Aberschismic temperaments: Difference between revisions
Move kwai back cuz mirkwai clan is a no-2 clan, which doesn't explain its structure very well |
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* [[Rodan]] (+245/243) → [[Gamelismic clan #Rodan|Gamelismic clan]] | * [[Rodan]] (+245/243) → [[Gamelismic clan #Rodan|Gamelismic clan]] | ||
* ''[[Alphatrimot]]'' (+2430/2401) → [[Alphatricot family #Alphatrimot|Alphatricot family]] | * ''[[Alphatrimot]]'' (+2430/2401) → [[Alphatricot family #Alphatrimot|Alphatricot family]] | ||
* | * [[Misty]] (+3136/3125) → [[Misty family #Misty|Misty family]] | ||
* [[Monkey]] (+875/864) → [[Tetracot family #Monkey|Tetracot family]] | |||
* [[Buzzard]] (+1728/1715) → [[Buzzardsmic clan #Buzzard|Buzzardsmic clan]] | * [[Buzzard]] (+1728/1715) → [[Buzzardsmic clan #Buzzard|Buzzardsmic clan]] | ||
* ''[[Undim]]'' (+390625/388962) → [[Undim family #Septimal undim|Undim family]] | * ''[[Undim]]'' (+390625/388962) → [[Undim family #Septimal undim|Undim family]] | ||
* ''[[Quinticosiennic]]'' (+395136/390625) → [[Quintaleap family #Quinticosiennic|Quintaleap family]] | * ''[[Quinticosiennic]]'' (+395136/390625) → [[Quintaleap family #Quinticosiennic|Quintaleap family]] | ||
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* [[Amity]] (+4375/4374) → [[Amity family #Septimal amity|Amity family]] | * [[Amity]] (+4375/4374) → [[Amity family #Septimal amity|Amity family]] | ||
* ''[[Countercata]]'' (+15625/15552) → [[Kleismic family #Countercata|Kleismic family]] | * ''[[Countercata]]'' (+15625/15552) → [[Kleismic family #Countercata|Kleismic family]] | ||
* ''[[Abergravity]]'' (+177147/175000) → [[Gravity family #Abergravity|Gravity family]] | |||
* ''[[Supers]]'' (+118098/117649) → [[Stearnsmic clan #Supers|Stearnsmic clan]] | |||
* ''[[Warrior]]'' (+78732/78125) → [[Sensipent family #Warrior|Sensipent family]] | * ''[[Warrior]]'' (+78732/78125) → [[Sensipent family #Warrior|Sensipent family]] | ||
* ''[[Alphaquarter]]'' (+29360128/29296875) → [[Escapade family #Alphaquarter|Escapade family]] | * ''[[Alphaquarter]]'' (+29360128/29296875) → [[Escapade family #Alphaquarter|Escapade family]] | ||
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== Ketchup == | == Ketchup == | ||
Ketchup may be described as the {{nowrap| 46 & 94 }} temperament. It has a semi-octave period and a generator for a syntonic~septimal comma, four of which plus a period gives the perfect fifth; its ploidacot is diploid gamma-tetracot. [[140edo]] is an obvious tuning for this temperament. | Ketchup may be described as the {{nowrap| 46 & 94 }} temperament. It has a semi-octave period and a generator for a syntonic~septimal comma, four of which plus a period gives the perfect fifth; its [[ploidacot]] is diploid gamma-tetracot. [[140edo]] is an obvious tuning for this temperament. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
Comma list: 289/288, 325/324, 352/351, 385/384, | Comma list: 289/288, 325/324, 352/351, 385/384, 442/441 | ||
Mapping: {{mapping| 2 3 4 6 7 8 8 | 0 4 15 -9 -2 -14 4 }} | Mapping: {{mapping| 2 3 4 6 7 8 8 | 0 4 15 -9 -2 -14 4 }} | ||
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Badness (Sintel): 0.845 | Badness (Sintel): 0.845 | ||
=== | === 2.3.5.7.11.13.17.23 subgroup === | ||
Subgroup: 2.3.5.7.11.13.17. | Subgroup: 2.3.5.7.11.13.17.23 | ||
Comma list: | Comma list: 253/252, 289/288, 325/324, 352/351, 385/384, 391/390 | ||
