Cataharry temperaments: Difference between revisions
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This is a collection of rank-2 temperaments tempering out the [[cataharry comma]], {{monzo| -4 9 -2 -2 }} = 19683/19600. These include swetneus, considered below, as well as others discussed elsewhere: | |||
* [[godzilla]], {49/48, 81/80} → [[Meantone family #Godzilla]] | |||
* ''[[immunized]]'', {64/63, 8748/8575} → [[Immunity family #Immunized]] | |||
* ''[[unicorn]]'', {126/125, 10976/10935} → [[Unicorn family #Septimal unicorn]] | |||
* [[catakleismic]], {225/224, 4375/4374} → [[Kleismic family #Catakleismic]] | |||
* ''[[hemiseven]]'', {1029/1024, 19683/19600} → [[Gamelismic clan #Hemiseven]] | |||
* ''[[buzzard]]'', {1728/1715, 5120/5103} → [[Hemifamity temperaments #Buzzard]] | |||
* [[harry]], {2401/2400, 19683/19600} → [[Breedsmic temperaments #Harry]] | |||
* [[hamity]], {2430/2401, 4000/3969} → [[Amity family #Hamity]] | |||
* ''[[subpental]]'', {3136/3125, 19683/19600} → [[Hemimean clan #Subpental]] | |||
* ''[[hemischis]]'', {6144/6125, 19683/19600} → [[Porwell temperaments #Hemischis]] | |||
* ''[[mirkat]]'', {16875/16807, 19683/19600} → [[Mirkwai clan #Mirkat]] | |||
* ''[[hours]]'', {19683/19600, 33075/32768} → [[Compton family #Hours]] | |||
= Swetneus = | = Swetneus = | ||
The swetneus temperament takes its name from the fact that an approximate swetismic neutral second, ~49/45, is the generator. | The swetneus temperament takes its name from the fact that an approximate swetismic neutral second, ~49/45, is the generator. | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 19683/19600, 50421/50000 | |||
[[Mapping]]: [{{val| 1 4 8 8 }}, {{val| 0 -20 -47 -43 }}] | |||
{{Multival|legend=1| 20 47 43 28 12 -32 }} | |||
[[POTE generator]]: ~49/45 = 144.956 | |||
Badness: 0.1332 | {{Val list|legend=1| 58, 91, 149, 505d, 654bd, 803bd }} | ||
[[Badness]]: 0.1332 | |||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | |||
Comma list: 441/440, 3388/3375, 19683/19600 | |||
Mapping: [{{val| 1 4 8 8 13 }}, {{val| 0 -20 -47 -43 -79 }}] | |||
POTE generator: ~49/45 = 144.941 | POTE generator: ~49/45 = 144.941 | ||
Vals: {{Val list| 58, 149, 207, 356e, 563cde, 919bcde }} | |||
{{ | |||
Badness: 0.0552 | Badness: 0.0552 | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 351/350, 441/440, 676/675, 847/845 | |||
Mapping: [{{val| 1 4 8 8 13 13 }}, {{val| 0 -20 -47 -43 -79 -77 }}] | |||
POTE generator: ~49/45 = 144.939 | POTE generator: ~49/45 = 144.939 | ||
Vals: {{Val list| 58, 149, 207, 356e, 563cde, 919bcdef }} | |||
{{ | |||
Badness: 0.0289 | Badness: 0.0289 | ||
[[Category: | [[Category:Regular temperament theory]] | ||
[[Category:Temperament]] | [[Category:Temperament collection]] | ||
[[Category:Cataharry]] | [[Category:Cataharry temperaments| ]] <!-- main article --> | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
Revision as of 11:25, 6 June 2021
This is a collection of rank-2 temperaments tempering out the cataharry comma, [-4 9 -2 -2⟩ = 19683/19600. These include swetneus, considered below, as well as others discussed elsewhere:
- godzilla, {49/48, 81/80} → Meantone family #Godzilla
- immunized, {64/63, 8748/8575} → Immunity family #Immunized
- unicorn, {126/125, 10976/10935} → Unicorn family #Septimal unicorn
- catakleismic, {225/224, 4375/4374} → Kleismic family #Catakleismic
- hemiseven, {1029/1024, 19683/19600} → Gamelismic clan #Hemiseven
- buzzard, {1728/1715, 5120/5103} → Hemifamity temperaments #Buzzard
- harry, {2401/2400, 19683/19600} → Breedsmic temperaments #Harry
- hamity, {2430/2401, 4000/3969} → Amity family #Hamity
- subpental, {3136/3125, 19683/19600} → Hemimean clan #Subpental
- hemischis, {6144/6125, 19683/19600} → Porwell temperaments #Hemischis
- mirkat, {16875/16807, 19683/19600} → Mirkwai clan #Mirkat
- hours, {19683/19600, 33075/32768} → Compton family #Hours
Swetneus
The swetneus temperament takes its name from the fact that an approximate swetismic neutral second, ~49/45, is the generator.
Subgroup: 2.3.5.7
Comma list: 19683/19600, 50421/50000
Mapping: [⟨1 4 8 8], ⟨0 -20 -47 -43]]
Wedgie: ⟨⟨ 20 47 43 28 12 -32 ]]
POTE generator: ~49/45 = 144.956
Badness: 0.1332
11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 3388/3375, 19683/19600
Mapping: [⟨1 4 8 8 13], ⟨0 -20 -47 -43 -79]]
POTE generator: ~49/45 = 144.941
Vals: Template:Val list
Badness: 0.0552
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 441/440, 676/675, 847/845
Mapping: [⟨1 4 8 8 13 13], ⟨0 -20 -47 -43 -79 -77]]
POTE generator: ~49/45 = 144.939
Vals: Template:Val list
Badness: 0.0289