@@ Line 9: / Line 9: @@
 * [[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]]
@@ Line 26: / Line 27: @@
 * ''[[Alphaquarter]]'' (+29360128/29296875) → [[Escapade family #Alphaquarter|Escapade family]]
-Considered below are septiquarter, kwai, ketchup, undecental, leapday, mystery, hemidromeda, countriton, artoneutral, quanic and jorgensen, in the order of increasing [[TE logflat badness]].
+Considered below are septiquarter, kwai, ketchup, undecental, mystery, hemidromeda, countriton, artoneutral, quanic and jorgensen, in the order of increasing [[TE logflat badness]].
 == Septiquarter ==
@@ Line 53: / Line 54: @@
 Comma list: 5120/5103, 9801/9800, 14641/14580
-Mapping: {{mapping| 2 -8 -56 12 -25 | 0 7 38 -4 20 }}
+{{Mapping|legend=0| 2 -8 -56 12 -25 | 0 7 38 -4 20 }}
 Optimal tunings:
@@ Line 68: / Line 69: @@
 Comma list: 352/351, 847/845, 1716/1715, 14641/14580
-Mapping: {{mapping| 2 -8 -56 12 -25 9 | 0 7 38 -4 20 -1 }}
+{{Mapping|legend=0| 2 -8 -56 12 -25 9 | 0 7 38 -4 20 -1 }}
 Optimal tunings:
@@ Line 105: / Line 106: @@
 Comma list: 540/539, 1375/1372, 5120/5103
-Mapping: {{mapping| 1 0 -50 -40 32 | 0 1 33 27 -18 }}
+{{Mapping|legend=0| 1 0 -50 -40 32 | 0 1 33 27 -18 }}
 Optimal tunings:
@@ Line 120: / Line 121: @@
 Comma list: 352/351, 540/539, 729/728, 1375/1372
-Mapping: {{mapping| 1 0 -50 -40 32 27 | 0 1 33 27 -18 -21 }}
+{{Mapping|legend=0| 1 0 -50 -40 32 27 | 0 1 33 27 -18 -21 }}
 Optimal tunings:
@@ Line 135: / Line 136: @@
 Comma list: 256/255, 352/351, 540/539, 715/714, 1089/1088
-Mapping: {{mapping| 1 0 -50 -40 32 27 58 | 0 1 33 27 -18 -21 -34 }}
+{{Mapping|legend=0| 1 0 -50 -40 32 27 58 | 0 1 33 27 -18 -21 -34 }}
 Optimal tunings:
@@ Line 150: / Line 151: @@
 Comma list: 256/255, 352/351, 400/399, 456/455, 715/714, 847/845
-Mapping: {{mapping| 1 0 -50 -40 32 27 58 -56 | 0 1 33 27 -18 -21 -34 38 }}
+{{Mapping|legend=0| 1 0 -50 -40 32 27 58 -56 | 0 1 33 27 -18 -21 -34 38 }}
 Optimal tunings:
@@ Line 165: / Line 166: @@
 Comma list: 540/539, 676/675, 1375/1372, 5120/5103
-Mapping: {{mapping| 1 0 -50 -40 32 -51 | 0 2 66 54 -36 69 }}
+{{Mapping|legend=0| 1 0 -50 -40 32 -51 | 0 2 66 54 -36 69 }}
 : mapping generators: ~2, ~26/15
@@ Line 181: / Line 182: @@
 Comma list: 442/441, 540/539, 676/675, 715/714, 5120/5103
-Mapping: {{mapping| 1 0 -50 -40 32 -51 -30 | 0 2 66 54 -36 69 43 }}
+{{Mapping|legend=0| 1 0 -50 -40 32 -51 -30 | 0 2 66 54 -36 69 43 }}
 Optimal tunings:
@@ Line 196: / Line 197: @@
 Comma list: 400/399, 442/441, 540/539, 676/675, 715/714, 1445/1444
-Mapping: {{mapping| 1 0 -50 -40 32 -51 -30 -56 | 0 2 66 54 -36 69 43 76 }}
+{{Mapping|legend=0| 1 0 -50 -40 32 -51 -30 -56 | 0 2 66 54 -36 69 43 76 }}
