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Associated temperament: Difference between revisions

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By an ''associated temperament'' to a p-limit comma is meant a p-limit temperament tempering out that comma which shares the same [[Optimal_patent_val|optimal patent val]] as the [[Rank_and_codimension|codimension one]] temperament tempering out that comma. By definition, the optimal patent val defines the unique rank one associated temperament. For rank two temperaments, it is possible for more than one temperament to be associated, and some of these are listed below. The column headings are the comma being associated, the optimal patent val, the rank two temperament, and a comma basis for the rank two temperament.
By an ''associated temperament'' to a p-limit comma is meant a p-limit temperament tempering out that comma which shares the same [[optimal patent val]] as the [[Rank and codimension|codimension one]] temperament tempering out that comma. By definition, the optimal patent val defines the unique rank one associated temperament. For rank two temperaments, it is possible for more than one temperament to be associated, and some of these are listed below. The column headings are the comma being associated, the optimal patent val, the rank two temperament, and a comma basis for the rank two temperament.


=7 limit=
=7 limit=
Line 62: Line 62:
| 875/864
| 875/864
| [[41edo]]
| [[41edo]]
| [[Magic|magic]]
| [[Magic]]
| [[225/224]], [[245/243]]
| [[225/224]], [[245/243]]
|-
|-
Line 80: Line 80:
| [[225/224]], 1728/1715
| [[225/224]], 1728/1715
|-
|-
| | 245/243
| 245/243
| | [[283edo|283edo]]
| [[283edo]]
| | [[Escapade_family#Escaped|escaped]]
| [[Escapade family#Escaped|escaped]]
| | 245/243, 65625/65536
| 245/243, 65625/65536
|-
|-
| | 126/125
| 126/125
| | [[185edo|185edo]]
| [[185edo]]
| | [[Valentine|valentine]]
| [[Valentine]]
| | 126/125, 1029/1024
| 126/125, 1029/1024
|-
|-
| | 1728/1715
| 1728/1715
| | [[111edo|111edo]]
| [[111edo]]
| | [[Hemifamity_temperaments#Buzzard|buzzard]]
| [[Hemifamity temperaments#Buzzard|buzzard]]
| | 1728/1715, 5120/5103
| 1728/1715, 5120/5103
|-
|-
| | 1728/1715
| 1728/1715
| | [[111edo|111edo]]
| [[111edo]]
| | [[Semisept|semisept]]
| [[Semisept]]
| | 1728/1715, 3136/3125
| 1728/1715, 3136/3125
|-
|-
| | 1029/1024
| 1029/1024
| | [[190edo|190edo]]
| [[190edo]]
| | [[Unidec|unidec]]
| [[Unidec]]
| | 1029/1024, 4375/4374
| 1029/1024, 4375/4374
|-
|-
| | 225/224
| 225/224
| | [[197edo|197edo]]
| [[197edo]]
| | [[catakleismic|catakleismic]]
| [[catakleismic]]
| | 225/224, 4375/4374
| 225/224, 4375/4374
|-
|-
| | 3136/3125
| 3136/3125
| | [[446edo|446edo]]
| [[446edo]]
| | [[Hemimean_clan#Sengagen|sengagen]]
| [[Hemimean clan#Sengagen|sengagen]]
| | 3136/3125, 420175/419904
| 3136/3125, 420175/419904
|-
|-
| | 5120/5103
| 5120/5103
| | [[391edo|391edo]]
| [[391edo]]
| | [[Hemifamity_temperaments#Alphaquarter|alphaquarter]]
| [[Hemifamity temperaments#Alphaquarter|alphaquarter]]
