Greenwoodmic temperaments: Difference between revisions

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These temperament temper out the greenwoodma, {{monzo|-3 4 1 -2}} = 405/392.
These temper out the greenwoodma, |-3 4 1 -2> = 405/392.


=Greenwood=
== Greenwood ==
Commas: 405/392, 1323/1280
{{see also|Apotome family}}


POTE generator: ~8/7 = 241.490
[[Comma list]]: 405/392, 1323/1280


Map: [<7 11 1 12|, <0 0 2 1|]
[[Mapping]]: [{{val|7 11 1 12}}, {{val|0 0 2 1}}]


Wedgie: <<0 14 7 22 11 -23||
{{Multival|legend=1|0 14 7 22 11 -23}}


EDOs: 14c, 21, 35, 84bcd
[[POTE generator]]: ~8/7 = 241.490


Badness: 0.1218
{{Val list|legend=1| 14c, 21, 35 }}


==11-limit==
[[Badness]]: 0.121752
Commas: 45/44, 99/98, 1323/1280
 
=== 11-limit ===
Comma list: 45/44, 99/98, 1323/1280
 
Mapping: [{{val|7 11 1 12 9}}, {{val|0 0 2 1 2}}]


POTE generator: ~8/7 = 242.711
POTE generator: ~8/7 = 242.711


Map: [<7 11 1 12 9|, <0 0 2 1 2|]
Vals: {{Val list| 14c, 21, 35, 49bcde, 84bbccde }}
 
Badness: 0.057471


EDOs: 14c, 21, 35, 49bcde, 84bcde
=== 13-limit ===
Comma list: 27/26, 45/44, 99/98, 640/637


Badness: 0.0575
Mapping: [{{val|7 11 1 12 9 26}}, {{val|0 0 2 1 2 0}}]


==13-limit==
POTE generator: ~8/7 = 238.607
Commas: 27/26, 45/44, 99/98, 640/637


POTE generaor: ~8/7 = 238.607
Vals: {{Val list| 14c, 21, 35 }}


Map: [<7 11 1 12 9 26|, <0 0 2 1 2 0|]
Badness: 0.054009


EDOs: 14c, 21, 35, 91bf
== Secund ==
{{see also|Avicennmic temperaments #Secund}}


Badness: 0.0540
[[Comma list]]: 405/392, 525/512


=Secund=
[[Mapping]]: [{{val|1 1 3 2}}, {{val|0 5 -6 7}}]
Commas: 405/392, 525/512


POTE generator: ~16/15 = 137.958
{{Multival|legend=1|5 -6 7 -21 -3 33}}


Map: [<1 1 3 2|, <0 5 -6 7|]
[[POTE generator]]: ~16/15 = 137.958


Wedgie: <<5 -6 7 -21 -3 33||
{{Val list|legend=1| 9, 17, 26, 61bc, 87bcc }}


EDOs: 9, 17, 26, 61bc, 87bc
[[Badness]]: 0.089840


Badness: 0.0898
=== 11-limit ===
Comma list: 45/44, 99/98, 385/384


==11-limit==
Mapping: [{{val|1 1 3 2 3}}, {{val|0 5 -6 7 4}}]
Commas: 45/44, 99/98, 385/384


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 }}
 
Badness: 0.049684
 
=== Secundly ===
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
 
Vals: {{Val list| 9, 17, 26, 61bcf, 87bccf }}


EDOs: 9, 26f, 35
Badness: 0.026212


Badness: 0.0497
[[Category:Theory]]
[[Category:Temperament]]
[[Category:Temperament collection]]
[[Category:Greenwoodmic]]
[[Category:Rank 2]]

Revision as of 01:24, 2 August 2021

These temperament temper out the greenwoodma, [-3 4 1 -2⟩ = 405/392.

Greenwood

See also: Apotome family

Comma list: 405/392, 1323/1280

Mapping: [⟨7 11 1 12], ⟨0 0 2 1]]

Wedgie: ⟨⟨ 0 14 7 22 11 -23 ]]

POTE generator: ~8/7 = 241.490

Template:Val list

Badness: 0.121752

11-limit

Comma list: 45/44, 99/98, 1323/1280

Mapping: [⟨7 11 1 12 9], ⟨0 0 2 1 2]]

POTE generator: ~8/7 = 242.711

Vals: Template:Val list

Badness: 0.057471

13-limit

Comma list: 27/26, 45/44, 99/98, 640/637

Mapping: [⟨7 11 1 12 9 26], ⟨0 0 2 1 2 0]]

POTE generator: ~8/7 = 238.607

Vals: Template:Val list

Badness: 0.054009

Secund

See also: Avicennmic 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

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