you somewhere. :(

Here's the detempered version, which doesn't even manage to be
epimorphic, though I am sure it must have tried.

36/35-21/20-35/32-6/5-5/4-21/16-48/35-3/2-49/32-12/7-7/4-9/5-2

It's a bit irregular, but it does have a nice collection of chords.