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Revision as of 11:54, 26 January 2021
Septimal meantone
Period: 1\1
Optimal (POTE) generator: ~3/2 = 696.495
EDO generators: 7\12, 11\19, 18\31, 25\43, 29\50
Scales: Meantone5, Meantone7, Meantone12
Period-generator mapping: [<1 0 -4 -13|, <0 1 4 10|]
Commas: 81/80, 126/125
7 and 9-limit minimax
[[1 0 0 0⟩, [1 0 1/4 0⟩, [0 0 1 0⟩, [-3 0 5/2 0⟩]
Eigenmonzos: 2, 5
Valid range: [694.737, 700.000] (19 to 12)
Nice range: [694.786, 701.955]
Strict range: [694.786, 700.000]
Mapping generator: ~3
Algebraic generator: Cybozem, the real root of 15x3 - 10x2 - 18, which comes to 503.4257 cents. The recurrence converges quickly.
Wedgie: <<1 4 10 4 13 12||
Vals: 5, 7, 12, 19, 26, 31, 43, 45, 50, 55, 67, 69, 74, 81, 88, 98, 105, 117, 131b, 212bb, 293bb
Badness: 0.0137
Commas
41edo tempers out the following commas using its patent val, ⟨41 65 95 115 142 152 168 174 185 199 203].
| Prime limit |
Ratio[1] | Name(s) |
|---|---|---|
| 3 | [65 -41⟩ | 41-comma |
| 5 | [-5 -10 9⟩ | Shibboleth |
| 5 | [-25 7 6⟩ | Ampersand |
| 5 | 3125/3072 | Magic comma |
| 5 | [5 -9 4⟩ | Tetracot comma |
| 5 | [20 -17 3⟩ | Roda |
| 5 | [-15 8 1⟩ | Schisma |
| 7 | [0 -7 6 -1⟩ | Great BP diesis |
| 7 | [-10 7 8 -7⟩ | Blackjackisma |
| 7 | 875/864 | Keema |
| 7 | 3125/3087 | Gariboh |
| 7 | [10 -11 2 1⟩ | Tolerma |
| 7 | [-15 3 2 2⟩ | Mirwomo comma |
| 7 | 245/243 | Sensamagic |
| 7 | 4000/3969 | Octagar |
| 7 | [-15 0 -2 7⟩ | Quince |
| 7 | 1029/1024 | Gamelisma |
| 7 | 225/224 | Marvel comma |
| 7 | [0 3 4 -5⟩ | Mirkwai |
| 7 | [5 -7 -1 3⟩ | Hemimage |
| 7 | 5120/5103 | Hemifamity |
| 7 | [25 -14 0 -1⟩ | Garischisma |
| 7 | 2401/2400 | Breedsma |
| 11 | [15 0 1 0 -5⟩ | Thuja comma |
| 11 | 245/242 | Cassacot |
| 11 | 100/99 | Ptolemisma |
| 11 | 1344/1331 | Hemimin |
| 11 | 896/891 | Pentacircle |
| 11 | [16 0 0 -2 -3⟩ | Orgonisma |
| 11 | 243/242 | Rastma |
| 11 | 385/384 | Keenanisma |
| 11 | 441/440 | Werckisma |
| 11 | 1375/1372 | Moctdel |
| 11 | 540/539 | Swetisma |
| 11 | 3025/3024 | Lehmerisma |
| 11 | [-1 2 -4 5 -2⟩ | Odiheim |
| 13 | 343/338 | |
| 13 | 105/104 | Animist comma |
| 13 | [12 -7 0 1 0 -1⟩ | Secorian |
| 13 | 275/273 | Gassorma |
| 13 | 144/143 | Grossma |
| 13 | 196/195 | Mynucuma |
| 13 | 640/637 | Huntma |
| 13 | 1188/1183 | Kestrel comma |
| 13 | 325/324 | Marveltwin |
| 13 | 352/351 | Minthma |
| 13 | 364/363 | Gentle comma |
| 13 | 847/845 | Cuthbert |
| 13 | 729/728 | Squbema |
| 13 | 4096/4095 | Schismina |
| 13 | [3 -2 0 -1 3 -2⟩ | Harmonisma |
| 17 | 2187/2176 | Septendecimal schisma |
| 17 | 256/255 | Septendecimal kleisma |
| 17 | 715/714 | Septendecimal bridge comma |
| 19 | 210/209 | Spleen comma |
| 19 | 361/360 | Go comma |
| 19 | 513/512 | Undevicesimal comma |
| 19 | 1216/1215 | Eratosthenes' comma |
| 23 | 736/729 | Vicesimotertial comma |
| 29 | 145/144 | 29th-partial chroma |
- ↑ Ratios with more than 9 digits are presented in monzos