Avicennmic temperaments: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
4,516 edits
mNo edit summary
-roman -secund (addressed in wesley family and greenwoodmic temperaments respectively); rework intro
Line 1: Line 1:
These temper out the avicennma, [[525/512]], also known as Avicenna's enharmonic diesis. Avicennmic temperaments include [[negri]], [[Dicot family|dichotic]], [[flattone]], [[hexadecimal]], [[muggles]], [[lemba]], [[Augmented family|deflated]], and [[pycnic]].
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.  


== Roman ==
See:
{{see also|Wesley family #Roman}}
* ''[[Dichotic]]'' (+25/24) → [[Dicot family #Dichotic|Dicot family]]
 
* [[Hexadecimal]] (+36/35) → [[Pelogic family #Pelogic|Pelogic family]]
=== 7-limit (Crusher) ===
* [[Negri]] (+49/48) → [[Slendro clan #Negri|Slendro clan]]
Subgroup: 2.3.5.7
* [[Lemba]] (+50/49) → [[Jubilismic clan #Lemba|Jubilismic clan]]
 
* [[Flattone]] (+81/80) → [[Meantone family #Flattone|Meantone family]]
[[Comma list]]: 525/512, 3125/3024
* [[Muggles]] (+126/125) → [[Magic family #Muggles|Magic family]]
 
* ''[[Deflated]]'' (+21/20) → [[Augmented family #Deflated|Augmented family]]
[[Mapping]]: [{{Val|1 4 3 -1}}, {{Val|0 -7 -2 11}}]
* ''[[Pycnic]]'' (+245/243) → [[Sensamagic clan #Pycnic|Sensamagic clan]]
 
* ''[[Secund]]'' (+405/392) → [[Greenwoodmic temperaments #Secund|Greenwoodmic temperaments]]
{{Multival|legend=1|7 2 -11 -13 -37 -31}}
* ''[[Roman]]'' (+3125/3024) → [[Wesley family #Roman|Wesley family]]
 
[[POTE generator]]: ~63/50 = 414.552
 
{{Optimal ET sequence|legend=1| 3, 23, 26, 29, 55c }}
 
[[Badness]]: 0.113386
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 100/99, 245/242, 525/512
 
Mapping: [{{Val|1 4 3 -1 0}}, {{Val|0 -7 -2 11 10}}]
 
POTE generator: ~14/11 = 414.471
 
{{Optimal ET sequence|legend=1| 3, 23, 26, 29, 55c }}
 
Badness: 0.052841
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 65/64, 100/99, 105/104, 245/242
 
Mapping: [{{Val|1 4 3 -1 0 3}}, {{Val|0 -7 -2 11 10 2}}]
 
POTE generator: ~14/11 = 414.472
 
{{Optimal ET sequence|legend=1| 3, 23, 26, 29, 55cf }}
 
Badness: 0.030043
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 35/34, 52/51, 65/64, 100/99, 121/119
 
Mapping: [{{Val|1 4 3 -1 0 3 1}}, {{Val|0 -7 -2 11 10 2 9}}]
 
POTE generator: ~14/11 = 414.164
 
{{Optimal ET sequence|legend=1| 3, 26g, 29 }}
 
Badness: 0.041555
 
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 35/34, 52/51, 65/64, 100/99, 121/119, 133/132
 
Mapping: [{{Val|1 4 3 -1 0 3 1 7}}, {{Val|0 -7 -2 11 10 2 9 -8}}]
 
POTE generator: ~14/11 = 414.130
 
{{Optimal ET sequence|legend=1| 3, 26g, 29 }}
 
Badness: 0.033730
 
== Secund ==
{{see also|Greenwoodmic temperaments #Secund}}
 
Subgroup: 2.3.5.7
 
[[Comma list]]: 405/392, 525/512
 
[[Mapping]]: [{{val|1 1 3 2}}, {{val|0 5 -6 7}}]
 
{{Multival|legend=1|5 -6 7 -21 -3 33}}
 
[[POTE generator]]: ~16/15 = 137.958
 
{{Optimal ET sequence|legend=1| 9, 17, 26, 61bc, 87bcc }}
 
[[Badness]]: 0.089840
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 45/44, 99/98, 385/384
 
Mapping: [{{val|1 1 3 2 3}}, {{val|0 5 -6 7 4}}]
 
POTE generator: ~12/11 = 137.900
 
Optimal ET sequence: {{Optimal ET sequence| 9, 17, 26, 61bc, 87bcc }}
 
Badness: 0.042562
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 27/26, 45/44, 99/98, 385/384
 
Mapping: [{{val|1 1 3 2 3 2}}, {{val|0 5 -6 7 4 15}}]
 
POTE generator: ~12/11 = 136.937
 
Optimal ET sequence: {{Optimal ET sequence| 9, 26f, 35 }}
 
Badness: 0.049684
 
==== Secundly ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 45/44, 65/64, 78/77, 99/98
 
Mapping: [{{val|1 1 3 2 3 3}}, {{val|0 5 -6 7 4 6}}]
 
POTE generator: ~12/11 = 137.917
 
Optimal ET sequence: {{Optimal ET sequence| 9, 17, 26, 61bcf, 87bccf }}
 
Badness: 0.026212


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

Revision as of 09:22, 21 September 2023

This is a collection of rank-2 temperaments tempering out the avicennma, 525/512, also known as Avicenna's enharmonic diesis.

See:

Retrieved from "https://en.xen.wiki/index.php?title=Avicennmic_temperaments&oldid=124524"