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Archytas clan: Difference between revisions

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= Archy =
= Archy =
Period: 1\1
Optimal ([[POTE]]) generator: ~3/2 = 709.321
EDO generators: [[17edo|10\17]], [[22edo|13\22]], [[27edo|16\27]], [[39edo|23\39]], [[49edo|29\49]]
Scales (Scala files): [[archy5]], [[archy7]], [[archy12]]
<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">


Subgroup: 2.3.7
Subgroup: 2.3.7


Comma list: 64/63
[[Comma list]]: 64/63


Sval mapping: [{{val| 1 0 6 }}, {{val| 0 1 -2 }}]
[[Sval]] [[mapping]]: [{{val| 1 0 6 }}, {{val| 0 1 -2 }}]


Sval mapping generators: ~2, ~3
Sval mapping generators: ~2, ~3
Line 29: Line 17:
Gencom mapping: [{{val| 1 1 0 4 }}, {{val| 0 1 0 -2 }}]
Gencom mapping: [{{val| 1 1 0 4 }}, {{val| 0 1 0 -2 }}]


Gencom: [2 3/2; 64/63]
[[Gencom]]: [2 3/2; 64/63]
 
[[POTE generator]]: ~3/2 = 709.321


{{Val list|legend=1| 2, 3, 5, 12, 17, 22 }}
{{Val list|legend=1| 2, 3, 5, 12, 17, 22 }}


</div></div>
Scales: [[archy5]], [[archy7]], [[archy12]]


== Supra ==
== Supra ==
Period: 1\1
Optimal ([[POTE]]) generator: ~3/2 = 707.192
EDO generators: [[17edo|10\17]], [[22edo|13\22]], [[39edo|23\39]], [[56edo|33\56]]
Scales (Scala files): [[supra7]], [[supra12]]
<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">


Subgroup: 2.3.7.11
Subgroup: 2.3.7.11
Line 60: Line 38:


Gencom: [2 3/2; 64/63 99/98]
Gencom: [2 3/2; 64/63 99/98]
POTE generator: ~3/2 = 707.192


{{Val list|legend=1| 5, 12, 17, 39d, 56d }}
{{Val list|legend=1| 5, 12, 17, 39d, 56d }}


</div></div>
Scales: [[supra7]], [[supra12]]


=== Supraphon ===
=== Supraphon ===
Period: 1\1
Optimal ([[POTE]]) generator: ~3/2 = 706.137
EDO generators: [[17edo|10\17]], [[22edo|13\22]], [[39edo|23\39]], [[56edo|33\56]]
Scales (Scala files): [[supra7]], [[supra12]]
<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">


Subgroup: 2.3.7.11.13
Subgroup: 2.3.7.11.13
Line 90: Line 58:


Gencom: [2 3/2; 64/63 78/77 99/98]
Gencom: [2 3/2; 64/63 78/77 99/98]
POTE generator: ~3/2 = 706.137


{{Val list|legend=1| 12f, 17 }}
{{Val list|legend=1| 12f, 17 }}


</div></div>
Scales: [[supra7]], [[supra12]]


== Suhajira ==
== Suhajira ==
Period: 1\1
Optimal ([[POTE]]) generator: ~11/9 = 353.958
EDO generators: [[7edo|4\7]], [[10edo|6\10]], [[17edo|10\17]], [[27edo|16\27]], [[44edo|26\44]]
Scales (Scala files): [[suhajira7]], [[suhajira10]], [[suhajira17]]
<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">


Subgroup: 2.3.7.11
Subgroup: 2.3.7.11
Line 120: Line 78:


Gencom: [2 3/2; 64/63 99/98]
Gencom: [2 3/2; 64/63 99/98]
POTE generator: ~11/9 = 353.958


{{Val list|legend=1| 7, 10, 17, 44e, 61de }}
{{Val list|legend=1| 7, 10, 17, 44e, 61de }}


</div></div>
Scales: [[suhajira7]], [[suhajira10]], [[suhajira17]]


=== 2.3.7.11.13 ===
=== 2.3.7.11.13 ===
Period: 1\1
Optimal ([[POTE]]) generator: ~11/9 = 353.775
EDO generators: [[7edo|4\7]], [[10edo|6\10]], [[17edo|10\17]], [[27edo|16\27]], [[44edo|26\44]]
Scales (Scala files): [[suhajira7]], [[suhajira10]], [[suhajira17]]
<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">


Subgroup: 2.3.7.11.13
Subgroup: 2.3.7.11.13
Line 150: Line 98:


Gencom: [2 3/2; 64/63 78/77 99/98]
Gencom: [2 3/2; 64/63 78/77 99/98]
POTE generator: ~11/9 = 353.775


{{Val list|legend=1| 7, 10, 17, 44e, 61de }}
{{Val list|legend=1| 7, 10, 17, 44e, 61de }}