 Optimal tunings:
@@ Line 231: / Line 232: @@
 Comma list: 385/384, 1331/1323, 2200/2187
-Mapping: {{mapping| 2 3 4 6 7 | 0 4 15 -9 -2 }}
+{{Mapping|legend=0| 2 3 4 6 7 | 0 4 15 -9 -2 }}
 Optimal tunings:
@@ Line 246: / Line 247: @@
 Comma list: 325/324, 352/351, 385/384, 1331/1323
-Mapping: {{mapping| 2 3 4 6 7 8 | 0 4 15 -9 -2 -14 }}
+{{Mapping|legend=0| 2 3 4 6 7 8 | 0 4 15 -9 -2 -14 }}
 Optimal tunings:
@@ Line 261: / Line 262: @@
 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|legend=0| 2 3 4 6 7 8 8 | 0 4 15 -9 -2 -14 4 }}
 Optimal tunings:
@@ Line 276: / Line 277: @@
 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 1 }}
+{{Mapping|legend=0| 2 3 4 6 7 8 8 9 | 0 4 15 -9 -2 -14 4 1 }}
 Optimal tunings:
@@ Line 305: / Line 306: @@
 [[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 ==
@@ Line 421: / Line 335: @@
 Comma list: 441/440, 896/891, 3388/3375
-Mapping: {{mapping| 29 46 0 14 33 | 0 0 1 1 1 }}
+{{Mapping|legend=0| 29 46 0 14 33 | 0 0 1 1 1 }}
 Optimal tunings:
@@ Line 436: / Line 350: @@
 Comma list: 196/195, 352/351, 364/363, 676/675
-Mapping: {{mapping| 29 46 0 14 33 40 | 0 0 1 1 1 1 }}
+{{Mapping|legend=0| 29 46 0 14 33 40 | 0 0 1 1 1 1 }}
 Optimal tunings:
@@ Line 471: / Line 385: @@
 Comma list: 1331/1323, 1375/1372, 5120/5103
-Mapping: {{mapping| 1 0 38 48 32 | 0 2 -45 -57 -36 }}
+{{Mapping|legend=0| 1 0 38 48 32 | 0 2 -45 -57 -36 }}
 Optimal tunings:
@@ Line 486: / Line 400: @@
 Comma list: 352/351, 676/675, 847/845, 1331/1323
-Mapping: {{mapping| 1 0 38 48 32 37 | 0 2 -45 -57 -36 -42 }}
+{{Mapping|legend=0| 1 0 38 48 32 37 | 0 2 -45 -57 -36 -42 }}
 Optimal tunings:
@@ Line 501: / Line 415: @@
 Comma list: 352/351, 442/441, 561/560, 676/675, 715/714
-Mapping: {{mapping| 1 0 38 48 32 37 58 | 0 2 -45 -57 -36 -42 -68 }}
+{{Mapping|legend=0| 1 0 38 48 32 37 58 | 0 2 -45 -57 -36 -42 -68 }}
 Optimal tunings:
@@ Line 516: / Line 430: @@
 Comma list: 286/285, 352/351, 363/361, 442/441, 476/475, 561/560
-Mapping: {{mapping| 1 0 38 48 32 37 58 32 | 0 2 -45 -57 -36 -42 -68 -35 }}
+{{Mapping|legend=0| 1 0 38 48 32 37 58 32 | 0 2 -45 -57 -36 -42 -68 -35 }}
 Optimal tunings:
@@ Line 531: / Line 445: @@
 Comma list: 253/252, 286/285, 352/351, 363/361, 391/390, 442/441, 460/459
-Mapping: {{mapping| 1 0 38 48 32 37 58 32 18 | 0 2 -45 -57 -36 -42 -68 -35 -17 }}
+{{Mapping|legend=0| 1 0 38 48 32 37 58 32 18 | 0 2 -45 -57 -36 -42 -68 -35 -17 }}
 Optimal tunings:
@@ Line 570: / Line 484: @@
 Comma list: 176/175, 5120/5103, 41503/41472
-Mapping: {{mapping| 1 -3 -15 13 -21 | 0 9 34 -20 48 }}
+{{Mapping|legend=0| 1 -3 -15 13 -21 | 0 9 34 -20 48 }}
 Optimal tunings:
@@ Line 585: / Line 499: @@
