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Notating 13-ET as a no-3, no-7 temperament

🔗Herman Miller <hmiller@IO.COM>

11/24/2007 3:50:39 PM

An alternative to a chain of fifths notation for ET's that don't have good fifths, while still using Sagittal notation, is to notate only intervals without factors of 3. In the case of 13-ET, you can use 2, 5, and 11 as the prime factors, skipping 3 and 7 (13-ET's approximation of 7 is even worse than its approximation of 3).

0 D 1/1
1 D'~||). 128/121
2 E(!( 11/10
3 F!/ 64/55
4 F||\ 5/4
5 G)!!( 32/25
6 G/|\ 11/8
7 A\!/ 16/11
8 A)||( 25/16
9 B!!/ 8/5
10 B|\ 55/32
11 C(|( 20/11
12 D.~!!)' 121/64
13 D 2/1

One drawback with using higher limits is that the notation starts to get awkward, as in the D'~||). for 128/121. A simpler notation for (+1) exists in the 17-limit:

1 E(!!( 17/16