</div></div>
Scales: [[suhajira7]], [[suhajira10]], [[suhajira17]]


= Superpyth =
= Superpyth =
{{main| Superpyth }}
{{main| Superpyth }}


Period: 1\1
Subgroup: 2.3.5.7


Optimal ([[POTE]]) generator: ~3/2 = 710.291
[[Comma list]]: 64/63, 245/243


EDO generators: [[17edo|10\17]], [[22edo|13\22]], [[27edo|16\27]], [[49edo|29\49]]
[[Mapping]]: [{{val| 1 0 -12 6 }}, {{val| 0 1 9 -2 }}]


Scales (Scala files):
{{Multival|legend=1| 1 9 -2 12 -6 -30 }}


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
[[POTE generator]]: ~3/2 = 710.291
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
Subgroup: 2.3.5.7
 
Comma list: 64/63, 245/243
 
Mapping: [{{val| 1 0 -12 6 }}, {{val| 0 1 9 -2 }}]
 
Wedgie: {{wedgie| 1 9 -2 12 -6 -30 }}


{{Val list|legend=1| 5, 17, 22, 27, 49 }}
{{Val list|legend=1| 5, 17, 22, 27, 49 }}


Badness: 0.0323
[[Badness]]: 0.0323
 
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~3/2 = 710.175
EDO generators: [[22edo|13\22]], [[27edo|16\27]], [[49edo|29\49]]
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">


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 203: Line 129:


Mapping: [{{val| 1 0 -12 6 -22 }}, {{val| 0 1 9 -2 16 }}]
Mapping: [{{val| 1 0 -12 6 -22 }}, {{val| 0 1 9 -2 16 }}]
POTE generator: ~3/2 = 710.175


{{Val list|legend=1| 22, 27e, 49 }}
{{Val list|legend=1| 22, 27e, 49 }}


Badness: 0.0250
Badness: 0.0250
</div></div>


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generator: ~3/2 = 710.479
EDO generators: [[22edo|13\22]], [[27edo|16\27]], [[49edo|29\49]]
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">


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
Line 229: Line 143:


Mapping: [{{val| 1 0 -12 6 -22 -17 }}, {{val| 0 1 9 -2 16 13 }}]
Mapping: [{{val| 1 0 -12 6 -22 -17 }}, {{val| 0 1 9 -2 16 13 }}]
POTE generator: ~3/2 = 710.479


{{Val list|legend=1| 22, 27e, 49, 76bcde }}
{{Val list|legend=1| 22, 27e, 49, 76bcde }}


Badness: 0.0247
Badness: 0.0247
</div></div>


== Suprapyth ==
== Suprapyth ==
Period: 1\1
Optimal ([[POTE]]) generator: ~3/2 = 709.495
EDO generators: [[17edo|10\17]], [[22edo|13\22]]
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">


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 255: Line 157:


Mapping: [{{val| 1 0 -12 6 13 }}, {{val| 0 1 9 -2 -6 }}]
Mapping: [{{val| 1 0 -12 6 13 }}, {{val| 0 1 9 -2 -6 }}]
POTE generator: ~3/2 = 709.495


{{Val list|legend=1| 17, 22 }}
{{Val list|legend=1| 17, 22 }}


Badness: 0.0328
Badness: 0.0328
</div></div>


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generator: ~3/2 = 708.703
EDO generators: [[17edo|10\17]], [[22edo|13\22]]
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">


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
Line 281: Line 171:


Mapping: [{{val| 1 0 -12 6 13 18 }}, {{val| 0 1 9 -2 -6 -9 }}]
Mapping: [{{val| 1 0 -12 6 13 18 }}, {{val| 0 1 9 -2 -6 -9 }}]
POTE generator: ~3/2 = 708.703


{{Val list|legend=1| 17, 22, 83cdf }}
{{Val list|legend=1| 17, 22, 83cdf }}


Badness: 0.0363
Badness: 0.0363
</div></div>


= Quasisuper =
= Quasisuper =


Period: 1\1
Subgroup: 2.3.5.7


Optimal ([[POTE]]) generator: ~3/2 = 708.328
[[Comma list]]: 64/63, 2430/2401


EDO generators: [[17edo|10\17]], [[22edo|13\22]], [[39edo|23\39]], [[61edo|36\61]]
[[Mapping]]: [{{val| 1 0 23 6 }}, {{val| 0 1 -13 -2 }}]


Scales (Scala files):
{{Multival|legend=1| 1 -13 -2 -23 -2 -6 32 }}


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
[[POTE generator]]: ~3/2 = 708.328
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
Subgroup: 2.3.5.7
 
Comma list: 64/63, 2430/2401
 
Mapping: [{{val| 1 0 23 6 }}, {{val| 0 1 -13 -2 }}]
 
