Meantone family: Difference between revisions

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@@ Line 2,154: / Line 2,154: @@
 </div></div>
-= Ptolemy =
+= Migration =
+Migration takes [[#septimal meantone]] mapping of 7 and [[#mohaha]] mapping of 11.
 Period: 1\1
-Optimal ([[POTE]]) generator: ~11/9 = 346.922
+Optimal ([[POTE]]) generator: ~11/9 = 348.182
-EDO generators: [[38edo|11\38]], [[45edo|13\45]]
+EDO generators: [[24edo|7\24]], [[31edo|9\31]]
 Scales (Scala files):
@@ Line 2,167: / Line 2,168: @@
 <div style="line-height:1.6;">Technical data</div>
 <div class="mw-collapsible-content">
-Comma list: 81/80, 121/120, 525/512
+Comma list: 81/80, 121/120, 126/125
+Mapping: [{{val| 1 1 0 -3 2 }}, {{val| 0 2 8 20 5 }}]
-Mapping: [{{val| 1 1 0 8 2 }}, {{val| 0 2 8 -18 5 }}]
+Mapping generators: ~2, ~11/9
-{{Vals|legend=1| 7, 31dd, 38d, 45e, 83bcddee }}
+{{Vals|legend=1| 7d, 31, 100de, 131bdee, 162bdee }}
-Badness: 0.0588
+Badness: 0.0255
 </div></div>
@@ Line 2,180: / Line 2,183: @@
 Period: 1\1
-Optimal ([[POTE]]) generator: ~11/9 = 346.910
+Optimal ([[POTE]]) generator: ~11/9 = 348.490
-EDO generators: [[38edo|11\38]], [[45edo|13\45]]
+EDO generators: [[24edo|7\24]], [[31edo|9\31]]
 Scales (Scala files):
@@ Line 2,189: / Line 2,192: @@
 <div style="line-height:1.6;">Technical data</div>
 <div class="mw-collapsible-content">
-Comma list: 65/64, 81/80, 105/104, 121/120
+Comma list: 66/65, 81/80, 121/120, 126/125
+Mapping: [{{val| 1 1 0 -3 2 4 }}, {{val| 0 2 8 20 5 -1 }}]
-Mapping: [{{val| 1 1 0 8 2 6 }}, {{val| 0 2 8 -18 5 -8 }}]
+Mapping generators: ~2, ~11/9
-{{Vals|legend=1| 7, 31ddf, 38df, 45ef, 83bcddeeff }}
+{{Vals|legend=1| 7d, 24d, 31, 55d }}
-Badness: 0.0343
+Badness: 0.0281
 </div></div>
-= Maqamic =
+= Ptolemy =
-<span style="display: block; text-align: right;">[[:de:maqamisch|Deutsch]]</span>
+Ptolemy takes [[#flattone]] mapping of 7 and [[#mohaha]] mapping of 11.
-{{main| Maqamic }}
-Maqamic temperament is much like Mohajira, except in that it 36/35 vanishes instead of 176/175. It makes the most sense if viewed as an adaptive temperament, whereby 7/4 and 9/5 simply share an equivalence class in the resulting scales, but don't need to share a particular tempered "middle-of-the-road" intonation.
