User:Dummy index
(Redirected from Dummy Index)
Jump to navigation
Jump to search
Hello. I'm a engineer and weekend mathematician, not for music.
List of subpages
- 2-dimensional tuning spectrum
- About harmonics
- Bimetallic MOS
- Chromatic pairs and how we define haplotonic
- Heuristics for picking a basis of JI subgroup
- Just odd intonation
- Layouts
- MOS tree with continued fraction
- No-1s odd-limit consistency
- Random lists of temperaments by generator size
- Related to 1729/1728
- SandBox
- Semitritave
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) -> named tetrameantone, "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 |
~~ hoge ~~
- [1] Mersenne prime basis
| Subgroup | Chord | Condition | Comma | Temperament |
|---|---|---|---|---|
| 2.3 | 2:3:4 | 3/2~4/3 | S3 | 2et |
| 4.3.5 | 3:4:5 | 4/3~5/4 | S4 | tetrafather |
| 2.3.5 | father | |||
| 8.9.7 | 7:8:9 | 8/7~9/8 | S8 | sixscared |
| 8.9.10 | 8:9:10 | 9/8~10/9 | S9 | israocto |
| 2.3 | 1:2:3:4 | (2/1)/(3/2)~(3/2)/(4/3) | S2/S3 | 3et |
| 2.3.5 | 2:3:4:5 | (3/2)/(4/3)~(4/3)/(5/4) | S3/S4 | mavila |
| 3/2.5/4.7/4 | 4:5:6:7 | (5/4)/(6/5)~(6/5)/(7/6) | S5/S6 | |
| 4.6.5.7 | supermagicquad | |||
| 10/7.20/11.20/17 | 11:14:17:20 | (14/11)/(17/14)~(17/14)/(20/17) | 54880/54043 | |
| 2.7/5.11/5.17/5 | + 7p~2/1 | + *** | non-over-1 greenwood |