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39 indecent 7-limit temperaments

🔗Gene Ward Smith <gwsmith@svpal.org>

1/8/2006 2:53:57 PM

I went through my list of 32201 wedgies, and found 39 temperaments
which were not "decent" in the sense of having the pre-wedgie round
off to the correct wedgie. The best one, badnesswise, was this:

<<0 0 5 0 8 11||, TM basis {10/9, 75/64}

The pre-wedgie here rounds off instead to this:

<<0 0 5 0 8 12||, TM basis {16/15, 27/25}

Next up is <<0 10 5 16 8 -17||, TM basis {160/147, 256/243}. That one
rounds off to <<0 10 5 16 8 -16||, TM basis {49/45, 256/243}. Next we
have <<6 10 11 2 1 -2||, TM basis {49/45, 250/243}. That rounds off to
a non-wedgie.

Sometimes the pre-wedgie rounds off to something with torsion.
Starting from <<0 0 20 0 32 47||, with TM basis {256/243, 648/625},
which could, I suppose, be something someone might actually use, we
round off the pre-wedgie and it's torsional, reducing to <<0 0 10 0 16
23|| with TM basis {25/24, 256/243}.

There was a distinct tendency for the lowest badness scores on this
list to be those of higher error. Higher complexity temperaments, to
be indecent, must have increasingly worse logflat badness figures.