Aberschismic temperaments: Difference between revisions

+ more known naming history
+ abergravity
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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]]
* ''[[Monkey]]'' (+875/864) → [[Tetracot family #Monkey|Tetracot 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]]
* [[Misty]] (+3136/3125) → [[Misty family #Misty|Misty family]]
* ''[[Supers]]'' (+118098/117649) → [[Stearnsmic clan #Supers|Stearnsmic 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, 561/560
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


=== 19-limit ===
=== 2.3.5.7.11.13.17.23 subgroup ===
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.23


Comma list: 190/189, 209/208, 289/288, 352/351, 385/384, 561/560
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 -12 }}
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 = 600.1639{{c}}, ~66/65 = 25.6669{{c}}
* WE: ~17/12 = 600.1139{{c}}, ~66/65 = 25.7053{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~66/65 = 25.6597{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~66/65 = 25.7013{{c}}


{{Optimal ET sequence|legend=0| 46, 94, 140h }}
{{Optimal ET sequence|legend=0| 46, 94, 140 }}
 
Badness (Sintel): 1.11
 
=== 23-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23
 
Comma list: 190/189, 209/208, 253/252, 289/288, 323/322, 352/351, 385/384
 
Mapping: {{mapping| 2 3 4 6 7 8 8 9 9 | 0 4 15 -9 -2 -14 4 -12 1 }}
 
Optimal tunings:
* WE: ~17/12 = 600.1777{{c}}, ~66/65 = 25.6682{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~66/65 = 25.6605{{c}}


{{Optimal ET sequence|legend=0| 46, 94, 140h }}
Badness (Sintel): 0.772
 
Badness (Sintel): 1.00


== Undecental ==
== Undecental ==
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Badness (Sintel): 0.910
Badness (Sintel): 0.910


==== 19-limit ====
=== 2.3.5.7.11.13.17.23 subgroup ===
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.23


Comma list: 91/90, 121/120, 133/132, 136/135, 154/153, 169/168
Comma list: 91/90, 121/120, 136/135, 154/153, 161/160, 169/168


Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 9 | 0 1 21 15 11 8 24 -3 }}
Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 -5 | 0 1 21 15 11 8 24 6 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1201.0192{{c}}, ~3/2 = 704.7333{{c}}
* WE: ~2 = 1200.5169{{c}}, ~3/2 = 704.5279{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.1680{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2450{{c}}


{{Optimal ET sequence|legend=0| 17cg, 29g, 46, 75dfgh, 121defgh }}
{{Optimal ET sequence|legend=0| 17cg, 29g, 46, 121defg }}
 
Badness (Sintel): 1.06
 
===== 23-limit =====
Subgroup: 2.3.5.7.11.13.17.19.23
 
Comma list: 91/90, 121/120, 133/132, 136/135, 154/153, 161/160, 169/168
 
Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 9 -5 | 0 1 21 15 11 8 24 -3 6 }}
 
Optimal tunings:
* WE: ~2 = 1200.9738{{c}}, ~3/2 = 704.7120{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.1695{{c}}
 
{{Optimal ET sequence|legend=0| 17cg, 29g, 46, 75dfgh, 121defgh }}
 
Badness (Sintel): 1.01
 
==== Leapling ====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 77/76, 91/90, 121/120, 136/135, 153/152, 169/168
 
Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 -37 | 0 1 21 15 11 8 24 26 }}
 
Optimal tunings:
* WE: ~2 = 1200.4745{{c}}, ~3/2 = 704.4016{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.1442{{c}}
 
{{Optimal ET sequence|legend=0| 17cgh, 29g, 46h, 75dfg }}
 
Badness (Sintel): 1.16
 
===== 23-limit =====
Subgroup: 2.3.5.7.11.13.17.19.23
 
Comma list: 77/76, 91/90, 115/114, 121/120, 136/135, 153/152, 161/160
 
Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 -37 -5 | 0 1 21 15 11 8 24 26 6 }}
 
Optimal tunings:
* WE: ~2 = 1200.5425{{c}}, ~3/2 = 704.4319{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.1349{{c}}
 
{{Optimal ET sequence|legend=0| 17cgh, 29g, 46h, 75dfg }}


Badness (Sintel): 1.15
Badness (Sintel): 0.872


== Mystery ==
== Mystery ==