88CET Variants and Their Approximations

For you folks out there who have also been experimenting with 88CET, the two
cases in Manuel's 88CET calculations that struck me as especially interesting
were:

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1: 4 2: 7 3: 10
88.2160 cents, 13.6030/oct. Std. dev: 2.9412 cents
1: 11/9 -5.4561 undecimal neutral third
2: 10/7 -0.0242 septimal augmented fourth, Euler's tritone
3: 5/3 2.1987 major sixth

1: 3 2: 4 3: 10
88.2707 cents, 13.5946/oct. Std. dev: 3.1293 cents
1: 7/6 2.0588 septimal minor third
2: 11/9 -5.6749 undecimal neutral third
3: 5/3 1.6517 major sixth

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I found them particularly interesting, because stretching the step size to 88
1/4 cents or thereabouts, would make the 41-step triple-octave approximation
pretty far off. It would be sufficiently far off to make that tuning pretty
much unequivocally different from simply every third step of 41TET.

Perhaps that's something of an ignoble goal - making it different just to be
different. I suppose that's a matter of perspective. But it's a thought
anyway.


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Neat! Corngrats on finishing it up! I'll toss a check in the mail.