| | 5120/5103, 29360128/29296875
| 5120/5103, 29360128/29296875
|-
|-
| | 5120/5103
| 5120/5103
| | [[391edo|391edo]]
| [[391edo]]
| | [[Hemifamity_temperaments#Septiquarter|septiquarter]]
| [[Hemifamity temperaments#Septiquarter|septiquarter]]
| | 5120/5103, 420175/419904
| 5120/5103, 420175/419904
|-
|-
| | 6144/6125
| 6144/6125
| | [[381edo|381edo]]
| [[381edo]]
| | [[Porwell_temperaments#Nessafof|nessafof]]
| [[Porwell temperaments#Nessafof|nessafof]]
| | 6144/6125, 250047/250000
| 6144/6125, 250047/250000
|-
|-
| | 65625/65536
| 65625/65536
| | [[171edo|171edo]]
| [[171edo]]
| | [[Breedsmic_temperaments#Tertiaseptal|tertiaseptal]]
| [[Breedsmic temperaments#Tertiaseptal|tertiaseptal]]
| | 2401/2400, 65625/65536
| 2401/2400, 65625/65536
|-
|-
| 703125/702464
| 703125/702464
| [[2185edo]]
| [[2185edo]]
| [[Ragismic_microtemperaments#Enneadecal|enneadecal]]
| [[Ragismic microtemperaments#Enneadecal|enneadecal]]
| 4375/4374, 703125/702464
| 4375/4374, 703125/702464
|-
|-
Line 155: Line 155:
{| class="wikitable"
{| class="wikitable"
|-
|-
| | Comma
| Comma
| | OPV
| OPV
| | Temperament
| Temperament
| | Basis
| Basis
|-
|-
| | 33/32
| 33/32
| | [[16edo|16edo]]
| [[16edo]]
| | [[Pelogic_family#Armodue|armodue]]
| [[Pelogic family#Armodue|armodue]]
| | 33/32, 36/35, 45/44
| 33/32, 36/35, 45/44
|-
|-
| | 77/75
| 77/75
| | [[39edo|39edo]]
| [[39edo]]
| | [[Triforce|triforce]]
| [[Triforce]]
| | 49/48, 56/55, 77/75
| 49/48, 56/55, 77/75
|-
|-
| | 352/343
| 352/343
| | [[22edo|22edo]]
| [[22edo]]
| | [[Hedgehog|hedgehog]]
| [[Hedgehog]]
| | 50/49, 55/54, 99/98
| 50/49, 55/54, 99/98
|-
|-
| | 45/44
| 45/44
| | [[45edo|45edo]]
| [[45edo]]
| | [[Flattone|flattone]]
| [[Flattone]]
| | 45/44, 81/80, 385/384
| 45/44, 81/80, 385/384
|-
|-
| | 55/54
| 55/54
| | [[51edo|51edo]]
| [[51edo]]
| | [[Porky|porky]]
| [[Porky]]
| | 55/54, 100/99, 225/224
| 55/54, 100/99, 225/224
|-
|-
| | 56/55
| 56/55
| | [[36edo|36edo]]
| [[36edo]]
| | [[Pythagorean_family#Catler temperament|catcall]]
| [[Pythagorean family#Catler temperament|catcall]]
| | 56/55, 81/80, 128/125
| 56/55, 81/80, 128/125
|-
|-
| | 245/242
| 245/242
| | [[91edo|91edo]]
| [[91edo]]
| | [[Septimin|septimin]]
| [[Septimin]]
| | 225/224, 245/242, 385/384
| 225/224, 245/242, 385/384
|-
|-
| | 99/98
| 99/98
| | [[127edo|127edo]]
| [[127edo]]
| | [[Würschmidt_family#Würschmidt|würschmidt]]
| [[Würschmidt family#Würschmidt|würschmidt]]
| | 99/98, 176/175, 243/242
| 99/98, 176/175, 243/242
|-
|-
| | 100/99
| 100/99
| | [[104edo|104edo]]
| [[104edo]]
| | [[Magic|magic]]
| [[Magic]]
| | 100/99, 225/224, 245/243
| 100/99, 225/224, 245/243
|-
|-
| | 121/120
| 121/120
| | [[99edo|99edo]]
| [[99edo]]
| | [[Hitchcock|hitchcock]]
| [[Hitchcock]]
| | 121/120, 176/175, 2200/2187
| 121/120, 176/175, 2200/2187
|-
|-
| | 121/120
| 121/120
| | [[99edo|99edo]]
| [[99edo]]
| | [[Würschmidt_family#Hemiwürschmidt|hemiwur]]
| [[Würschmidt family#Hemiwürschmidt|hemiwur]]
| | 121/120, 176/175, 1375/1372
| 121/120, 176/175, 1375/1372
|-
|-
| | 176/175
| 176/175
