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Hello. I'm a engineer and weekend mathematician, not for music.
List of subpages
Memo
basis including | examples | remarks |
---|---|---|
2.9 | Subgroup temperaments #2.9.5.7 subgroup | |
4.3 | Subgroup temperaments #4.3.5 subgroup, not meanquad (p=4/1, g=4/3 or 3/1), "mistyquad", "mirquad" |
|
4.6 = 4.3/2 = 6.3/2 = 6.9 = 3/2.9 |
meanquad (p=4/1, g=3/2), "ennealimmalquad" | plain weave |
4.9 | Subgroup temperaments #Meansquared | 4.9.25 meansquared is insane |
4/3.9 = 12.9 = 16.12 | 39ed9 | |
4.9/2 = 4.18 | "israquad" | |
4/3.9/2 = 8.6 = 6.27 | twill weave | |
12.18 = 12.3/2 = 8.3/2 = 18.3/2 = 27.3/2 = 8.12 |
"septimal meanocto" | twill weave |
12.9/2 = 8/3.9/2 = 8/3.12 = 9/2.54 = 9/2.243 = 8/3.32 = 12.32 |
satin weave | |
4/3.18 = 4/3.27/2 = 18.27/2 = 4/3.24 = 4/3.32 = 24.32 |
satin weave | |
8.9 | Subgroup temperaments #Sixscared, "israocto" |
9/7 | 5/4 | 11/9 | 6/5 | 13/11 | 7/6 | 15/13 | 8/7 |
13/10 | 14/11 | 16/13 | 17/14 | 19/16 | 20/17 | 22/19 | 23/20 |
17/13 | 19/15 | 21/17 | 23/19 | 25/21 | 27/23 | ||
21/16 22/17 24/19 | 26/21 27/22 | 32/27 33/28 | |||||
32/25 33/26 34/27 | 39/32 40/33 |
9-odd-limit diamond (not care of beginning at 1)
9/5 | ||||||||
8/5 | 3/2 | |||||||
7/5 | 4/3 | 9/7 | ||||||
6/5 | 7/6 | 8/7 | 9/8 | |||||
5/5 | 3/3 | 7/7 | 1/1 | 9/9 | ||||
5/3 | 12/7 | 7/4 | 16/9 | |||||
10/7 | 3/2 | 14/9 | ||||||
5/4 | 4/3 | |||||||
10/9 |
1.3.9.11.17 diamond, for 24edo (not cover 1\24, 5\24, 6\24, 8\24, ...)
18/11 | ||||||||
17/11 | 3/2 | |||||||
16/11 | 17/12 | 9/8 | ||||||
12/11 | 4/3 | 17/16 | 18/17 | |||||
11/11 | 3/3 | 1/1 | 17/17 | 9/9 | ||||
11/6 | 3/2 | 32/17 | 17/9 | |||||
11/8 | 24/17 | 16/9 | ||||||
22/17 | 4/3 | |||||||
11/9 |
tritave 1.2.4.5.7 diamond
7/3 | ||||||||
2/1 | 7/4 | |||||||
5/3 | 3/2 | 7/5 | ||||||
4/3 | 5/4 | 6/5 | 7/6 | |||||
1/1 | 4/4 | 5/5 | 2/2 | 7/7 | ||||
9/4 | 12/5 | 5/2 | 18/7 | |||||
9/5 | 2/1 | 15/7 | ||||||
3/2 | 12/7 | |||||||
9/7 |
~~ what's this? ~~
[1] Rank 2 temperament (17/11, 2/1)
- (17/11)^(-9) ~ 14/11
- (17/11)^(-5) ~ 20/11
- Hence (17/11)^4 ~ 10/7
- 11:14:17:20 tetrad
- 2.5.7.11.17 subgroup
- sintel/uvs->edos->x31/net
- a weak extension 19p&16 -> muggles
- (17/11)^(-9) ~ 14/11 ~ 5/4 19p&8d -> near sensi, sensis
- 2.7/5.11/5.17/5 subgroup
- 2.5/3.7/3.11/3.17/3 subgroup
- by adding 5/3 @ -2 gen (not 5/4), (17/11)^(-2) ~ 5/3, [3], non-over-1 sensis
- 2.5/3.7/3.11/3.13/3.17/3 -> [4]