Avicennmic temperaments: Difference between revisions
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This is a collection of [[ | 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. | ||
Tempereaments discussed elsewhere are: | |||
* ''[[Dichotic]]'' (+25/24) → [[Dicot family #Dichotic|Dicot family]] | * ''[[Dichotic]]'' (+25/24) → [[Dicot family #Dichotic|Dicot family]] | ||
* [[Armodue]] (+36/35) → [[ | * ''[[Armodue (temperament)|Armodue]]'' (+36/35) → [[Mavila family #Pelogic|Mavila family]] | ||
* [[Negri]] (+49/48) → [[ | * [[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]] | ||
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* ''[[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:Rank 2]] | [[Category:Rank 2]] | ||