| | [[111edo|111edo]]
| [[111edo]]
| | [[Semisept|semisept]]
| [[Semisept]]
| | 176/175, 540/539, 1331/1323
| 176/175, 540/539, 1331/1323
|-
|-
| | 896/891
| 896/891
| | [[208edo|208edo]]
| [[208edo]]
| | [[Kleismic_family#Metakleismic|metakleismic]]
| [[Kleismic family#Metakleismic|metakleismic]]
| | 896/891, 2200/2187, 14700/14641
| 896/891, 2200/2187, 14700/14641
|-
|-
| | 65536/65219
| 65536/65219
| | [[282edo|282edo]]
| [[282edo]]
| | [[Porwell_temperaments#Septisuperfourth|septisuperfourth]]
| [[Porwell temperaments#Septisuperfourth|septisuperfourth]]
| | 540/539, 4000/3993, 5632/5625
| 540/539, 4000/3993, 5632/5625
|-
|-
| | 243/242
| 243/242
| | [[202edo|202edo]]
| [[202edo]]
| | [[Harry|harry]]
| [[Harry]]
| | 243/242, 441/440, 4000/3993
| 243/242, 441/440, 4000/3993
|-
|-
| | 243/242
| 243/242
| | [[202edo|202edo]]
| [[202edo]]
| | [[Breedsmic_temperaments#Tertiaseptal|tertiaseptal]]
| [[Breedsmic temperaments#Tertiaseptal|tertiaseptal]]
| | 243/242, 441/440, 65625/65536
| 243/242, 441/440, 65625/65536
|-
|-
| | 3388/3375
| 3388/3375
| | [[316edo|316edo]]
| [[316edo]]
| | [[Ragismic_microtemperaments#Semiparakleismic|semiparakleismic]]
| [[Ragismic microtemperaments#Semiparakleismic|semiparakleismic]]
| | 3025/3024, 3136/3125, 4375/4374
| 3025/3024, 3136/3125, 4375/4374
|-
|-
| | 385/384
| 385/384
| | [[284edo|284edo]]
| [[284edo]]
| | [[Quadritikleismic|quadritikleismic]]
| [[Quadritikleismic]]
| | 385/384, 1375/1372, 6250/6237
| 385/384, 1375/1372, 6250/6237
|-
|-
| | 441/400
| 441/400
| | [[320edo|320edo]]
| [[320edo]]
| | [[Octowerck|octowerck]]
| [[Octowerck]]
| | 441/440, 8019/8000, 41503/41472
| 441/440, 8019/8000, 41503/41472
|-
|-
| | 540/539
| 540/539
| | [[578edo|578edo]]
| [[578edo]]
| | [[Schismatic_family#Pogo|pogo]]
| [[Schismatic family#Pogo|pogo]]
| | 540/539, 4000/3993, 32805/32768
| 540/539, 4000/3993, 32805/32768
|-
|-
| | 4000/3993
| 4000/3993
| | [[665edo|665edo]]
| [[665edo]]
| | [[Ragismic_microtemperaments#Brahmagupta|brahmagupta]]
| [[Ragismic microtemperaments#Brahmagupta|brahmagupta]]
| | 4000/3993, 4375/4374, 131072/130977
| 4000/3993, 4375/4374, 131072/130977
|-
|-
| | 5632/5625
| 5632/5625
| | [[1092edo|1092edo]]
| [[1092edo]]
| | [[Landscape_microtemperaments#Sextile|sextile]]
| [[Landscape microtemperaments#Sextile|sextile]]
| | 5632/5625, 9801/9800, 151263/151250
| 5632/5625, 9801/9800, 151263/151250
|-
|-
| | 3025/3024
| 3025/3024
| | [[2554edo|2554edo]]
| [[2554edo]]
| | [[Ragismic_microtemperaments#Supermajor-Semisupermajor|semisupermajor]]
| [[Ragismic microtemperaments#Supermajor-Semisupermajor|semisupermajor]]
| | 3025/3024, 4375/4374, 35156250/35153041
| 3025/3024, 4375/4374, 35156250/35153041
|}
|}


Line 280: Line 280:
{| class="wikitable"
{| class="wikitable"
|-
|-
| | Comma
| Comma
| | OPV
| OPV
| | Temperament
| Temperament
| | Basis
| Basis
|-
|-
| | 26/25
| 26/25
| | [[12edo|12edo]]
| [[12edo]]
| | [[Augmented_family#August|augustus]]
| [[Augmented family#August|augustus]]
| | 26/25, 36/35, 45/44, 56/55
| 26/25, 36/35, 45/44, 56/55
