back to list

Planar temperaments -- 245/243

🔗genewardsmith@juno.com

11/10/2001 4:22:30 PM

Good generators for this are a sharp fifth, "f", and and even sharper
supermajor third (9/7), "t". That 245/243~1 means that (9/7)^2~5/3,
which is basic to this system.

We have 3 ~ 2f, 5 ~ 2ft^2 and 7 ~ 2^2f^2t^(-1), and the 7-limit least
squares fit has the curious feature that the 7 is pure. We have a
fifth 2.92 cents sharp and a major third 0.417 cents sharp, again
quite nice values. Here is a rectangle of notes of this system:

27/20 -- 7/4 -- 9/8 -- 35/24 -- 15/8
| | | | |
9/5 -- 7/6 -- 3/2 -- 27/14 -- 5/4
| | | | |
6/5 -- 14/9-- 1 -- 9/7 -- 5/3
| | | | |
8/5 --28/27-- 4/3 -- 12/7 -- 10/9