Aberschismic temperaments: Difference between revisions

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 * [[Dominant (temperament)|Dominant]] (+36/35) → [[Meantone family #Dominant|Meantone family]]
 * [[Garibaldi]] (+225/224) → [[Schismatic family #Garibaldi|Schismatic family]]
+* [[Leapday]] (+686/675) → [[Sengic temperaments #Leapday|Sengic temperaments]]
 * [[Diaschismic]] (+126/125) → [[Diaschismic family #Septimal diaschismic|Diaschismic family]]
 * [[Hemififths]] (+2401/2400) → [[Breedsmic temperaments #Hemififths|Breedsmic temperaments]]
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 [[Badness]] (Sintel): 2.39
-== Leapday ==
-{{Main| Leapday }}
-: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Leapday]].''
-Leapday tempers out [[686/675]], the senga, in addition to the aberschisma, and may be described as the {{nowrap| 29 & 46 }} temperament. It extends [[leapfrog]], such that [[7/4]] is found by 15 generators up, as a double-augmented fifth (a major sixth and a diesis). 5/4 is found by a tritone above that, as a triple-augmented unison (a minor third and two dieses). [[46edo]] itself is an excellent tuning for this.
-Leapday is more notable in the higher limits than the lower, as it nails the 13-limit pretty well from identifying [[14/11]] by a major third and [[13/11]] by a minor third, tempering out not only [[352/351]] and [[364/363]] but [[91/90]], [[121/120]], [[169/168]] and [[196/195]]. It can be further extended to include the [[17/1|17th]] and [[23/1|23rd]] [[harmonic]]s. Adding 17 would fix the valid diamond monotone tuning to 46edo, however.
-Leapday has an alternative extension called [[porwell temperaments #Polypyth|polypyth]], which tempers out the same 5-limit comma as leapday, but with the porwell comma ([[6144/6125]]) rather than the aberschisma tempered out.
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 686/675, 5120/5103
-{{Mapping|legend=1| 1 0 -31 -21 | 0 1 21 15 }}
-: mapping generators: ~2, ~3
-[[Optimal tuning]]s:
-* [[WE]]: ~2 = 1199.7167{{c}}, ~3/2 = 704.0971{{c}}
-: [[error map]]: {{val| -0.283 +1.859 +2.559 -5.669 }}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.2504{{c}}
-: error map: {{val| 0.000 +2.295 +2.945 -5.070 }}
-{{Optimal ET sequence|legend=1| 17c, 29, 46 }}
-[[Badness]] (Sintel): 2.43
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 121/120, 441/440, 686/675
-Mapping: {{mapping| 1 0 -31 -21 -14 | 0 1 21 15 11 }}
-Optimal tunings:
-* WE: ~2 = 1200.0731{{c}}, ~3/2 = 704.2933{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2538{{c}}
-{{Optimal ET sequence|legend=0| 17c, 29, 46 }}
-Badness (Sintel): 1.28
-=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 91/90, 121/120, 169/168, 352/351
-Mapping: {{mapping| 1 0 -31 -21 -14 -9 | 0 1 21 15 11 8 }}
-Optimal tunings:
-* WE: ~2 = 1200.4758{{c}}, ~3/2 = 704.4930{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2346{{c}}
-{{Optimal ET sequence|legend=0| 17c, 29, 46, 121def }}
-Badness (Sintel): 1.02
-=== 17-limit ===
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 91/90, 121/120, 136/135, 154/153, 169/168
-Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 | 0 1 21 15 11 8 24 }}
-Optimal tunings:
-* WE: ~2 = 1200.4818{{c}}, ~3/2 = 704.5121{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2507{{c}}
-{{Optimal ET sequence|legend=0| 17cg, 29g, 46, 121defg }}
-Badness (Sintel): 0.910
-=== 2.3.5.7.11.13.17.23 subgroup ===
-Subgroup: 2.3.5.7.11.13.17.23
-Comma list: 91/90, 121/120, 136/135, 154/153, 161/160, 169/168
-Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 -5 | 0 1 21 15 11 8 24 6 }}
-Optimal tunings:
-* WE: ~2 = 1200.5169{{c}}, ~3/2 = 704.5279{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2450{{c}}
-{{Optimal ET sequence|legend=0| 17cg, 29g, 46, 121defg }}
-Badness (Sintel): 0.872
 == Mystery ==