Keemic temperaments: Difference between revisions
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These temper out the keema, {{monzo| -5 -3 3 1 }} = [[875/864]]. Keemic temperaments include [[Jubilismic clan #Doublewide|doublewide]], [[Meantone family #Flattone|flattone]], [[Porcupine family #Porcupine|porcupine]], [[Gamelismic clan #Superkleismic|superkleismic]], [[Magic family #Magic|magic]], [[Kleismic family #Keemun|keemun]], and [[Sycamore family #Sycamore|sycamore]]. Discussed below are quasitemp and barbad. | These temper out the keema, {{monzo| -5 -3 3 1 }} = [[875/864]]. Keemic temperaments include [[Jubilismic clan #Doublewide|doublewide]], [[Meantone family #Flattone|flattone]], [[Porcupine family #Porcupine|porcupine]], [[Gamelismic clan #Superkleismic|superkleismic]], [[Magic family #Magic|magic]], [[Kleismic family #Keemun|keemun]], and [[Sycamore family #Sycamore|sycamore]]. Discussed below are quasitemp and barbad. | ||
= Quasitemp = | == Quasitemp == | ||
== 5-limit == | === 5-limit === | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
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[[Badness]]: 0.7678 | [[Badness]]: 0.7678 | ||
== 7-limit == | === 7-limit === | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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[[Badness]]: 0.0603 | [[Badness]]: 0.0603 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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POTE generator: ~25/21 = 292.547 | POTE generator: ~25/21 = 292.547 | ||
{{Val list | Vals: {{Val list| 37, 41, 119 }} | ||
Badness: 0.0432 | Badness: 0.0432 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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POTE generator: ~25/21 = 292.457 | POTE generator: ~25/21 = 292.457 | ||
{{Val list | Vals: {{Val list| 37, 41, 78, 119f }} | ||
Badness: 0.0329 | Badness: 0.0329 | ||
== Quato == | === Quato === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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POTE generator: ~25/21 = 292.851 | POTE generator: ~25/21 = 292.851 | ||
{{Val list | Vals: {{Val list| 41, 127cd, 168cd }} | ||
Badness: 0.0412 | Badness: 0.0412 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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POTE generator: ~13/11 = 292.928 | POTE generator: ~13/11 = 292.928 | ||
{{Val list | Vals: {{Val list| 41, 86ce, 127cd }} | ||
Badness: 0.0301 | Badness: 0.0301 | ||
= Barbad = | == Barbad == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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[[Badness]]: 0.1104 | [[Badness]]: 0.1104 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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POTE generator: ~98/75 = 468.367 | POTE generator: ~98/75 = 468.367 | ||
{{Val list | Vals: {{Val list| 18e, 23de, 41, 228ccdd }} | ||
Badness: 0.0501 | Badness: 0.0501 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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POTE generator: ~13/10 = 468.270 | POTE generator: ~13/10 = 468.270 | ||
{{Val list | Vals: {{Val list| 18e, 23de, 41 }} | ||
Badness: 0.0392 | Badness: 0.0392 | ||
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[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
[[Category:Temperament collection]] | [[Category:Temperament collection]] | ||
[[Category:Keemic]] | [[Category:Keemic temperaments| ]] <!-- main article --> | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
Revision as of 07:52, 19 July 2021
These temper out the keema, [-5 -3 3 1⟩ = 875/864. Keemic temperaments include doublewide, flattone, porcupine, superkleismic, magic, keemun, and sycamore. Discussed below are quasitemp and barbad.
Quasitemp
5-limit
Subgroup: 2.3.5
Comma list: 6103515625/5804752896
Mapping: [⟨1 5 5], ⟨0 -14 -11]]
POTE generator: ~3125/2592 = 292.702
Badness: 0.7678
7-limit
Subgroup: 2.3.5.7
Comma list: 875/864, 2401/2400
Mapping: [⟨1 5 5 5], ⟨0 -14 -11 -9]]
Wedgie: ⟨⟨ 14 11 9 -15 -25 -10 ]]
POTE generator: ~25/21 = 292.710
Badness: 0.0603
11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 385/384, 1375/1372
Mapping: [⟨1 5 5 5 2], ⟨0 -14 -11 -9 6]]
POTE generator: ~25/21 = 292.547
Vals: Template:Val list
Badness: 0.0432
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 196/195, 275/273, 385/384
POTE generator: ~13/11 = 292.457
Mapping: [⟨1 5 5 5 2 2], ⟨0 -14 -11 -9 6 7]]
POTE generator: ~25/21 = 292.457
Vals: Template:Val list
Badness: 0.0329
Quato
Subgroup: 2.3.5.7.11
Comma list: 243/242, 441/440, 625/616
Mapping: [⟨1 5 5 5 12], ⟨0 -14 -11 -9 -35]]
POTE generator: ~25/21 = 292.851
Vals: Template:Val list
Badness: 0.0412
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 243/242, 275/273, 325/324
Mapping: [⟨1 5 5 5 12 12], ⟨0 -14 -11 -9 -35 -34]]
POTE generator: ~13/11 = 292.928
Vals: Template:Val list
Badness: 0.0301
Barbad
Subgroup: 2.3.5.7
Comma list: 875/864, 16875/16807
Mapping: [⟨1 9 7 11], ⟨0 -19 -12 -21]]
POTE generator: ~98/75 = 468.331
Wedgie: ⟨⟨ 19 12 21 -25 -20 15 ]]
Badness: 0.1104
11-limit
Subgroup: 2.3.5.7.11
Comma list: 245/242, 540/539, 625/616
Mapping: [⟨1 9 7 11 14], ⟨0 -19 -12 -21 -27]]
POTE generator: ~98/75 = 468.367
Vals: Template:Val list
Badness: 0.0501
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 196/195, 245/242, 275/273
Mapping: [⟨1 9 7 11 14 8], ⟨0 -19 -12 -21 -27 -11]]
POTE generator: ~13/10 = 468.270
Vals: Template:Val list
Badness: 0.0392