Meantone family: Difference between revisions

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 = Sharptone =
-[[Comma]]s: 21/20, 28/27
 Sharptone is a low-accuracy temperament tempering out 21/20 and 28/27. In sharptone, a 7/4 is a major sixth, a 7/6 a whole tone, and a 7/5 a fourth. Genuinely septimal sounding harmony therefore cannot be expected, but it can be used to translate, more or less, 7-limit JI into 5-limit meantone. [[12edo]] tuning does sharptone about as well as such a thing can be done, of course not in its patent val.
-[[POTE generator]]: ~3/2 = 700.140
+Period: 1\1
-Mapping generator: ~3
+Optimal ([[POTE]]) generator: ~3/2 = 700.140
-Map: [&lt;1 0 -4 -2|, &lt;0 1 4 3|]
+EDO generators: [[5edo|3\5]], [[7edo|4\7]], [[12edo|7\12]]
-[[Wedgie]]: &lt;&lt;1 4 3 4 2 -4||
+Scales (Scala files):
+<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+<div style="line-height:1.6;">Technical data</div>
+<div class="mw-collapsible-content">
+[[Comma]] list: 21/20, 28/27
+Mapping: [{{val| 1 0 -4 -2 }}, {{val| 0 1 4 3 }}]
+Mapping generators: ~2, ~3
+[[Wedgie]]: {{wedgie| 1 4 3 4 2 -4 }}
 {{Vals|legend=1| 5, 7d, 12d }}
 [[Badness]]: 0.0248
+</div></div>
 == Meanertone ==
-Commas: 21/20, 28/27, 33/32
-POTE generator: ~3/2 = 696.615
+Period: 1\1
+Optimal ([[POTE]]) generator: ~3/2 = 696.615
+EDO generators: [[5edo|3\5]], [[7edo|4\7]], [[12edo|7\12]]
+Scales (Scala files):
+<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+<div style="line-height:1.6;">Technical data</div>
+<div class="mw-collapsible-content">
+Comma list: 21/20, 28/27, 33/32
-Map: [&lt;1 0 -4 -2 5|, &lt;0 1 4 3 -1|]
+Mapping: [{{val| 1 0 -4 -2 5 }}, {{val| 0 1 4 3 -1 }}]
 {{Vals|legend=1| 5, 7d, 12de }}
 Badness: 0.0252
+</div></div>
 = Meansept =
-Commas: 15/14, 81/80
+Period: 1\1
+Optimal ([[POTE]]) generator: ~3/2 = 682.895
+EDO generators: [[7edo|4\7]]
+Scales (Scala files):
+<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+<div style="line-height:1.6;">Technical data</div>
+<div class="mw-collapsible-content">
+Comma list: 15/14, 81/80
 POTE generator: ~3/2 = 682.895
-Mapping generator: ~3
+Mapping: [{{val| 1 0 -4 -5 }}, {{val| 0 1 4 5 }}]
-Map: [&lt;1 0 -4 -5|, &lt;0 1 4 5|]
+Mapping generators: ~2, ~3
-Wedgie: &lt;&lt;1 4 5 4 5 0||
+Wedgie: {{wedgie| 1 4 5 4 5 0 }}
 {{Vals|legend=1| 5d, 7, 12dd }}
 Badness: 0.0453
+</div></div>
 == 11-limit ==
-Commas: 15/14, 22/21, 81/80
-POTE generator: ~3/2 = 685.234
+Period: 1\1
+Optimal ([[POTE]]) generator: ~3/2 = 685.234
+EDO generators: [[7edo|4\7]]
-Mapping generator: ~3
+Scales (Scala files):
-Map: [&lt;1 0 -4 -5 -6|, &lt;0 1 4 5 6|]
+<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+<div style="line-height:1.6;">Technical data</div>
+<div class="mw-collapsible-content">
+Comma list: 15/14, 22/21, 81/80
+Mapping: [{{val| 1 0 -4 -5 -6 }}, {{val| 0 1 4 5 6 }}]
+Mapping generators: ~2, ~3
 {{Vals|legend=1| 5de, 7, 12dd }}
 Badness: 0.0325
+</div></div>
 = Supermean =
-Commas: 81/80, 672/625
-POTE generator: ~3/2 = 704.889
+Period: 1\1
+Optimal ([[POTE]]) generator: ~3/2 = 704.889
+EDO generators: [[12edo|7\12]], [[17edo|10\17]], [[29edo|17\29]]
+Scales (Scala files):
+<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+<div style="line-height:1.6;">Technical data</div>
+<div class="mw-collapsible-content">
+Comma list: 81/80, 672/625
-Map: [&lt;1 0 -4 -21|, &lt;0 1 4 15|]
+Mapping: [{{val| 1 0 -4 -21 }}, {{val| 0 1 4 15 }}]
 {{Vals|legend=1| 5d, 12d, 17c, 29c }}
 Badness: 0.1342
+</div></div>
 == 11-limit ==
-Commas: 56/55, 81/80, 132/125
+Period: 1\1
+Optimal ([[POTE]]) generator: ~3/2 = 705.096
+EDO generators: [[12edo|7\12]], [[17edo|10\17]], [[29edo|17\29]]
+Scales (Scala files):
+<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+<div style="line-height:1.6;">Technical data</div>
+<div class="mw-collapsible-content">
+Comma list: 56/55, 81/80, 132/125
 POTE generator: ~3/2 = 705.096
-Map: [&lt;1 0 -4 -21 -14|, &lt;0 1 4 15 11|]
+Mapping: [{{val| 1 0 -4 -21 -14 }}, {{val| 0 1 4 15 11 }}]
 {{Vals|legend=1| 5de, 12de, 17c, 29c }}
 Badness: 0.0633
+</div></div>
 == 13-limit ==
-Commas: 26/25, 56/55, 66/65, 81/80
+Period: 1\1
+Optimal ([[POTE]]) generator: ~3/2 = 705.094
+EDO generators: [[12edo|7\12]], [[17edo|10\17]], [[29edo|17\29]]
+Scales (Scala files):
+<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+<div style="line-height:1.6;">Technical data</div>
+<div class="mw-collapsible-content">
+Comma list: 26/25, 56/55, 66/65, 81/80
 POTE generator: ~3/2 = 705.094
-Map: [&lt;1 0 -4 -21 -14 -9|, &lt;0 1 4 15 11 8|]
+Mapping: [{{val| 1 0 -4 -21 -14 -9 }}, {{val| 0 1 4 15 11 8 }}]
 {{Vals|legend=1| 5de, 12de, 17c, 29c }}
+</div></div>
 = Injera =