Avicennmic temperaments: Difference between revisions

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{{Technical data page}}
{{Technical data page}}
This is a collection of [[Rank-2 temperament|rank-2]] [[temperament]]s [[tempering out]] the avicennma, [[525/512]], also known as Avicenna's enharmonic diesis.  
This is a collection of [[rank-2 temperament|rank-2]] [[temperament]]s [[tempering out]] the avicennma, [[525/512]], also known as Avicenna's enharmonic diesis.  


See:  
Tempereaments discussed elsewhere are:  
* ''[[Dichotic]]'' (+25/24) → [[Dicot family #Dichotic|Dicot family]]
* ''[[Dichotic]]'' (+25/24) → [[Dicot family #Dichotic|Dicot family]]
* [[Armodue]] (+36/35) → [[Pelogic family #Pelogic|Pelogic family]]
* ''[[Armodue (temperament)|Armodue]]'' (+36/35) → [[Mavila family #Pelogic|Mavila family]]
* [[Negri]] (+49/48) → [[Slendro clan #Negri|Slendro clan]]
* [[Negri]] (+49/48) → [[Semaphoresmic clan #Negri|Semaphoresmic clan]]
* [[Lemba]] (+50/49) → [[Jubilismic clan #Lemba|Jubilismic clan]]
* [[Lemba]] (+50/49) → [[Jubilismic clan #Lemba|Jubilismic clan]]
* [[Flattone]] (+81/80) → [[Meantone family #Flattone|Meantone family]]
* [[Flattone]] (+81/80) → [[Meantone family #Flattone|Meantone family]]
Line 13: Line 13:
* ''[[Secund]]'' (+405/392) → [[Greenwoodmic temperaments #Secund|Greenwoodmic temperaments]]
* ''[[Secund]]'' (+405/392) → [[Greenwoodmic temperaments #Secund|Greenwoodmic temperaments]]
* ''[[Roman]]'' (+3125/3024) → [[Wesley family #Roman|Wesley family]]
* ''[[Roman]]'' (+3125/3024) → [[Wesley family #Roman|Wesley family]]
Considered below is submerged.
== Submerged ==
{{Main| Submerged }}
Named by [[Fitzgerald Lee]] in 2025, submerged tempers out 3125/3087, the [[gariboh comma]]. It may be described as the {{nowrap| 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|legend=1| 1 -6 3 9 | 0 11 -1 -9 }}
: mapping generators: ~2, ~8/5
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1203.3342{{c}}, ~8/5 = 829.2070{{c}}
: [[error map]]: {{val| +3.334 -0.683 -5.518 -1.681 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/5 = 826.9483{{c}}
: error map: {{val| 0.000 -5.523 -13.262 -11.361 }}
{{Optimal ET sequence|legend=1| 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: {{mapping| 1 -6 3 9 0 | 0 11 -1 -9 5 }}
Optimal tunings:
* WE: ~2 = 1203.6231{{c}}, ~8/5 = 829.4195{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/5 = 826.9730{{c}}
{{Optimal ET sequence|legend=0| 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: {{mapping| 1 -6 3 9 0 3 | 0 11 -1 -9 5 1 }}
Optimal tunings:
* WE: ~2 = 1203.6316{{c}}, ~8/5 = 829.4249{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/5 = 826.9677{{c}}
{{Optimal ET sequence|legend=0| 16, 29, 45ef, 74cdef, 119bccddeeeff }}
Badness (Sintel): 1.35


[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Avicennmic temperaments| ]] <!-- main article -->
[[Category:Avicennmic temperaments| ]] <!-- main article -->
[[Category:Avicennmic| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]

Latest revision as of 18:46, 24 May 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

Main article: 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 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

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