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7-limit yantra temperaments

🔗Gene Ward Smith <gwsmith@svpal.org>

3/20/2004 12:00:32 PM

I went through the 7-limit yantras up to yantra_7(1000), and took the
two smallest interval steps, and found the corresponding temperament.
This is what I got:

dicot 9
father 10-11
decimal 12
pajara 13-14
dominant seventh 15-16
meantone 17-37
miracle 38-53
hemiwuerschmidt 54-58
ennealimmal 59-556
<<88 151 183 35 43 1|| 557-1000+

The last temperament has the following properties:

Mapping: [<1 -19 -33 -40|, <0 88 151 183|]
TM basis: {78125000/78121827, 645700815/645657712}
generators: [1, 731/3125]

As a 7-limit system it is pretty strongly wedded to the 3125-et, but
6079, a very strong 13-limit system which I used for the Mozart
Victims piece, also supports it, which means it has a natural
extension to the 13-limit. The generator then is 1422/6079, and since
I know how eager people are going to be to rush out and tune their
microtonal guitars to this thing, I give the mapping:

[<1 -19 -33 -40 312 163|, <0 88 151 183 -1319 -681|]