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Meantone family: Difference between revisions

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<div style="line-height:1.6;">Technical data</div>
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
<div class="mw-collapsible-content">
[[Mappings|Period-generator mapping]]: [&lt;1 0 -4|, &lt;0 1 4|]
[[Mappings|Period-generator mapping]]: [{{val|1 0 -4}}, {{val|0 1 4}}]


Comma: 81/80
Comma: 81/80
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{{EDOs|legend=1| 5, 7, 12, 19, 26, 31, 43, 45, 50, 55, 67, 69, 74, 81, 88, 98, 105, 117, 131b, 212bb, 293bb }}
{{EDOs|legend=1| 5, 7, 12, 19, 26, 31, 43, 45, 50, 55, 67, 69, 74, 81, 88, 98, 105, 117, 131b, 212bb, 293bb }}


[[Wedgie]]: &lt;&lt;1 4 4||
[[Wedgie]]: {{wedgie|1 4 4}}


[[Badness]]: 0.00736
[[Badness]]: 0.00736
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<div style="line-height:1.6;">Technical data</div>
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
<div class="mw-collapsible-content">
[[Mappings|Period-generator mapping]]: [&lt;1 0 -4 -13|, &lt;0 1 4 10|]
[[Mappings|Period-generator mapping]]: [{{val|1 0 -4 -13}}, {{val|0 1 4 10}}]


[[Comma]]s: 81/80, 126/125
[[Comma]]s: 81/80, 126/125
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Algebraic generator: Cybozem, the real root of 15''x''<sup>3</sup> - 10''x''<sup>2</sup> - 18, which comes to 503.4257 cents. The recurrence converges quickly.
Algebraic generator: Cybozem, the real root of 15''x''<sup>3</sup> - 10''x''<sup>2</sup> - 18, which comes to 503.4257 cents. The recurrence converges quickly.


[[Wedgie]]: &lt;&lt;1 4 10 4 13 12||
[[Wedgie]]: {{wedgie|1 4 10 4 13 12}}


[[Vals]]: 5, 7, 12, 19, 26, 31, 43, 45, 50, 55, 67, 69, 74, 81, 88, 98, 105, 117, 131b, 212bb, 293bb
[[Vals]]: 5, 7, 12, 19, 26, 31, 43, 45, 50, 55, 67, 69, 74, 81, 88, 98, 105, 117, 131b, 212bb, 293bb
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[[POTE generator]]: ~3/2 = 696.016
[[POTE generator]]: ~3/2 = 696.016


Map: [&lt;2 0 -8 -26 -31|, &lt;0 1 4 10 12|]
Map: [{{val|2 0 -8 -26 -31}}, {{val|0 1 4 10 12}}]


{{EDOs|legend=1| 12, 38d, 50 }}
{{EDOs|legend=1| 12, 38d, 50 }}
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<div style="line-height:1.6;">Technical data</div>
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
<div class="mw-collapsible-content">
[[Mappings|Period-generator mapping]]: [&lt;1 0 -4 17|, &lt;0 1 4 -9|]
[[Mappings|Period-generator mapping]]: [{{val|1 0 -4 17}}, {{val|0 1 4 -9}}]


[[7-odd-limit|7-limit]] minimax
[[7-odd-limit|7-limit]] minimax
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Algebraic generator: Squarto, the positive root of 8''x''<sup>2</sup> - 4''x'' - 9, at 506.3239 cents, equal to (1 + sqrt (19))/4.
Algebraic generator: Squarto, the positive root of 8''x''<sup>2</sup> - 4''x'' - 9, at 506.3239 cents, equal to (1 + sqrt (19))/4.


[[Wedgie]]: &lt;&lt;1 4 -9 4 -17 -32||
[[Wedgie]]: {{wedgie|1 4 -9 4 -17 -32}}


[[Generator]]s: 2, 3
[[Generator]]s: 2, 3
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