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Semaphoresmic family: Difference between revisions

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= Semiphore =
= Semiphore =


Period: 1\1
Subgroup: 2.3.5.7


Optimal ([[POTE]]) generators: ~7/6 = 250.3846, ~5/4 = 379.7035
[[Comma list]]: 49/48


EDO generators: [[15edo|(3, 5)\15]], [[19edo|(4, 6)\19]], [[24edo|(5, 8)\24]]
[[Mapping]]: [{{val| 1 0 2 2 }}, {{val| 0 2 0 1 }}, {{val| 0 0 1 0 }}]
 
Scales:
 
<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: 49/48
 
Mapping: [{{val| 1 0 2 2 }}, {{val| 0 2 0 1 }}, {{val| 0 0 1 0 }}]


Mapping generators: ~2, ~7/4, ~5
Mapping generators: ~2, ~7/4, ~5
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: 7/6 length = 0.7627, 5/4 length = 2.322
: 7/6 length = 0.7627, 5/4 length = 2.322
: Angle (7/6, 5/4) = 90 degrees
: Angle (7/6, 5/4) = 90 degrees
[[POTE generator]]s: ~7/6 = 250.3846, ~5/4 = 379.7035


{{Val list|legend=1| 4, 5, 9, 10, 14c, 15, 19 }}
{{Val list|legend=1| 4, 5, 9, 10, 14c, 15, 19 }}


Badness: 0.116 × 10<sup>-3</sup>
[[Badness]]: 0.116 × 10<sup>-3</sup>


</div></div>
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= Selenium =
= Selenium =


Period: 1\1
[[Comma list]]: 49/48, 56/55
 
Optimal ([[POTE]]) generators: ~7/6 = 248.2710, ~5/4 = 390.6487
 
EDO generators: [[15edo|(3, 5)\15]], [[19edo|(4, 6)\19]], [[24edo|(5, 8)\24]]
 
Scales:
 
<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: 49/48, 56/55
[[Mapping]]: [{{val| 1 0 2 2 5 }}, {{val| 0 2 0 1 1 }}, {{val| 0 0 1 0 -1 }}]


Mapping: [{{val| 1 0 2 2 5 }}, {{val| 0 2 0 1 1 }}, {{val| 0 0 1 0 -1 }}]
[[POTE generator]]s: ~7/6 = 248.2710, ~5/4 = 390.6487


{{Val list|legend=1| 4, 5, 9, 10, 15, 19, 24, 34 }}
{{Val list|legend=1| 4, 5, 9, 10, 15, 19, 24, 34 }}


Badness: 0.665 × 10<sup>-3</sup>
[[Badness]]: 0.665 × 10<sup>-3</sup>
 
</div></div>


== 13-limit ==
== 13-limit ==
Period: 1\1
Optimal ([[POTE]]) generators: ~7/6 = 248.7559, ~5/4 = 389.5957
EDO generators: [[15edo|(3, 5)\15]], [[19edo|(4, 6)\19]], [[24edo|(5, 8)\24]]
Scales:
<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: 49/48, 56/55, 91/90
Comma list: 49/48, 56/55, 91/90


Mapping: [{{val| 1 0 2 2 5 -1 }}, {{val| 0 2 0 1 1 3 }}, {{val| 0 0 1 0 -1 1 }}]
Mapping: [{{val| 1 0 2 2 5 -1 }}, {{val| 0 2 0 1 1 3 }}, {{val| 0 0 1 0 -1 1 }}]
POTE generators: ~7/6 = 248.7559, ~5/4 = 389.5957


{{Val list|legend=1| 5, 9, 10, 15, 19, 24, 34 }}
{{Val list|legend=1| 5, 9, 10, 15, 19, 24, 34 }}


Badness: 0.787 × 10<sup>-3</sup>
Badness: 0.787 × 10<sup>-3</sup>
</div></div>


= Negric =
= Negric =


Period: 1\1
Subgroup: 2.3.5.7.11
 
Optimal ([[POTE]]) generators: ~15/14 = 125.6080, ~11/8 = 539.2342
 
EDO generators: [[19edo|(2, 9)\19]], [[29edo|(3, 13)\29]], [[38edo|(4, 17)\38]]
 
Scales:


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
[[Comma list]]: 49/48, 225/224
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Comma list: 49/48, 225/224
[[Mapping]]: [{{val| 1 2 2 3 0 }}, {{val| 0 -4 3 -2 0 }}, {{val| 0 0 0 0 1 }}]


Mapping: [{{val| 1 2 2 3 0 }}, {{val| 0 -4 3 -2 0 }}, {{val| 0 0 0 0 1 }}]
[[POTE generator]]s: ~15/14 = 125.6080, ~11/8 = 539.2342


{{Val list|legend=1| 9, 10, 19, 29, 38d, 67cde }}
{{Val list|legend=1| 9, 10, 19, 29, 38d, 67cde }}


Badness: 1.087 × 10<sup>-3</sup>
[[Badness]]: 1.087 × 10<sup>-3</sup>
 
</div></div>


== 13-limit ==
== 13-limit ==


Period: 1\1
Subgroup: 2.3.5.7.11.13
 
Optimal ([[POTE]]) generators: ~14/13 = 125.5675, ~11/8 = 538.4845
 
EDO generators: [[19edo|(2, 9)\19]], [[29edo|(3, 13)\29]], [[38edo|(4, 17)\38]]
 
Scales:
 
<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: 49/48, 65/64, 91/90
Comma list: 49/48, 65/64, 91/90


Mapping: [{{val| 1 2 2 3 0 4 }}, {{val| 0 -4 3 -2 0 -3 }}, {{val| 0 0 0 0 1 0 }}]
Mapping: [{{val| 1 2 2 3 0 4 }}, {{val| 0 -4 3 -2 0 -3 }}, {{val| 0 0 0 0 1 0 }}]
POTE generators: ~14/13 = 125.5675, ~11/8 = 538.4845


{{Val list|legend=1| 9, 10, 19, 29, 38df, 67cdef }}
{{Val list|legend=1| 9, 10, 19, 29, 38df, 67cdef }}


Badness: 0.8076 × 10<sup>-3</sup>
Badness: 0.8076 × 10<sup>-3</sup>
</div></div>


[[Category:Theory]]
[[Category:Theory]]
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