 Period: 1\1
-Optimal ([[POTE]]) generator: ~11/9 = 350.934
+Optimal ([[POTE]]) generator: ~11/9 = 346.922
-EDO generators: [[7edo|2\7]], [[10edo|3\10]], [[17edo|5\17]], [[24edo|7\24]]
+EDO generators: [[38edo|11\38]], [[45edo|13\45]]
 Scales (Scala files):
@@ Line 2,216: / Line 2,217: @@
 <div style="line-height:1.6;">Technical data</div>
 <div class="mw-collapsible-content">
-[[Comma]] list: 81/80, 36/35, 121/120
+Comma list: 81/80, 121/120, 525/512
-Mapping: [{{val| 1 1 0 4 2 }}, {{val| 0 2 8 -4 5 }}]
+Mapping: [{{val| 1 1 0 8 2 }}, {{val| 0 2 8 -18 5 }}]
-Mapping generators: ~2, ~11/9
+{{Vals|legend=1| 7, 31dd, 38d, 45e, 83bcddee }}
-{{Vals|legend=1| 7, 10c, 17c, 24d, 31d }}
+Badness: 0.0588
 </div></div>
@@ Line 2,229: / Line 2,230: @@
 Period: 1\1
-Optimal ([[POTE]]) generator: ~11/9 = 350.816
+Optimal ([[POTE]]) generator: ~11/9 = 346.910
-EDO generators: [[7edo|2\7]], [[10edo|3\10]], [[17edo|5\17]], [[24edo|7\24]]
+EDO generators: [[38edo|11\38]], [[45edo|13\45]]
 Scales (Scala files):
@@ Line 2,238: / Line 2,239: @@
 <div style="line-height:1.6;">Technical data</div>
 <div class="mw-collapsible-content">
-[[Comma]] list: 81/80, 36/35, 121/120, 144/143
+Comma list: 65/64, 81/80, 105/104, 121/120
-Mapping: [{{val| 1 1 0 4 2 4 }}, {{val| 0 2 8 -4 5 -1 }}]
+Mapping: [{{val| 1 1 0 8 2 6 }}, {{val| 0 2 8 -18 5 -8 }}]
-Mapping generators: ~2, ~11/9
+{{Vals|legend=1| 7, 31ddf, 38df, 45ef, 83bcddeeff }}
-{{Vals|legend=1| 7, 10c, 17c, 24d, 31d }}
+Badness: 0.0343
 </div></div>
-= Migration =
+= Maqamic =
+<span style="display: block; text-align: right;">[[:de:maqamisch|Deutsch]]</span>
+{{main| Maqamic }}
+Maqamic takes [[#dominant]] mapping of 7 and [[#mohaha]] mapping of 11, so it is [[36/35]] that vanishes instead of [[176/175]] as in mohajira. It makes the most sense if viewed as an adaptive temperament, whereby 7/4 and 9/5 simply share an equivalence class in the resulting scales, but don't need to share a particular tempered "middle-of-the-road" intonation.
 Period: 1\1
-Optimal ([[POTE]]) generator: ~11/9 = 348.182
+Optimal ([[POTE]]) generator: ~11/9 = 350.934
-EDO generators: [[24edo|7\24]], [[31edo|9\31]]
+EDO generators: [[7edo|2\7]], [[10edo|3\10]], [[17edo|5\17]], [[24edo|7\24]]
 Scales (Scala files):
@@ Line 2,260: / Line 2,266: @@
 <div style="line-height:1.6;">Technical data</div>
 <div class="mw-collapsible-content">
-Comma list: 81/80, 121/120, 126/125
+[[Comma]] list: 81/80, 36/35, 121/120
-Mapping: [{{val| 1 1 0 -3 2 }}, {{val| 0 2 8 20 5 }}]
+Mapping: [{{val| 1 1 0 4 2 }}, {{val| 0 2 8 -4 5 }}]
 Mapping generators: ~2, ~11/9
-{{Vals|legend=1| 7d, 31, 100de, 131bdee, 162bdee }}
+{{Vals|legend=1| 7, 10c, 17c, 24d, 31d }}
-Badness: 0.0255
 </div></div>
@@ Line 2,275: / Line 2,279: @@
 Period: 1\1
-Optimal ([[POTE]]) generator: ~11/9 = 348.490
+Optimal ([[POTE]]) generator: ~11/9 = 350.816
-EDO generators: [[24edo|7\24]], [[31edo|9\31]]
+EDO generators: [[7edo|2\7]], [[10edo|3\10]], [[17edo|5\17]], [[24edo|7\24]]
 Scales (Scala files):
@@ Line 2,284: / Line 2,288: @@
 <div style="line-height:1.6;">Technical data</div>
 <div class="mw-collapsible-content">
-Comma list: 66/65, 81/80, 121/120, 126/125
+[[Comma]] list: 81/80, 36/35, 121/120, 144/143
-Mapping: [{{val| 1 1 0 -3 2 4 }}, {{val| 0 2 8 20 5 -1 }}]
+Mapping: [{{val| 1 1 0 4 2 4 }}, {{val| 0 2 8 -4 5 -1 }}]
 Mapping generators: ~2, ~11/9
-{{Vals|legend=1| 7d, 24d, 31, 55d }}
+{{Vals|legend=1| 7, 10c, 17c, 24d, 31d }}
-Badness: 0.0281
 </div></div>