Hemimage temperaments: Difference between revisions

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 {{Technical data page}}
-This is a collection of [[rank-2 temperament|rank-2]] [[temperament]]s [[tempering out]] the [[hemimage comma]] ({{monzo|legend=1| 5 -7 -1 3 }}, [[ratio]]: 10976/10935). These include chromat, degrees, bicommatic, bisupermajor, and squarschmidt, considered below, as well as the following discussed elsewhere:
+This is a collection of [[rank-2 temperament|rank-2]] [[temperament]]s [[tempering out]] the [[hemimage comma]] ({{monzo|legend=1| 5 -7 -1 3 }}, [[ratio]]: 10976/10935).
+Temperaments discussed elsewhere are:
 * ''[[Quasisuper]]'' (+64/63) → [[Archytas clan #Quasisuper|Archytas clan]]
 * ''[[Liese]]'' (+81/80) → [[Meantone family #Liese|Meantone family]]
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 * ''[[Cotoneum]]'' (+33554432/33480783) → [[Garischismic clan #Cotoneum|Garischismic clan]]
 * ''[[Yarman I]]'' (+244140625/243045684) → [[Quartonic family]]
+Considered below are chromat, degrees, bicommatic, bisupermajor, squarschmidt, and leapmonth, in the order of increasing [[badness]].
 == Chromat ==
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 Badness (Sintel): 1.26
+== Leapmonth ==
+Leapmonth may be described as the {{nowrap| 63 & 80 }} temperament, generated by a [[3/2|perfect fifth]] and being a strong extension of [[leapfrog]]. It was named by [[Flora Canou]] in 2025 following the pattern demonstrated by ''leapday'' and ''leapweek'', the two simpler extensions of leapfrog.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 10976/10935, 51200/50421
+{{Mapping|legend=1| 1 0 -58 -21 | 0 1 38 15 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1198.8005{{c}}, ~3/2 = 704.2543{{c}}
+: [[error map]]: {{val| -1.200 +1.100 -0.659 +2.186 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.9318{{c}}
+: error map: {{val| 0.000 +2.977 +1.093 +5.150 }}
+{{Optimal ET sequence|legend=1| 17c, 46c, 63, 80, 223bd, 303bdd, 383bcddd }}
+[[Badness]] (Sintel): 4.79
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 540/539, 896/891, 1331/1323
+Mapping: {{mapping| 1 0 -58 -21 -14 | 0 1 38 15 11 }}
+Optimal tunings:
+* WE: ~2 = 1198.8679{{c}}, ~3/2 = 704.2911{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.9318{{c}}
+{{Optimal ET sequence|legend=0| 17c, 46c, 63, 80, 223bde, 303bdde }}
+Badness (Sintel): 1.88
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 169/168, 352/351, 364/363, 540/539
+Mapping: {{mapping| 1 0 -58 -21 -14 -1 | 0 1 38 15 11 8 }}
+Optimal tunings:
+* WE: ~2 = 1199.1781{{c}}, ~3/2 = 704.4551{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.9218{{c}}
+{{Optimal ET sequence|legend=0| 17c, 46c, 63, 80, 143d }}
+Badness (Sintel): 1.53
 [[Category:Temperament collections]]
 [[Category:Hemimage temperaments| ]] <!-- main article -->
 [[Category:Rank 2]]