Avicennmic temperaments: Difference between revisions
→13-limit: complete the mapping |
m Sorting |
||
| Line 3: | Line 3: | ||
Tempereaments discussed elsewhere are: | Tempereaments discussed elsewhere are: | ||
* ''[[Armodue (temperament)|Armodue]]'' (+36/35) → [[Mavila family #Armodue|Mavila family]] | |||
* [[Flattone]] (+81/80) → [[Meantone family #Flattone|Meantone family]] | |||
* ''[[Dichotic]]'' (+25/24) → [[Dicot family #Dichotic|Dicot family]] | * ''[[Dichotic]]'' (+25/24) → [[Dicot family #Dichotic|Dicot family]] | ||
* ''[[Deflated]]'' (+21/20) → [[Augmented family #Deflated|Augmented family]] | * ''[[Deflated]]'' (+21/20) → [[Augmented family #Deflated|Augmented family]] | ||
* ''[[Pycnic]]'' (+245/243) → [[Sensamagic clan #Pycnic|Sensamagic clan]] | * ''[[Pycnic]]'' (+245/243) → [[Sensamagic clan #Pycnic|Sensamagic clan]] | ||
* [[Negri]] (+49/48) → [[Semaphoresmic clan #Negri|Semaphoresmic clan]] | |||
* ''[[Secund]]'' (+405/392) → [[Greenwoodmic temperaments #Secund|Greenwoodmic temperaments]] | * ''[[Secund]]'' (+405/392) → [[Greenwoodmic temperaments #Secund|Greenwoodmic temperaments]] | ||
* [[Lemba]] (+50/49) → [[Jubilismic clan #Lemba|Jubilismic clan]] | |||
* ''[[Roman]]'' (+3125/3024) → [[Wesley family #Roman|Wesley family]] | * ''[[Roman]]'' (+3125/3024) → [[Wesley family #Roman|Wesley family]] | ||
* [[Muggles]] (+126/125) → [[Magic family #Muggles|Magic family]] | |||
Considered below is submerged. | Considered below is submerged. | ||
Latest revision as of 13:11, 8 August 2026
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
This is a collection of rank-2 temperaments tempering out the avicennma, 525/512, also known as Avicenna's enharmonic diesis.
Tempereaments discussed elsewhere are:
- Armodue (+36/35) → Mavila family
- Flattone (+81/80) → Meantone family
- Dichotic (+25/24) → Dicot family
- Deflated (+21/20) → Augmented family
- Pycnic (+245/243) → Sensamagic clan
- Negri (+49/48) → Semaphoresmic clan
- Secund (+405/392) → Greenwoodmic temperaments
- Lemba (+50/49) → Jubilismic clan
- Roman (+3125/3024) → Wesley family
- Muggles (+126/125) → Magic family
Considered below is submerged.
Submerged
Named by Fitzgerald Lee in 2025, submerged tempers out 3125/3087, the gariboh comma. It may be described as the 16 & 29 temperament, generated by a sharply tuned ~8/5, eleven of which minus seven octaves make a perfect fifth; its ploidacot is therefore zeta-hendecacot. 45edo makes for an excellent tuning.
Subgroup: 2.3.5.7
Comma list: 525/512, 3125/3087
Mapping: [⟨1 -6 3 9], ⟨0 11 -1 -9]]
- mapping generators: ~2, ~8/5
- WE: ~2 = 1203.3342 ¢, ~8/5 = 829.2070 ¢
- error map: ⟨+3.334 -0.683 -5.518 -1.681]
- CWE: ~2 = 1200.0000 ¢, ~8/5 = 826.9483 ¢
- error map: ⟨0.000 -5.523 -13.262 -11.361]
Optimal ET sequence: 16, 29, 45, 74cd, 119bccdd
Badness (Sintel): 3.98
11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 441/440, 525/512
Mapping: [⟨1 -6 3 9 0], ⟨0 11 -1 -9 5]]
Optimal tunings:
- WE: ~2 = 1203.6231 ¢, ~8/5 = 829.4195 ¢
- CWE: ~2 = 1200.0000 ¢, ~8/5 = 826.9730 ¢
Optimal ET sequence: 16, 29, 45e, 74cde, 119bccddeee
Badness (Sintel): 1.93
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 65/64, 105/104, 121/120, 441/440
Mapping: [⟨1 -6 3 9 0 3], ⟨0 11 -1 -9 5 1]]
Optimal tunings:
- WE: ~2 = 1203.6316 ¢, ~8/5 = 829.4249 ¢
- CWE: ~2 = 1200.0000 ¢, ~8/5 = 826.9677 ¢
Optimal ET sequence: 16, 29, 45ef, 74cdef, 119bccddeeeff
Badness (Sintel): 1.35