Octagar temperaments: Difference between revisions
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* ''[[Nautilus]]'', {49/48, 250/243} → [[Porcupine family #Nautilus|Porcupine family]] | * ''[[Nautilus]]'', {49/48, 250/243} → [[Porcupine family #Nautilus|Porcupine family]] | ||
* ''[[Injera]]'', {50/49, 81/80} → [[Meantone family #Injera|Meantone family]] | * ''[[Injera]]'', {50/49, 81/80} → [[Meantone family #Injera|Meantone family]] | ||
* | * [[Augene]], {64/63, 126/125} → [[Augmented family #Augene|Augmented family]] | ||
* [[Garibaldi temperament|Garibaldi]], {225/224, 3125/3087} → [[Schismatic family #Garibaldi|Schismatic family]] | * [[Garibaldi temperament|Garibaldi]], {225/224, 3125/3087} → [[Schismatic family #Garibaldi|Schismatic family]] | ||
* ''[[Octacot]]'', {245/243, 2401/2400} → [[Tetracot family #Octacot|Tetracot family]] | * ''[[Octacot]]'', {245/243, 2401/2400} → [[Tetracot family #Octacot|Tetracot family]] | ||
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[[Comma list]]: 4000/3969, 84035/82944 | [[Comma list]]: 4000/3969, 84035/82944 | ||
[[Mapping]]: [{{val|1 2 3 3}}, {{val|0 -17 -28 -8}}] | [[Mapping]]: [{{val| 1 2 3 3 }}, {{val| 0 -17 -28 -8 }}] | ||
{{Multival|legend=1|17 28 8 5 -35 -60}} | {{Multival|legend=1| 17 28 8 5 -35 -60 }} | ||
[[POTE generator]]: ~49/48 = 29.181 | [[POTE generator]]: ~49/48 = 29.181 | ||
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Comma list: 100/99, 245/242, 46656/46585 | Comma list: 100/99, 245/242, 46656/46585 | ||
Mapping: [{{val|1 2 3 3 4}}, {{val|0 -17 -28 -8 -22}}] | Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -17 -28 -8 -22 }}] | ||
POTE generator: ~49/48 = 29.180 | POTE generator: ~49/48 = 29.180 | ||
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Comma list: 100/99, 144/143, 245/242, 343/338 | Comma list: 100/99, 144/143, 245/242, 343/338 | ||
Mapping: [{{val|1 2 3 3 4 4}}, {{val|0 -17 -28 -8 -22 -1}}] | Mapping: [{{val| 1 2 3 3 4 4 }}, {{val| 0 -17 -28 -8 -22 -1 }}] | ||
POTE generator: ~49/48 = 29.125 | POTE generator: ~49/48 = 29.125 | ||
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[[Comma list]]: 4000/3969, 420175/419904 | [[Comma list]]: 4000/3969, 420175/419904 | ||
[[Mapping]]: [{{val|1 3 5 4}}, {{val|0 -19 -36 -16}}] | [[Mapping]]: [{{val| 1 3 5 4 }}, {{val| 0 -19 -36 -16 }}] | ||
{{Multival|legend=1|19 36 16 13 -28 -64}} | {{Multival|legend=1| 19 36 16 13 -28 -64 }} | ||
[[POTE generator]]: ~21/20 = 89.282 | [[POTE generator]]: ~21/20 = 89.282 | ||
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Comma list: 540/539, 2200/2187, 4375/4356 | Comma list: 540/539, 2200/2187, 4375/4356 | ||
Mapping: [{{val|1 3 5 4 8}}, {{val|0 -19 -36 -16 -61}}] | Mapping: [{{val| 1 3 5 4 8 }}, {{val| 0 -19 -36 -16 -61 }}] | ||
POTE generator: ~21/20 = 89.291 | POTE generator: ~21/20 = 89.291 | ||
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Comma list: 325/324, 352/351, 540/539, 1575/1573 | Comma list: 325/324, 352/351, 540/539, 1575/1573 | ||
Mapping: [{{val|1 3 5 4 8 4}}, {{val|0 -19 -36 -16 -61 -4}}] | Mapping: [{{val| 1 3 5 4 8 4 }}, {{val| 0 -19 -36 -16 -61 -4 }}] | ||
POTE generator: ~21/20 = 89.286 | POTE generator: ~21/20 = 89.286 | ||
Revision as of 15:46, 21 November 2021
This is a collection of temperaments tempering out the octagar comma, [5 -4 3 -2⟩ = 4000/3969.
Temperaments discussed elsewhere include:
- Ripple, {36/35, 2560/2401} → Ripple family
- Nautilus, {49/48, 250/243} → Porcupine family
- Injera, {50/49, 81/80} → Meantone family
- Augene, {64/63, 126/125} → Augmented family
- Garibaldi, {225/224, 3125/3087} → Schismatic family
- Octacot, {245/243, 2401/2400} → Tetracot family
- Roman, {525/512, 3125/3024} → Wesley family and Avicennmic temperaments
- Superkleismic, {875/864, 1029/1024} → Shibboleth family and Gamelismic clan
- Quartonic, {1728/1715, 4000/3969} → Orwellismic temperaments
- Bidia, {2048/2025, 3136/3125} → Diaschismic family
- Hamity, {2430/2401, 4000/3969} → Amity family
- Hemikleismic, {4000/3969, 6144/6125} → Kleismic family
- Pluto, {4000/3969, 10976/10935} → Mirkwai clan
- Quintupole, {4000/3969, 458752/455625} → Quintaleap family
Considered below are slendi and slithy.
Slendi
Subgroup: 2.3.5.7
Comma list: 4000/3969, 84035/82944
Mapping: [⟨1 2 3 3], ⟨0 -17 -28 -8]]
Wedgie: ⟨⟨ 17 28 8 5 -35 -60 ]]
POTE generator: ~49/48 = 29.181
Badness: 0.142903
11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 245/242, 46656/46585
Mapping: [⟨1 2 3 3 4], ⟨0 -17 -28 -8 -22]]
POTE generator: ~49/48 = 29.180
Vals: Template:Val list
Badness: 0.063217
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 144/143, 245/242, 343/338
Mapping: [⟨1 2 3 3 4 4], ⟨0 -17 -28 -8 -22 -1]]
POTE generator: ~49/48 = 29.125
Vals: Template:Val list
Badness: 0.043644
Slithy
Subgroup: 2.3.5.7
Comma list: 4000/3969, 420175/419904
Mapping: [⟨1 3 5 4], ⟨0 -19 -36 -16]]
Wedgie: ⟨⟨ 19 36 16 13 -28 -64 ]]
POTE generator: ~21/20 = 89.282
Badness: 0.107482
11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 2200/2187, 4375/4356
Mapping: [⟨1 3 5 4 8], ⟨0 -19 -36 -16 -61]]
POTE generator: ~21/20 = 89.291
Vals: Template:Val list
Badness: 0.045895
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 352/351, 540/539, 1575/1573
Mapping: [⟨1 3 5 4 8 4], ⟨0 -19 -36 -16 -61 -4]]
POTE generator: ~21/20 = 89.286
Vals: Template:Val list
Badness: 0.028492