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Meantone family: Difference between revisions

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Data box for ptolemy to mohamaq
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= Ptolemy =
= Ptolemy =
Commas: 81/80, 121/120, 525/512


POTE generator: ~11/9 = 346.922
Period: 1\1


Map: [<1 1 0 8 2|, <0 2 8 -18 5|]
Optimal ([[POTE]]) generator: ~11/9 = 346.922
 
EDO generators: [[38edo|22\38]], [[45edo|26\45]]
 
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, 121/120, 525/512
 
Mapping: [{{val| 1 1 0 8 2 }}, {{val| 0 2 8 -18 5 }}]


{{Vals|legend=1| 7, 31dd, 38d, 45e, 83bcddee }}
{{Vals|legend=1| 7, 31dd, 38d, 45e, 83bcddee }}


Badness: 0.0588
Badness: 0.0588
</div></div>


== 13-limit ==
== 13-limit ==
Commas: 65/64, 81/80, 105/104, 121/120


POTE generator: ~11/9 = 346.910
Period: 1\1


Map: [&lt;1 1 0 8 2 6|, &lt;0 2 8 -18 5 -8|]
Optimal ([[POTE]]) generator: ~11/9 = 346.910
 
EDO generators: [[38edo|22\38]], [[45edo|26\45]]
 
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: 65/64, 81/80, 105/104, 121/120
 
Mapping: [{{val| 1 1 0 8 2 6 }}, {{val| 0 2 8 -18 5 -8 }}]


{{Vals|legend=1| 7, 31ddf, 38df, 45ef, 83bcddeeff }}
{{Vals|legend=1| 7, 31ddf, 38df, 45ef, 83bcddeeff }}


Badness: 0.0343
Badness: 0.0343
</div></div>


= Maqamic =
= Maqamic =
Line 2,168: Line 2,190:
{{main| Maqamic }}
{{main| Maqamic }}


[[Comma]]s: 81/80, 36/35, 121/120
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


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.
Optimal ([[POTE]]) generator: ~11/9 = 350.934
 
EDO generators: [[7edo|4\7]], [[10edo|6\10]], [[17edo|10\17]], [[24edo|14\24]]


[[POTE generator]]: ~11/9 = 350.934
Scales (Scala files):  


Mapping generator: ~11/9
<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, 36/35, 121/120


Map: [&lt;1 1 0 4 2|, &lt;0 2 8 -4 5|]
Mapping: [{{val| 1 1 0 4 2 }}, {{val| 0 2 8 -4 5 }}]


[[generator|Generator]]s: 2, 11/9
Mapping generators: ~2, ~11/9


{{Vals|legend=1| 7, 10c, 17c, 24d, 31d }}
{{Vals|legend=1| 7, 10c, 17c, 24d, 31d }}
</div></div>


== 13-limit ==
== 13-limit ==
[[Comma]]s: 81/80, 36/35, 121/120, 144/143


[[POTE generator]]: ~11/9 = 350.816
Period: 1\1


Mapping generator: ~11/9
Optimal ([[POTE]]) generator: ~11/9 = 350.816


Map: [&lt;1 1 0 4 2 4|, &lt;0 2 8 -4 5 -1|]
EDO generators: [[7edo|4\7]], [[10edo|6\10]], [[17edo|10\17]], [[24edo|14\24]]


Generators: 2, 11/9
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, 36/35, 121/120, 144/143
 
Mapping: [{{val| 1 1 0 4 2 4 }}, {{val| 0 2 8 -4 5 -1 }}]
 
Mapping generators: ~2, ~11/9


{{Vals|legend=1| 7, 10c, 17c, 24d, 31d }}
{{Vals|legend=1| 7, 10c, 17c, 24d, 31d }}
</div></div>


= Migration =
= Migration =
Commas: 81/80, 121/120, 126/125


POTE generator: ~11/9 = 348.182
Period: 1\1
 
Optimal ([[POTE]]) generator: ~11/9 = 348.182
 
EDO generators: [[24edo|14\24]], [[31edo|18\31]]
 
