Octagar temperaments: Difference between revisions
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Octagar temperaments temper out the octagar comma, {{monzo|5 -4 3 -2}} = 4000/3969. | Octagar temperaments temper out the octagar comma, {{monzo|5 -4 3 -2}} = 4000/3969. | ||
Temperaments discussed elsewhere | Temperaments discussed elsewhere include [[Garibaldi temperament|garibaldi]], [[Augmented family #Augene|augene]], [[Tetracot family #Octacot|octacot]], [[Orwellismic temperaments #Quartonic|quartonic]], [[superkleismic]], [[Meantone family #Injera|injera]], [[Diaschismic family #Bidia|bidia]], [[Kleismic family #Hemikleismic|hemikleismic]], [[Mirkwai clan #Pluto|pluto]], [[Porcupine family #Nautilus|nautilus]], [[Ripple family|ripple]], and [[Amity family #Hamity|hamity]]. | ||
== Slendi == | == Slendi == | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 4000/3969, 84035/82944 | [[Comma list]]: 4000/3969, 84035/82944 | ||
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=== 11-limit === | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | |||
Comma list: 100/99, 245/242, 46656/46585 | Comma list: 100/99, 245/242, 46656/46585 | ||
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=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 100/99, 144/143, 245/242, 343/338 | Comma list: 100/99, 144/143, 245/242, 343/338 | ||
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== Slithy == | == Slithy == | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 4000/3969, 420175/419904 | [[Comma list]]: 4000/3969, 420175/419904 | ||
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=== 11-limit === | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | |||
Comma list: 540/539, 2200/2187, 4375/4356 | Comma list: 540/539, 2200/2187, 4375/4356 | ||
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=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 325/324, 352/351, 540/539, 1575/1573 | Comma list: 325/324, 352/351, 540/539, 1575/1573 | ||
Revision as of 22:10, 24 June 2021
Octagar temperaments temper out the octagar comma, [5 -4 3 -2⟩ = 4000/3969.
Temperaments discussed elsewhere include garibaldi, augene, octacot, quartonic, superkleismic, injera, bidia, hemikleismic, pluto, nautilus, ripple, and hamity.
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