Hemimage temperaments: Difference between revisions
mNo edit summary |
|||
| Line 14: | Line 14: | ||
* ''[[yarman]]'', {10976/10935, 244140625/243045684} → [[Turkish maqam music temperaments #Yarman]] | * ''[[yarman]]'', {10976/10935, 244140625/243045684} → [[Turkish maqam music temperaments #Yarman]] | ||
= Commatic = | == Commatic == | ||
The commatic temperament has a period of half octave and a generator of 20.4 cents. It is so named because the generator is a small interval ("commatic") which represents 81/80, 99/98, and 100/99 all tempered together. | The commatic temperament has a period of half octave and a generator of 20.4 cents. It is so named because the generator is a small interval ("commatic") which represents 81/80, 99/98, and 100/99 all tempered together. | ||
| Line 31: | Line 31: | ||
[[Badness]]: 0.084317 | [[Badness]]: 0.084317 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 44: | Line 44: | ||
Badness: 0.030461 | Badness: 0.030461 | ||
= Chromat = | == Chromat == | ||
The chromat temperament has a period of 1/3 octave and tempers out the hemimage (10976/10935) and the triwellisma (235298/234375). It is also described as an [[Amity family|amity extension]] with third-octave period. | The chromat temperament has a period of 1/3 octave and tempers out the hemimage (10976/10935) and the triwellisma (235298/234375). It is also described as an [[Amity family|amity extension]] with third-octave period. | ||
| Line 61: | Line 61: | ||
[[Badness]]: 0.057499 | [[Badness]]: 0.057499 | ||
= Degrees = | == Degrees == | ||
Degrees temperament has a period of 1/20 octave and tempers out the hemimage (10976/10935) and the dimcomp (390625/388962). In this temperament, one period equals ~28/27, two equals ~15/14, three equals ~10/9, five equals ~25/21, six equals ~16/13, seven equals ~14/11, nine equals ~15/11, and ten equals ~99/70. | Degrees temperament has a period of 1/20 octave and tempers out the hemimage (10976/10935) and the dimcomp (390625/388962). In this temperament, one period equals ~28/27, two equals ~15/14, three equals ~10/9, five equals ~25/21, six equals ~16/13, seven equals ~14/11, nine equals ~15/11, and ten equals ~99/70. | ||
| Line 78: | Line 78: | ||
[[Badness]]: 0.106471 | [[Badness]]: 0.106471 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 91: | Line 91: | ||
Badness: 0.046770 | Badness: 0.046770 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 104: | Line 104: | ||
Badness: 0.032718 | Badness: 0.032718 | ||
= Subfourth = | == Subfourth == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 119: | Line 119: | ||
[[Badness]]: 0.140722 | [[Badness]]: 0.140722 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 132: | Line 132: | ||
Badness: 0.045323 | Badness: 0.045323 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 145: | Line 145: | ||
Badness: 0.023800 | Badness: 0.023800 | ||
= Bisupermajor = | == Bisupermajor == | ||
{{see also| Very high accuracy temperaments #Kwazy }} | {{see also| Very high accuracy temperaments #Kwazy }} | ||
| Line 162: | Line 162: | ||
[[Badness]]: 0.065492 | [[Badness]]: 0.065492 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 175: | Line 175: | ||
Badness: 0.032080 | Badness: 0.032080 | ||
= Cotoneum = | == Cotoneum == | ||
{{Main| Cotoneum }} | {{Main| Cotoneum }} | ||
| Line 208: | Line 208: | ||
[[Badness]]: 0.105632 | [[Badness]]: 0.105632 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 230: | Line 230: | ||
Badness: 0.050966 | Badness: 0.050966 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 256: | Line 256: | ||
Badness: 0.036951 | Badness: 0.036951 | ||
== 17-limit == | === 17-limit === | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 278: | Line 278: | ||
Badness: 0.029495 | Badness: 0.029495 | ||
== 19-limit == | === 19-limit === | ||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||