|-
|-
| | 27/26
| 27/26
| | [[35edo|35edo]]
| [[35edo]]
| | [[Avicennmic_temperaments#Secund|secund]]
| [[Avicennmic temperaments#Secund|secund]]
| | 27/26, 45/44, 99/98, 385/384
| 27/26, 45/44, 99/98, 385/384
|-
|-
| | 27/26
| 27/26
| | [[35edo|35edo]]
| [[35edo]]
| | [[Greenwoodmic_temperaments#Greenwood|greenwood]]
| [[Greenwoodmic temperaments#Greenwood|greenwood]]
| | 27/26, 45/44, 99/98, 640/637
| 27/26, 45/44, 99/98, 640/637
|-
|-
| | 40/39
| 40/39
| | [[15edo|15edo]]
| [[15edo]]
| | [[Archytas_clan#Blacksmith|blacksmith]]
| [[Archytas clan#Blacksmith|blacksmith]]
| | 28/27, 40/39, 49/48, 55/54
| 28/27, 40/39, 49/48, 55/54
|-
|-
| | 65/64
| 65/64
| | [[29edo|29edo]]
| [[29edo]]
| | [[Marvel_temperaments#Negril|negril]]
| [[Marvel temperaments#Negril|negril]]
| | 49/48, 65/64, 91/90, 875/858
| 49/48, 65/64, 91/90, 875/858
|-
|-
| | 65/64
| 65/64
| | [[29edo|29edo]]
| [[29edo]]
| | [[Porcupine_family#Coendou|coendou]]
| [[Porcupine family#Coendou|coendou]]
| | 55/54, 65/64, 100/99, 105/104
| 55/54, 65/64, 100/99, 105/104
|-
|-
| | 66/65
| 66/65
| | [[31edo|31edo]]
| [[31edo]]
| | [[Semicomma_family#Winston|winston]]
| [[Semicomma family#Winston|winston]]
| | 66/65, 99/98, 105/104, 121/120
| 66/65, 99/98, 105/104, 121/120
|-
|-
| | 66/65
| 66/65
| | [[31edo|31edo]]
| [[31edo]]
| | [[Meantone_family#Mohajira-13-limit|mohajira]]
| [[Meantone family#Mohajira-13-limit|mohajira]]
| | 66/65, 81/80, 105/104, 121/120
| 66/65, 81/80, 105/104, 121/120
|-
|-
| | 66/65
| 66/65
| | [[31edo|31edo]]
| [[31edo]]
| | [[Meantone_family#Squares-13-limit|squares]]
| [[Meantone family#Squares-13-limit|squares]]
| | 66/65, 81/80, 99/98, 121/120
| 66/65, 81/80, 99/98, 121/120
|-
|-
| | 78/77
| 78/77
| | [[43edo|43edo]]
| [[43edo]]
| | [[Marvel_temperaments#Amavil|amavil]]
| [[Marvel temperaments#Amavil|amavil]]
| | 78/77, 99/98, 144/143, 176/175
| 78/77, 99/98, 144/143, 176/175
|-
|-
| | 78/77
| 78/77
| | [[43edo|43edo]]
| [[43edo]]
| | [[Meantone_family#Jerome|jerome]]
| [[Meantone family#Jerome|jerome]]
| | 78/77, 81/80, 99/98, 144/143
| 78/77, 81/80, 99/98, 144/143
|-
|-
| | 91/90
| 91/90
| | [[102edo|102edo]]
| [[102edo]]
| | [[Diaschismic_family#Echidnic|echidnic]]
| [[Diaschismic family#Echidnic|echidnic]]
| | 91/90, 169/168, 385/384, 441/440
| 91/90, 169/168, 385/384, 441/440
|-
|-
| | 105/104
| 105/104
| | [[91edo|91edo]]
| [[91edo]]
| | [[Marvel_temperaments#Septimin|septimin]]
| [[Marvel temperaments#Septimin|septimin]]
| | 105/104, 144/143, 196/195, 245/242
| 105/104, 144/143, 196/195, 245/242
|-
|-
| | 275/273
| 275/273
| | [[94edo|94edo]]
| [[94edo]]
| | [[Schismatic_family#Garibaldi|garibaldi]]
| [[Schismatic family#Garibaldi|garibaldi]]
| | 225/224, 275/273, 325/324, 385/384
| 225/224, 275/273, 325/324, 385/384
|-
|-
| | 144/143
| 144/143
| | [[84edo|84edo]]
| [[84edo]]
| | [[Marvel_temperaments#Merman|merman]]
| [[Marvel temperaments#Merman|merman]]
| | 144/143, 225/224, 364/363, 441/440
| 144/143, 225/224, 364/363, 441/440
|-
|-
| | 144/143
| 144/143
| | [[84edo|84edo]]
