Avicennmic temperaments: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
4,516 edits
mNo edit summary
Line 1: Line 1:
__FORCETOC__
These temper out the avicennma, [[525/512]], also known as Avicenna's enharmonic diesis. Avicennmic temperaments include negri, flattone, hexadecimal, muggles, lemba and roman.
These temper out the avicennma, [[525/512]], also known as Avicenna's enharmonic diesis. Avicennmic temperaments include negri, flattone, hexadecimal, muggles, lemba and roman.


== Roman ==
== Roman ==
Commas: 525/512, 4000/3969
{{see also|Wesley family #Crusher}}


[[POTE_tuning|POTE generator]]: ~63/50 = 414.552
=== 7-limit (Crusher) ===
[[Comma list]]: 525/512, 3125/3024


Map: [<1 4 3 -1|, <0 -7 -2 11|]
[[Mapping]]: [{{Val|1 4 3 -1}}, {{Val|0 -7 -2 11}}]


Wedgie: <<7 2 -11 -13 -37 -31||
{{Multival|legend=1|7 2 -11 -13 -37 -31}}


EDOs: [[23edo|23]], [[26edo|26]], [[29edo|29]], [[55edo|55c]]
[[POTE generator]]: ~63/50 = 414.552


Badness: 0.1134
{{Val list|legend=1| 3, 23, 26, 29, 55c }}
 
[[Badness]]: 0.113386


=== 11-limit ===
=== 11-limit ===
Commas: 100/99, 245/242, 1375/1344
Comma list: 100/99, 245/242, 525/512


[[POTE_tuning|POTE generator]]: ~14/11 = 414.471
Mapping: [{{Val|1 4 3 -1 0}}, {{Val|0 -7 -2 11 10}}]


Map: [<1 4 3 -1 0|, <0 -7 -2 11 10|]
POTE generator: ~14/11 = 414.471


EDOs: 23, 26, 29, 55c
Vals: {{Val list| 3, 23, 26, 29, 55c }}


Badness: 0.0528
Badness: 0.052841


=== 13-limit ===
=== 13-limit ===
Commas: 65/64, 100/99, 105/104, 245/243
Comma list: 65/64, 100/99, 105/104, 245/242


[[POTE_tuning|POTE generator]]: ~14/11 = 414.472
Mapping: [{{Val|1 4 3 -1 0 3}}, {{Val|0 -7 -2 11 10 2}}]


Map: [<1 4 3 -1 0 3|, <0 -7 -2 11 10 2|]
POTE generator: ~14/11 = 414.472


EDOs: 23, 26, 29, 55
Vals: {{Val list| 3, 23, 26, 29, 55cf }}


Badness: 0.0300
Badness: 0.030043


=== 17-limit ===
=== 17-limit ===
Commas: 35/34, 52/51, 100/99, 169/168, 275/273
Comma list: 35/34, 52/51, 65/64, 100/99, 121/119


[[POTE_tuning|POTE generator]]: ~14/11 = 414.164
Mapping: [{{Val|1 4 3 -1 0 3 1}}, {{Val|0 -7 -2 11 10 2 9}}]


Map: [<1 4 3 -1 0 3 1|, <0 -7 -2 11 10 2 9|]
POTE generator: ~14/11 = 414.164


EDOs: 26, 29, [[84edo|84]], [[113edo|113]]
Vals: {{Val list| 3, 26g, 29 }}


Badness: 0.0416
Badness: 0.041555


=== 19-limit ===
=== 19-limit ===
Commas: 35/34, 52/51, 100/99, 121/119, 133/132, 169/168
Comma list: 35/34, 52/51, 65/64, 100/99, 121/119, 133/132


[[POTE_tuning|POTE generator]]: ~14/11 = 414.130
Mapping: [{{Val|1 4 3 -1 0 3 1 7}}, {{Val|0 -7 -2 11 10 2 9 -8}}]


Map: [<1 4 3 -1 0 3 1 7|, <0 -7 -2 11 10 2 9 -8|]
POTE generator: ~14/11 = 414.130


EDOs: 26g, 29
Vals: {{Val list| 3, 26g, 29 }}


Badness: 0.0337
Badness: 0.033730


== Secund ==
== Secund ==
Commas: 405/392, 525/512
{{see also|Greenwoodmic temperaments #Secund}}
 
[[Comma list]]: 405/392, 525/512


POTE generator: ~16/15 = 137.958
[[Mapping]]: [{{val|1 1 3 2}}, {{val|0 5 -6 7}}]


Map: [<1 1 3 2|, <0 5 -6 7|]
{{Multival|legend=1|5 -6 7 -21 -3 33}}


Wedgie: <<5 -6 7 -21 -3 33||
[[POTE generator]]: ~16/15 = 137.958


EDOs: [[9edo|9]], [[17edo|17]], 26, [[61edo|61bc]], [[87edo|87bc]]
{{Val list|legend=1| 9, 17, 26, 61bc, 87bcc }}


