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2/25 < 3/37 vs meantone

🔗genewardsmith@juno.com

10/26/2001 5:47:31 PM

This turns out to be an interesting generator, and it makes for a
fine head-to-head with the meantone. Multiplying the generator steps
in 2/25 by two, to make for a direct comparison, I get the following
for 50:

3 1 4
5 4 16
7 10 -10
11 -13 -2
13 15 10
17 -24 4
19 -22 12

Here the first column are the primes, the second is meantone
generator steps, and the third is 2/25 generator steps. While it
isn't a good way to get at the 5-limit, it is an interesting way to
get at the higher prime limits. Here also is 74:

3 1 4
5 4 16
7 10 -34
11 18 -2
13 -16 10
17 -36 4
19 -34 12

The 3/37 generator is closer to the corresponding 50 generator then
they are as meantones, the only difference coming at 11. We again
have 11,13,17 and 19 harmonies to play with.