| [[84edo]]
| | [[Orwellismic_temperaments|secant]]
| [[Orwellismic temperaments|secant]]
| | 144/143, 351/350, 364/363, 441/440
| 144/143, 351/350, 364/363, 441/440
|-
|-
| | 169/168
| 169/168
| | [[152edo|152edo]]
| [[152edo]]
| | [[Ragismic_microtemperaments#Octoid-Octopus|octopus]]
| [[Ragismic microtemperaments#Octoid-Octopus|octopus]]
| | 169/168, 325/324, 364/363, 540/539
| 169/168, 325/324, 364/363, 540/539
|-
|-
| | 196/195
| 196/195
| | [[232edo|232edo]]
| [[232edo]]
| | [[Hemifamity_temperaments#Mystery|mystery]]
| [[Hemifamity temperaments#Mystery|mystery]]
| | 196/195, 352/351, 364/363, 676/675
| 196/195, 352/351, 364/363, 676/675
|-
|-
| | 640/637
| 640/637
| | [[205edo|205edo]]
| [[205edo]]
| | [[Hemifamity_temperaments#Quanic|quanic]]
| [[Hemifamity temperaments#Quanic|quanic]]
| | 352/351, 540/539, 729/728, 1331/1323
| 352/351, 540/539, 729/728, 1331/1323
|-
|-
| | 1188/1183
| 1188/1183
| | [[255edo|255edo]]
| [[255edo]]
| | [[Mirkwai_clan#Subsemifourth|subsemifourth]]
| [[Mirkwai clan#Subsemifourth|subsemifourth]]
| | 540/539, 847/845, 1375/1372, 1575/1573
| 540/539, 847/845, 1375/1372, 1575/1573
|-
|-
| | 325/324
| 325/324
| | [[333edo|333edo]]
| [[333edo]]
| | [[Kleismic_family#Novemkleismic|novemkleismic]]
| [[Kleismic family#Novemkleismic|novemkleismic]]
| | 325/324, 625/624, 1375/1372, 4000/3993
| 325/324, 625/624, 1375/1372, 4000/3993
|-
|-
| | 351/350
| 351/350
| | [[546edo|546edo]]
| [[546edo]]
| | [[11-limit_comma_temperaments#Fermionic|fermionic]]
| [[11-limit comma temperaments#Fermionic|fermionic]]
| | 351/350, 540/539, 40656/40625, 142884/142805
| 351/350, 540/539, 40656/40625, 142884/142805
|-
|-
| | 352/351
| 352/351
| | [[198edo|198edo]]
| [[198edo]]
| | [[Breedsmic_temperaments#Semihemi|semihemi]]
| [[Breedsmic temperaments#Semihemi|semihemi]]
| | 352/351, 676/675, 847/845, 1716/1715
| 352/351, 676/675, 847/845, 1716/1715
|-
|-
| | 352/351
| 352/351
| | [[198edo|198edo]]
| [[198edo]]
| | [[Misty_family#Hemimist|hemimist]]
| [[Misty family#Hemimist|hemimist]]
| | 352/351, 676/675, 847/845, 3025/3024
| 352/351, 676/675, 847/845, 3025/3024
|-
|-
| | 847/845
| 847/845
| | [[388edo|388edo]]
| [[388edo]]
| | [[Ragismic_microtemperaments#Neusec-13-limit|neusec]]
| [[Ragismic microtemperaments#Neusec-13-limit|neusec]]
| | 847/845, 1001/1000, 3025/3024, 4375/4374
| 847/845, 1001/1000, 3025/3024, 4375/4374
|-
|-
| | 676/675
| 676/675
| | [[940edo|940edo]]
| [[940edo]]
| | [[Breedsmic_temperaments#Decoid|decoid]]
| [[Breedsmic temperaments#Decoid|decoid]]
| | 676/675, 1001/1000, 1716/1715, 4225/4224
| 676/675, 1001/1000, 1716/1715, 4225/4224
|-
|-
| | 2200/2197
| 2200/2197
| | [[836edo|836edo]]
| [[836edo]]
| | [[Ragismic_microtemperaments#Quasithird-13-limit|quasithird]]
| [[Ragismic microtemperaments#Quasithird-13-limit|quasithird]]
| | 2200/2197, 3025/3024, 4375/4374, 468512/468195
| 2200/2197, 3025/3024, 4375/4374, 468512/468195
|}
|}
[[Category:Rank-2]]
[[Category:Temperament]]
Retrieved from "https://en.xen.wiki/w/Associated_temperament"