Wedgie: {{wedgie| 1 -13 -2 -23 -2 -6 32 }}


{{Val list|legend=1| 17c, 22, 61d }}
{{Val list|legend=1| 17c, 22, 61d }}


Badness: 0.0638
[[Badness]]: 0.0638
 
</div></div>


== Quasisupra ==
== Quasisupra ==
Quasisupra can be viewed as an extension of the excellent 2.3.7.11 temperament [[supra]], with the quasisuper mapping of 5 thrown in, rather than the superpyth mapping of 5 (which results in suprapyth).
Quasisupra can be viewed as an extension of the excellent 2.3.7.11 temperament [[supra]], with the quasisuper mapping of 5 thrown in, rather than the superpyth mapping of 5 (which results in suprapyth).
Period: 1\1
Optimal ([[POTE]]) generator: ~3/2 = 708.205
EDO generators: [[17edo|10\17]], [[22edo|13\22]], [[39edo|23\39]], [[61edo|36\61]]
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">


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 336: Line 202:


Mapping: [{{val| 1 2 -3 2 1 }}, {{val| 0 -1 13 2 6 }}]
Mapping: [{{val| 1 2 -3 2 1 }}, {{val| 0 -1 13 2 6 }}]
POTE generator: ~3/2 = 708.205


{{Val list|legend=1| 17c, 22, 39d, 61d }}
{{Val list|legend=1| 17c, 22, 39d, 61d }}


Badness: 0.0322
Badness: 0.0322
</div></div>


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generator: ~3/2 = 708.004
EDO generators: [[17edo|10\17]], [[22edo|13\22]], [[39edo|23\39]], [[61edo|36\61]]
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">


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
Line 362: Line 216:


Mapping: [{{val| 1 0 23 6 13 18 }}, {{val| 0 1 -13 -2 -6 -9 }}]
Mapping: [{{val| 1 0 23 6 13 18 }}, {{val| 0 1 -13 -2 -6 -9 }}]
POTE generator: ~3/2 = 708.004


{{Val list|legend=1| 17c, 22, 39d, 61df, 100bcdf }}
{{Val list|legend=1| 17c, 22, 39d, 61df, 100bcdf }}


Badness: 0.0302
Badness: 0.0302
</div></div>


== Quasisoup ==
== Quasisoup ==
Period: 1\1
Optimal ([[POTE]]) generator: ~3/2 = 709.021
EDO generators: [[22edo|13\22]]
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">


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 388: Line 230:


Mapping: [{{val| 1 0 23 6 -22 }}, {{val| 0 1 -13 -2 16 }}]
Mapping: [{{val| 1 0 23 6 -22 }}, {{val| 0 1 -13 -2 16 }}]
POTE generator: ~3/2 = 709.021


{{Val list|legend=1| 22 }}
{{Val list|legend=1| 22 }}


Badness: 0.0835
Badness: 0.0835
</div></div>


= Schism =
= Schism =
{{see also|Schismatic family #Schism}}
{{see also|Schismatic family #Schism}}


Period: 1\1
Subgroup: 2.3.5.7
 
Optimal ([[POTE]]) generator: ~3/2 = 701.556


EDO generators: [[12edo|7\12]], [[17edo|10\17]]
[[Comma list]]: 64/63, 360/343
 
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">
 
Subgroup: 2.3.5.7


Comma list: 64/63, 360/343
[[Mapping]]: [{{val| 1 0 15 6 }}, {{val| 0 1 -8 -2 }}]


Mapping: [{{val| 1 0 15 6 }}, {{val| 0 1 -8 -2 }}]
{{Multival|legend=1| 1 -8 -2 -15 -6 18 }}


Wedgie: {{wedgie| 1 -8 -2 -15 -6 18 }}
[[POTE generator]]: ~3/2 = 701.556


{{Val list|legend=1| 12, 41d, 53d }}
{{Val list|legend=1| 12, 41d, 53d }}


Badness: 0.0566
[[Badness]]: 0.0566
 
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~3/2 = 702.136
EDO generators: [[12edo|7\12]], [[17edo|10\17]]
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">


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 443: Line 261:


Mapping: [{{val| 1 0 15 6 13 }}, {{val| 0 1 -8 -2 -6 }}]
Mapping: [{{val| 1 0 15 6 13 }}, {{val| 0 1 -8 -2 -6 }}]
POTE generator: ~3/2 = 702.136


{{Val list|legend=1| 12, 29de, 41de }}
{{Val list|legend=1| 12, 29de, 41de }}


Badness: 0.0375
Badness: 0.0375
</div></div>


= Blacksmith =
= Blacksmith =
Line 455: Line 273:


