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Progression temperament

🔗genewardsmith <genewardsmith@sbcglobal.net>

2/23/2011 9:01:38 AM

This one pops up in surveys of low complexity, high prime limit temperaments, but it so far has lacked a name. You can see why I propose the name "progression" from the 19-limit normal val list:

<1 1 2 2 3 3 4 4|
<0 5 3 7 4 6 1 2|

The period val is a stuttering arithmetic progression; two repeated numbers, followed by the next two, etc. The generator val is a permutation of the numbers from 0 to 7 (so I suppose "permutation" would be another possible name, but I like "progression" better.) In 17edo, the val for it goes <17 27 40 48 59 63 70 72|. Using this, any piece in 19-limit JI can be massacred and played on a 17edo guitar. Commas tempered out are fond of having 5 in the denominator: 26/25, 36/35, 51/50, 56/55, 57/55, 66/65 being a comma basis.