Mapping: {{mapping| 2 3 4 6 7 8 8 9 | 0 4 15 -9 -2 -14 4 | Mapping: {{mapping| 2 3 4 6 7 8 8 9 | 0 4 15 -9 -2 -14 4 1 }} | ||
Optimal tunings: | Optimal tunings: | ||
* WE: ~17/12 = 600. | * WE: ~17/12 = 600.1139{{c}}, ~66/65 = 25.7053{{c}} | ||
* CWE: ~17/12 = 600.0000{{c}}, ~66/65 = 25. | * CWE: ~17/12 = 600.0000{{c}}, ~66/65 = 25.7013{{c}} | ||
{{Optimal ET sequence|legend=0| 46, 94, | {{Optimal ET sequence|legend=0| 46, 94, 140 }} | ||
Badness (Sintel): 0.772 | |||
Badness (Sintel): | |||
== Undecental == | == Undecental == | ||
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Badness (Sintel): 0.910 | Badness (Sintel): 0.910 | ||
=== | === 2.3.5.7.11.13.17.23 subgroup === | ||
Subgroup: 2.3.5.7.11.13.17. | Subgroup: 2.3.5.7.11.13.17.23 | ||
Comma list: 91/90, 121/120 | Comma list: 91/90, 121/120, 136/135, 154/153, 161/160, 169/168 | ||
Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 | Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 -5 | 0 1 21 15 11 8 24 6 }} | ||
Optimal tunings: | Optimal tunings: | ||
* WE: ~2 = | * WE: ~2 = 1200.5169{{c}}, ~3/2 = 704.5279{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704. | * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2450{{c}} | ||
{{Optimal ET sequence|legend=0| 17cg, 29g, 46, | {{Optimal ET sequence|legend=0| 17cg, 29g, 46, 121defg }} | ||
Badness (Sintel): 0.872 | |||
Badness (Sintel): | |||
== Mystery == | == Mystery == | ||
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== Hemidromeda == | == Hemidromeda == | ||
Hemidromeda may be described as the {{nowrap| 29 & 111 }} temperament. | Hemidromeda may be described as the {{nowrap| 29 & 111 }} temperament. Named by [[Xenllium]] in 2023, ''hemidromeda'' comes from ''hemi-'' (Ancient Greek for "one half") and ''[[andromeda]]'', because the generator is 1/2 of andromeda's perfect twelfth (~3/1, about 1902.4 cents); the ploidacot for this temperament is alpha-dicot. | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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Countriton may be described as the {{nowrap| 51c & 53 }} temperament. It splits the [[24/1|24th harmonic]] into nine tritone generators; its ploidacot is thus delta-enneacot. Among the possible tunings are [[157edo]] and [[210edo]], as well as [[104edo]] in the 104c val. | Countriton may be described as the {{nowrap| 51c & 53 }} temperament. It splits the [[24/1|24th harmonic]] into nine tritone generators; its ploidacot is thus delta-enneacot. Among the possible tunings are [[157edo]] and [[210edo]], as well as [[104edo]] in the 104c val. | ||
Countriton was named by [[Xenllium]] in 2022 as a counterpart of [[untriton]]. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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== Artoneutral == | == Artoneutral == | ||
Artoneutral can be described as the {{nowrap| 87 & 94 }} temperament. It is generated by an artoneutral third of ~11/9 (or a tendoneutral sixth of ~18/11), nine of which make the [[12/1|12th harmonic]]; its ploidacot is thus beta-enneacot. [[181edo]] may be recommended as a tuning. | Artoneutral can be described as the {{nowrap| 87 & 94 }} temperament. It is generated by an artoneutral third of ~11/9 (or a tendoneutral sixth of ~18/11), nine of which make the [[12/1|12th harmonic]]; its ploidacot is thus beta-enneacot. [[181edo]] may be recommended as a tuning. | ||
Artoneutral was named by [[Flora Canou]] in 2023 for its generator's quality. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||