Badness: 0.0898
[[Badness]]: 0.089840


=== 11-limit ===
=== 11-limit ===
Commas: 45/44, 99/98, 385/384
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
POTE generator: ~12/11 = 137.900


Map: [<1 1 3 2 3|, <0 5 -6 7 4|]
Vals: {{Val list| 9, 17, 26, 61bc, 87bcc }}


EDOs: 9, 17, 26, 61bc, 87bc
Badness: 0.042562


Badness: 0.0426
=== 13-limit ===
Comma list: 27/26, 45/44, 99/98, 385/384


=== 13-limit ===
Mapping: [{{val|1 1 3 2 3 2}}, {{val|0 5 -6 7 4 15}}]
Commas: 27/26, 45/44, 99/98, 385/384


POTE generator: ~12/11 = 136.937
POTE generator: ~12/11 = 136.937


Map: [<1 1 3 2 3 2|, <0 5 -6 7 4 15|]
Vals: {{Val list| 9, 26f, 35 }}


EDOs: 9, 26f, [[35edo|35]]
Badness: 0.049684


Badness: 0.0497
=== Secundly ===
Comma list: 45/44, 65/64, 78/77, 99/98


=== Secundly ===
Mapping: [{{val|1 1 3 2 3 3}}, {{val|0 5 -6 7 4 6}}]
Commas: 45/44, 78/77, 81/80, 640/637


POTE generator: ~12/11 = 137.917
POTE generator: ~12/11 = 137.917


Map: [<1 1 3 2 3 3|, <0 5 -6 7 4 6|]
Vals: {{Val list| 9, 17, 26, 61bcf, 87bccf }}
 
EDOs: 9, 17, 26, 61bcf, 87bcf


Badness: 0.0262
Badness: 0.026212


[[Category:Theory]]
[[Category:Theory]]
[[Category:Temperament]]
[[Category:Temperament]]
[[Category:Temperament collection]]
[[Category:Avicennmic]]
[[Category:Avicennmic]]
[[Category:Rank 2]]
[[Category:Rank 2]]

Revision as of 01:02, 2 August 2021

These temper out the avicennma, 525/512, also known as Avicenna's enharmonic diesis. Avicennmic temperaments include negri, flattone, hexadecimal, muggles, lemba and roman.

Roman

See also: Wesley family § Crusher

7-limit (Crusher)

Comma list: 525/512, 3125/3024

Mapping: [⟨1 4 3 -1], ⟨0 -7 -2 11]]

Wedgie: ⟨⟨ 7 2 -11 -13 -37 -31 ]]

POTE generator: ~63/50 = 414.552

Template:Val list

Badness: 0.113386

11-limit

Comma list: 100/99, 245/242, 525/512

Mapping: [⟨1 4 3 -1 0], ⟨0 -7 -2 11 10]]

POTE generator: ~14/11 = 414.471

Vals: Template:Val list

Badness: 0.052841

13-limit

Comma list: 65/64, 100/99, 105/104, 245/242

Mapping: [⟨1 4 3 -1 0 3], ⟨0 -7 -2 11 10 2]]

POTE generator: ~14/11 = 414.472

Vals: Template:Val list

Badness: 0.030043

17-limit

Comma list: 35/34, 52/51, 65/64, 100/99, 121/119

Mapping: [⟨1 4 3 -1 0 3 1], ⟨0 -7 -2 11 10 2 9]]

POTE generator: ~14/11 = 414.164

Vals: Template:Val list

Badness: 0.041555

19-limit

Comma list: 35/34, 52/51, 65/64, 100/99, 121/119, 133/132

Mapping: [⟨1 4 3 -1 0 3 1 7], ⟨0 -7 -2 11 10 2 9 -8]]

POTE generator: ~14/11 = 414.130

Vals: Template:Val list

Badness: 0.033730

Secund

See also: Greenwoodmic temperaments § Secund

Comma list: 405/392, 525/512

Mapping: [⟨1 1 3 2], ⟨0 5 -6 7]]

Wedgie: ⟨⟨ 5 -6 7 -21 -3 33 ]]

POTE generator: ~16/15 = 137.958

Template:Val list

Badness: 0.089840

11-limit

Comma list: 45/44, 99/98, 385/384

Mapping: [⟨1 1 3 2 3], ⟨0 5 -6 7 4]]

POTE generator: ~12/11 = 137.900

Vals: Template:Val list

Badness: 0.042562

13-limit

Comma list: 27/26, 45/44, 99/98, 385/384

Mapping: [⟨1 1 3 2 3 2], ⟨0 5 -6 7 4 15]]

POTE generator: ~12/11 = 136.937

Vals: Template:Val list

Badness: 0.049684

Secundly

Comma list: 45/44, 65/64, 78/77, 99/98

Mapping: [⟨1 1 3 2 3 3], ⟨0 5 -6 7 4 6]]

POTE generator: ~12/11 = 137.917

Vals: Template:Val list

Badness: 0.026212

Retrieved from "https://en.xen.wiki/index.php?title=Avicennmic_temperaments&oldid=75355"