Greenwoodmic temperaments: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Francium (talk | contribs)
4,621 edits
mNo edit summary
Update keys and links
Line 1: Line 1:
These temperament temper out the [[greenwoodma]], {{monzo|-3 4 1 -2}} = 405/392.
This is a collection of [[Rank-2 temperament|rank-2]] [[temperament]]s [[tempering out]] the greenwoodma, {{monzo| -3 4 1 -2 }} = [[405/392]].


Temperaments discussed elsewhere include [[Augmented family #August|august]], [[Meantone family #Injera|injera]], [[Archytas clan #Schism|schism]], [[Dicot family #Sidi|sidi]], and [[Pelogic family #Superpelog|superpelog]].
Temperaments discussed elsewhere include  
 
* ''[[Sidi]]'' (+25/24) → [[Dicot family #Sidi|Dicot family]]
== Greenwood ==
* ''[[August]]'' (+36/35) → [[Augmented family #August|Augmented family]]
{{see also|Apotome family #Greenwood}}
* ''[[Superpelog]]'' (+49/48) → [[Slendro clan #Superpelog|Slendro clan]]
 
* ''[[Injera]]'' (+50/49 or 81/80) → [[Meantone family #Injera|Meantone family]]
Subgroup: 2.3.5.7
* ''[[Schism]]'' (+64/63) → [[Archytas clan #Schism|Archytas clan]]
 
* ''[[Greenwood]]'' (+1323/1280) → [[Apotome family #Greenwood|Apotome family]]
[[Comma list]]: 405/392, 1323/1280
 
[[Mapping]]: [{{val|7 11 1 12}}, {{val|0 0 2 1}}]
 
{{Multival|legend=1|0 14 7 22 11 -23}}
 
[[POTE generator]]: ~8/7 = 241.490
 
{{Optimal ET sequence|legend=1| 14c, 21, 35 }}
 
[[Badness]]: 0.121752
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
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
 
{{Optimal ET sequence|legend=1| 14c, 21, 35, 49bcde, 84bbccde }}
 
Badness: 0.057471
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 27/26, 45/44, 99/98, 640/637
 
Mapping: [{{val|7 11 1 12 9 26}}, {{val|0 0 2 1 2 0}}]
 
POTE generator: ~8/7 = 238.607
 
{{Optimal ET sequence|legend=1| 14c, 21, 35 }}
 
Badness: 0.054009


== Secund ==
== Secund ==
{{see also|Avicennmic temperaments #Secund}}
[[Subgroup]]: 2.3.5.7
 
Subgroup: 2.3.5.7


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


[[Mapping]]: [{{val|1 1 3 2}}, {{val|0 5 -6 7}}]
{{Mapping|legend=1| 1 1 3 2 | 0 5 -6 7 }}


{{Multival|legend=1|5 -6 7 -21 -3 33}}
{{Multival|legend=1| 5 -6 7 -21 -3 33 }}


[[POTE generator]]: ~16/15 = 137.958
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~16/15 = 137.958


{{Optimal ET sequence|legend=1| 9, 17, 26, 61bc, 87bcc }}
{{Optimal ET sequence|legend=1| 9, 17, 26, 61bc, 87bcc }}
Line 68: Line 29:
Comma list: 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}}]
Mapping: {{mapping| 1 1 3 2 3 | 0 5 -6 7 4 }}


POTE generator: ~12/11 = 137.900
Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 137.900


Optimal ET sequence: {{Optimal ET sequence| 9, 17, 26, 61bc, 87bcc }}
Optimal ET sequence: {{Optimal ET sequence| 9, 17, 26, 61bc, 87bcc }}
Line 81: Line 42:
Comma list: 27/26, 45/44, 99/98, 385/384
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}}]
Mapping: {{mapping| 1 1 3 2 3 2 | 0 5 -6 7 4 15 }}


POTE generator: ~12/11 = 136.937
Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 136.937


Optimal ET sequence: {{Optimal ET sequence| 9, 26f, 35 }}
Optimal ET sequence: {{Optimal ET sequence| 9, 26f, 35 }}
Line 94: Line 55:
Comma list: 45/44, 65/64, 78/77, 99/98
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}}]
Mapping: {{mapping| 1 1 3 2 3 3 | 0 5 -6 7 4 6 }}


POTE generator: ~12/11 = 137.917
Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 137.917


Optimal ET sequence: {{Optimal ET sequence| 9, 17, 26, 61bcf, 87bccf }}
Optimal ET sequence: {{Optimal ET sequence| 9, 17, 26, 61bcf, 87bccf }}
Line 103: Line 64:


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

Revision as of 09:15, 21 September 2023

This is a collection of rank-2 temperaments tempering out the greenwoodma, [-3 4 1 -2⟩ = 405/392.

Temperaments discussed elsewhere include

Secund

Subgroup: 2.3.5.7

Comma list: 405/392, 525/512

Mapping: [⟨1 1 3 2], ⟨0 5 -6 7]]

Wedgie: ⟨⟨ 5 -6 7 -21 -3 33 ]]

Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 137.958

Optimal ET sequence: 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: [⟨1 1 3 2 3], ⟨0 5 -6 7 4]]

Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 137.900

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: [⟨1 1 3 2 3 2], ⟨0 5 -6 7 4 15]]

Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 136.937

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: [⟨1 1 3 2 3 3], ⟨0 5 -6 7 4 6]]

Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 137.917

Optimal ET sequence: 9, 17, 26, 61bcf, 87bccf

Badness: 0.026212

Retrieved from "https://en.xen.wiki/index.php?title=Greenwoodmic_temperaments&oldid=124522"