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, 121/120, 126/125


Mapping generator: ~11/9
Mapping: [{{val| 1 1 0 -3 2 }}, {{val| 0 2 8 20 5 }}]


Map: [&lt;1 1 0 -3 2|, &lt;0 2 8 20 5|]
Mapping generators: ~2, ~11/9


{{Vals|legend=1| 7d, 31, 100de, 131bdee, 162bdee }}
{{Vals|legend=1| 7d, 31, 100de, 131bdee, 162bdee }}


Badness: 0.0255
Badness: 0.0255
</div></div>


== 13-limit ==
== 13-limit ==
Commas: 66/65, 81/80, 121/120, 126/125


POTE generator: ~11/9 = 348.490
Period: 1\1


Map: [&lt;1 1 0 -3 2 4|, &lt;0 2 8 20 5 -1|]
Optimal ([[POTE]]) generator: ~11/9 = 348.490
 
EDO generators: [[24edo|14\24]], [[31edo|18\31]]
 
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: 66/65, 81/80, 121/120, 126/125
 
Mapping: [{{val| 1 1 0 -3 2 4 }}, {{val| 0 2 8 20 5 -1 }}]
 
Mapping generators: ~2, ~11/9


{{Vals|legend=1| 7d, 24d, 31, 55d }}
{{Vals|legend=1| 7d, 24d, 31, 55d }}


Badness: 0.0281
Badness: 0.0281
</div></div>


= Mohamaq =
= Mohamaq =
Commas: 81/80, 392/375


POTE generator: ~25/21 = 350.586
Period: 1\1
 
Optimal ([[POTE]]) generator: ~25/21 = 350.586
 
EDO generators: [[17edo|10\17]], [[24edo|14\24]]
 
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, 392/375


Mapping generator: ~25/21
Mapping: [{{val| 1 1 0 -1 }}, {{val| 0 2 8 13 }}]


Map: [&lt;1 1 0 -1|, &lt;0 2 8 13|]
Mapping generators: ~2, ~25/21


{{Vals|legend=1| 17c, 24, 65c, 89cd }}
{{Vals|legend=1| 17c, 24, 65c, 89cd }}


Badness: 0.0777
Badness: 0.0777
</div></div>


== 11-limit ==
== 11-limit ==
Commas: 56/55, 77/75, 243/242


POTE generator: ~11/9 = 350.565
Period: 1\1


Mapping generator: ~11/9
Optimal ([[POTE]]) generator: ~11/9 = 350.565


Map: [&lt;1 1 0 -1 2|, &lt;0 2 8 13 5|]
EDO generators: [[17edo|10\17]], [[24edo|14\24]]
 
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, 77/75, 243/242
 
Mapping: [{{val| 1 1 0 -1 2 }}, {{val| 0 2 8 13 5 }}]
 
Mapping generators: ~2, ~11/9


{{Vals|legend=1| 17c, 24, 65c, 89cd }}
{{Vals|legend=1| 17c, 24, 65c, 89cd }}


Badness: 0.0362
Badness: 0.0362
</div></div>


== 13-limit ==
== 13-limit ==
Commas: 56/55, 66/65, 77/75, 243/242


POTE generator: ~11/9 = 350.745
Period: 1\1
 
Optimal ([[POTE]]) generator: ~11/9 = 350.745
 
EDO generators: [[17edo|10\17]], [[24edo|14\24]]
 
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, 66/65, 77/75, 243/242


Mapping generator: ~11/9
Mapping: [{{val| 1 1 0 -1 2 4 }}, {{val| 0 2 8 13 5 -1 }}]


Map: [&lt;1 1 0 -1 2 4|, &lt;0 2 8 13 5 -1|]
Mapping generators: ~2, ~11/9


{{Vals|legend=1| 17c, 24, 41c, 65c }}
{{Vals|legend=1| 17c, 24, 41c, 65c }}


Badness: 0.0287
Badness: 0.0287
</div></div>


= Orphic =
= Orphic =
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