Avicennmic temperaments: Difference between revisions

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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]]
* ''[[Armodue (temperament)|Armodue]]'' (+36/35) → [[Mavila family #Pelogic|Mavila family]]
* [[Negri]] (+49/48) → [[Semaphoresmic clan #Negri|Semaphoresmic clan]]
* [[Lemba]] (+50/49) → [[Jubilismic clan #Lemba|Jubilismic clan]]
* [[Flattone]] (+81/80) → [[Meantone family #Flattone|Meantone family]]
* [[Muggles]] (+126/125) → [[Magic family #Muggles|Magic 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:

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

Optimal tunings:

  • 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 sequence16, 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