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Schismatic family: Difference between revisions

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= Schismatic aka Helmholtz =
= Schismatic aka Helmholtz =
The 5-limit version of the temperament is a [[microtemperament]], sometimes called '''Helmholtz''', '''schismic''' or '''schismatic''', which flattens the fifth by a fraction of a schisma, but some other members of the family are less accurate. As a 5-limit system, it is far more accurate than meantone but still with manageable complexity. [[53edo]] is a possible tuning for schismatic, but you need [[118edo]] if you want to get the full effect. In exact analogy with 1/4 comma meantone there is also 1/8 schismatic, with pure major thirds and fifths flattened by 1/8 schisma. Since 1/8 of a schisma is 0.244 cents, this falls into the range of microtempering. You could also try 1/9 schisma, with pure minor thirds and a minutely better 5th, or 2/17 schisma, with both thirds flat by 1/17 of a schisma, although the differences would be very hard to distinguish unless using a large gamut.
The 5-limit version of the temperament is a [[microtemperament]], sometimes called '''Helmholtz''', '''schismic''' or '''schismatic''', which flattens the fifth by a fraction of a schisma, but some other members of the family are less accurate. As a 5-limit system, it is far more accurate than meantone but still with manageable complexity. [[53edo]] is a possible tuning for schismatic, but you need [[118edo]] if you want to get the full effect. In exact analogy with 1/4 comma meantone there is also 1/8 schismatic, with pure major thirds and fifths flattened by 1/8 schisma. Since 1/8 of a schisma is 0.244 cents, this falls into the range of microtempering. You could also try 1/9 schisma, with pure minor thirds and a minutely better 5th, or 2/17 schisma, with both thirds flat by 1/17 of a schisma, although the differences would be very hard to distinguish unless using a large gamut.
Subgroup: 2.3.5


[[Comma list]]: 32805/32768
[[Comma list]]: 32805/32768
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= Garibaldi =
= Garibaldi =
Subgroup: 2.3.5.7
[[Comma list]]: 225/224, 3125/3087
[[Comma list]]: 225/224, 3125/3087


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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 2200/2187
Comma list: 225/224, 385/384, 2200/2187


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=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 275/273, 325/324, 385/384
Comma list: 225/224, 275/273, 325/324, 385/384


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== Andromeda ==
== Andromeda ==
Subgroup: 2.3.5.7.11
Comma list: 100/99, 225/224, 245/242
Comma list: 100/99, 225/224, 245/242


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=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 105/104, 196/195, 245/242
Comma list: 100/99, 105/104, 196/195, 245/242


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== Helenus ==
== Helenus ==
Subgroup: 2.3.5.7.11
Comma list: 99/98, 176/175, 3125/3087
Comma list: 99/98, 176/175, 3125/3087


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=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 176/175, 275/273, 847/845
Comma list: 99/98, 176/175, 275/273, 847/845


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== Hemigari ==
== Hemigari ==
Subgroup: 2.3.5.7.11
Comma list: 121/120, 225/224, 3125/3087
Comma list: 121/120, 225/224, 3125/3087


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=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 169/168, 225/224, 275/273
Comma list: 121/120, 169/168, 225/224, 275/273


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== Sanjaab ==
== Sanjaab ==
Subgroup: 2.3.5.7.11
Comma list: 225/224, 1331/1323, 3125/3087
Comma list: 225/224, 1331/1323, 3125/3087


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=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 275/273, 847/845, 1331/1323
Comma list: 225/224, 275/273, 847/845, 1331/1323


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= Guiron =
= Guiron =
{{see also| Gamelismic clan }}
{{see also| Gamelismic clan }}
Subgroup: 2.3.5.7


[[Comma list]]: 1029/1024, 10976/10935
[[Comma list]]: 1029/1024, 10976/10935
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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 10976/10935
Comma list: 385/384, 441/440, 10976/10935


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== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 385/384, 729/728
Comma list: 196/195, 352/351, 385/384, 729/728


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= Pogo =
= Pogo =
Subgroup: 2.3.5.7
[[Comma list]]: 32805/32768, 118098/117649
[[Comma list]]: 32805/32768, 118098/117649


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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 540/539, 4000/3993, 32805/32768
Comma list: 540/539, 4000/3993, 32805/32768


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== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 729/728, 4000/3993, 4225/4224
Comma list: 540/539, 729/728, 4000/3993, 4225/4224


