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Yantra commas

🔗Gene Ward Smith <gwsmith@svpal.org>

3/19/2004 1:57:28 PM

For yantra_p(n) for any p and n, there will be a smallest scale-step
interval. As n increases, these form a non-increasing sequence, which
only the more talented p-limit commas will form a part of. For 7-limit
yantras, for example, the sequence (ignoring repetitions) goes

2, 4/3, 6/5, 8/7, 10/9, 16/15, 21/20, 25/24, 28/27, 36/35, 50/49,
64/63, 81/80, 126/125, 225/224, 2401/2400, 4375/4374...

If I take two successive commas of this I get a sequence of linear
temperaments. Starting from 25/24 and 28/27, this sequence goes
dicot, father, diminished, pajara, dominant seventh, meantone,
meantone, miracle, ennealimmal ... . Each member of the sequence has a
relationship to those before and after, from a non-empty intersection
of their kernels, and the temperaments we get are clearly strong ones.