 Comma list: 176/175, 351/350, 847/845, 2197/2187
-Mapping: {{mapping| 1 -3 -15 13 -21 -7 | 0 9 34 -20 48 21 }}
+{{Mapping|legend=0| 1 -3 -15 13 -21 -7 | 0 9 34 -20 48 21 }}
 Optimal tunings:
@@ Line 622: / Line 536: @@
 Comma list: 385/384, 2200/2187, 4000/3993
-Mapping: {{mapping| 1 -1 -4 12 -2 | 0 9 22 -32 19 }}
+{{Mapping|legend=0| 1 -1 -4 12 -2 | 0 9 22 -32 19 }}
 Optimal tunings:
@@ Line 637: / Line 551: @@
 Comma list: 325/324, 352/351, 385/384, 1575/1573
-Mapping: {{mapping| 1 -1 -4 12 -2 6 | 0 9 22 -32 19 -8 }}
+{{Mapping|legend=0| 1 -1 -4 12 -2 6 | 0 9 22 -32 19 -8 }}
 Optimal tunings:
@@ Line 652: / Line 566: @@
 Comma list: 325/324, 352/351, 375/374, 385/384, 595/594
-Mapping: {{mapping| 1 -1 -4 12 -2 6 -12 | 0 9 22 -32 19 -8 56 }}
+{{Mapping|legend=0| 1 -1 -4 12 -2 6 -12 | 0 9 22 -32 19 -8 56 }}
 Optimal tunings:
@@ Line 667: / Line 581: @@
 Comma list: 325/324, 352/351, 375/374, 385/384, 400/399, 595/594
-Mapping: {{mapping| 1 -1 -4 12 -2 6 -12 -15 | 0 9 22 -32 19 -8 56 67 }}
+{{Mapping|legend=0| 1 -1 -4 12 -2 6 -12 -15 | 0 9 22 -32 19 -8 56 67 }}
 Optimal tunings:
@@ Line 682: / Line 596: @@
 Comma list: 300/299, 325/324, 352/351, 375/374, 385/384, 400/399, 484/483
-Mapping: {{mapping| 1 -1 -4 12 -2 6 -12 -15 -13 | 0 9 22 -32 19 -8 56 67 61 }}
+{{Mapping|legend=0| 1 -1 -4 12 -2 6 -12 -15 -13 | 0 9 22 -32 19 -8 56 67 61 }}
 Optimal tunings:
@@ Line 717: / Line 631: @@
 Comma list: 540/539, 1331/1323, 5120/5103
-Mapping: {{mapping| 1 1 -4 0 1 | 0 5 54 24 21 }}
+{{Mapping|legend=0| 1 1 -4 0 1 | 0 5 54 24 21 }}
 Optimal tunings:
@@ Line 732: / Line 646: @@
 Comma list: 352/351, 540/539, 729/728, 1331/1323
-Mapping: {{mapping| 1 1 -4 0 1 3 | 0 5 54 24 21 6 }}
+{{Mapping|legend=0| 1 1 -4 0 1 3 | 0 5 54 24 21 6 }}
 Optimal tunings:
@@ Line 747: / Line 661: @@
 Comma list: 352/351, 442/441, 540/539, 715/714, 847/845
-Mapping: {{mapping| 1 1 -4 0 1 3 -2 | 0 5 54 24 21 6 52 }}
+{{Mapping|legend=0| 1 1 -4 0 1 3 -2 | 0 5 54 24 21 6 52 }}
 Optimal tunings:
@@ Line 762: / Line 676: @@
 Comma list: 352/351, 400/399, 442/441, 456/455, 495/494, 715/714
-Mapping: {{mapping| 1 1 -4 0 1 3 -2 -5 | 0 5 54 24 21 6 52 79 }}
+{{Mapping|legend=0| 1 1 -4 0 1 3 -2 -5 | 0 5 54 24 21 6 52 79 }}
 Optimal tunings:
@@ Line 798: / Line 712: @@
 == References ==
+[[Category:Aberschismic temperaments| ]] <!-- main article -->
+[[Category:Aberschismic| ]] <!-- key article -->
 [[Category:Temperament collections]]
-[[Category:Hemifamity temperaments| ]] <!-- main article -->
+[[Category:Catalogs of rank-2 temperaments]]
-[[Category:Rank 2]]

Aberschismic temperaments: Difference between revisions

FloraC (talk | contribs)