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= Squirrel =
= Squirrel =
Subgroup: 2.3.5.7
[[Comma list]]: 686/675, 32805/32768
[[Comma list]]: 686/675, 32805/32768


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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 245/242, 686/675, 896/891
Comma list: 245/242, 686/675, 896/891


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== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 169/168, 245/242, 896/891
Comma list: 91/90, 169/168, 245/242, 896/891


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= Schism =
= Schism =
{{see also| Archytas clan #Schism }}
{{see also| Archytas clan #Schism }}
Subgroup: 2.3.5.7


[[Comma list]]: 64/63, 360/343
[[Comma list]]: 64/63, 360/343
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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 45/44, 64/63, 99/98
Comma list: 45/44, 64/63, 99/98


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= Pontiac =
= Pontiac =
Subgroup: 2.3.5.7
[[Comma list]]: 4375/4374, 32805/32768
[[Comma list]]: 4375/4374, 32805/32768


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= Grackle =
= Grackle =
Subgroup: 2.3.5.7
[[Comma list]]: 126/125, 32805/32768
[[Comma list]]: 126/125, 32805/32768


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= Bischismic =
= Bischismic =
Subgroup: 2.3.5.7
[[Comma list]]: 3136/3125, 32805/32768
[[Comma list]]: 3136/3125, 32805/32768


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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 441/440, 3136/3125, 8019/8000
Comma list: 441/440, 3136/3125, 8019/8000


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== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 441/440, 729/728, 1001/1000, 3136/3125
Comma list: 441/440, 729/728, 1001/1000, 3136/3125


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= Kleischismic =
= Kleischismic =
Subgroup: 2.3.5.7
[[Comma list]]: 32805/32768, 1500625/1492992
[[Comma list]]: 32805/32768, 1500625/1492992


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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 385/384, 9801/9800, 14641/14580
Comma list: 385/384, 9801/9800, 14641/14580


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== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 385/384, 729/728, 1575/1573
Comma list: 352/351, 385/384, 729/728, 1575/1573


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= Term =
= Term =
Subgroup: 2.3.5.7
[[Comma list]]: 32805/32768, 250047/250000
[[Comma list]]: 32805/32768, 250047/250000


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= Sesquiquartififths =
= Sesquiquartififths =
Subgroup: 2.3.5.7
[[Comma list]]: 2401/2400, 32805/32768
[[Comma list]]: 2401/2400, 32805/32768


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== Sesquart ==
== Sesquart ==
Subgroup: 2.3.5.7.11
Comma list: 243/242, 441/440, 16384/16335
Comma list: 243/242, 441/440, 16384/16335


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=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 243/242, 364/363, 441/440, 3584/3575
Comma list: 243/242, 364/363, 441/440, 3584/3575


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== Bisesqui ==
== Bisesqui ==
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 9801/9800, 32805/32768
Comma list: 2401/2400, 9801/9800, 32805/32768


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= Sextilififths =
= Sextilififths =
Subgroup: 2.3.5.7
[[Comma list]]: 32768/32805, 235298/234375
[[Comma list]]: 32768/32805, 235298/234375


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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 441/440, 4000/3993, 235298/234375
Comma list: 441/440, 4000/3993, 235298/234375


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== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 441/440, 676/675, 10985/10976
Comma list: 364/363, 441/440, 676/675, 10985/10976


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= Tsaharuk =
= Tsaharuk =
Subgroup: 2.3.5.7
[[Comma list]]: 32805/32768, 420175/419904
[[Comma list]]: 32805/32768, 420175/419904


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= Quanharuk =
= Quanharuk =
Subgroup: 2.3.5.7
[[Comma list]]: 16875/16807, 32805/32768
[[Comma list]]: 16875/16807, 32805/32768


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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 32805/32768
Comma list: 540/539, 1375/1372, 32805/32768


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== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 1375/1372, 4096/4095, 6656/6655
Comma list: 540/539, 1375/1372, 4096/4095, 6656/6655


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= Octant =
= Octant =
Subgroup: 2.3.5.7
Comma list: 32805/32768, 2259436291848/2251875390625
Comma list: 32805/32768, 2259436291848/2251875390625


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== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 32805/32768, 46656/46585
Comma list: 9801/9800, 32805/32768, 46656/46585


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== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Comma list: 729/728, 1575/1573, 2200/2197, 6656/6655
Comma list: 729/728, 1575/1573, 2200/2197, 6656/6655


Retrieved from "https://en.xen.wiki/w/Schismatic_family"