== 5-limit (blackwood) ==
== 5-limit (blackwood) ==
Period: 1\5
Optimal ([[POTE]]) generator: ~5/4 = 399.594
EDO generators: [[10edo|3\10]], [[15edo|4\15]]
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">


Subgroup: 2.3.5
Subgroup: 2.3.5
Line 475: Line 281:


Mapping generators: ~9/8, ~5
Mapping generators: ~9/8, ~5
POTE generator: ~5/4 = 399.594


{{Val list|legend=1| 5, 10, 15 }}
{{Val list|legend=1| 5, 10, 15 }}


Badness: 0.0638
Badness: 0.0638
</div></div>


== 7-limit ==
== 7-limit ==
Period: 1\5
Optimal ([[POTE]]) generator: ~5/4 = 392.767
EDO generators: [[10edo|3\10]], [[15edo|4\15]]
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">


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 504: Line 298:
Mapping generators: ~7/6, ~5
Mapping generators: ~7/6, ~5


Wedgie: {{wedgie| 0 5 0 8 0 -14 }}
{{Multival|legend=1| 0 5 0 8 0 -14 }}
 
POTE generator: ~5/4 = 392.767


{{Val list|legend=1| 5, 10, 15, 40b, 55b }}
{{Val list|legend=1| 5, 10, 15, 40b, 55b }}


Badness: 0.0256
Badness: 0.0256
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\5
Optimal ([[POTE]]) generator: ~5/4 = 394.948
EDO generators: [[10edo|3\10]], [[15edo|4\15]]
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">


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 531: Line 313:


Mapping: [{{val| 5 8 0 14 29 }}, {{val| 0 0 1 0 -1 }}]
Mapping: [{{val| 5 8 0 14 29 }}, {{val| 0 0 1 0 -1 }}]
POTE generator: ~5/4 = 394.948


{{Val list|legend=1| 5, 10, 15, 40be, 55be, 70bde, 85bcde}}
{{Val list|legend=1| 5, 10, 15, 40be, 55be, 70bde, 85bcde}}


Badness: 0.0246
Badness: 0.0246
</div></div>


=== 13-limit ===
=== 13-limit ===
Period: 1\5
Optimal ([[POTE]]) generator: ~5/4 = 391.0367
EDO generators: [[10edo|3\10]], [[15edo|4\15]]
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">


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
Line 557: Line 327:


Mapping: [{{val| 5 8 0 14 29 7 }}, {{val| 0 0 1 0 -1 1 }}]
Mapping: [{{val| 5 8 0 14 29 7 }}, {{val| 0 0 1 0 -1 1 }}]
POTE generator: ~5/4 = 391.0367


{{Val list|legend=1| 5, 10, 15, 25e, 40bef}}
{{Val list|legend=1| 5, 10, 15, 25e, 40bef}}


Badness: 0.0205
Badness: 0.0205
</div></div>


== Farrier ==
== Farrier ==
Period: 1\5
Optimal ([[POTE]]) generator: ~5/4 = 398.070
EDO generators: [[10edo|3\10]], [[15edo|4\15]]
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">


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 583: Line 341:


Mapping: [{{val| 5 8 0 14 -6 }}, {{val| 0 0 1 0 2 }}]
Mapping: [{{val| 5 8 0 14 -6 }}, {{val| 0 0 1 0 2 }}]
POTE generator: ~5/4 = 398.070


{{Val list|legend=1| 5e, 10e, 15 }}
{{Val list|legend=1| 5e, 10e, 15 }}


Badness: 0.0292
Badness: 0.0292
</div></div>


=== 13-limit ===
=== 13-limit ===
Period: 1\5
Optimal ([[POTE]]) generator: ~5/4 = 396.812
EDO generators: [[10edo|3\10]], [[15edo|4\15]]
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">


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
Line 609: Line 355:


Mapping: [{{val| 5 8 0 14 -6 7 }}, {{val| 0 0 1 0 2 1 }}]
Mapping: [{{val| 5 8 0 14 -6 7 }}, {{val| 0 0 1 0 2 1 }}]
POTE generator: ~5/4 = 396.812


{{Val list|legend=1| 5e, 10e, 15 }}
{{Val list|legend=1| 5e, 10e, 15 }}


Badness: 0.0223
Badness: 0.0223
</div></div>


== Ferrum ==
== Ferrum ==
Period: 1\5
Optimal ([[POTE]]) generator: ~5/4 = 374.763
EDO generators: [[10edo|3\10]]
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">


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 635: Line 369:


Mapping: [{{val| 5 8 0 14 6 }}, {{val| 0 0 1 0 1 }}]
Mapping: [{{val| 5 8 0 14 6 }}, {{val| 0 0 1 0 1 }}]
POTE generator: ~5/4 = 374.763


{{Val list|legend=1| 5e, 10 }}
{{Val list|legend=1| 5e, 10 }}


Badness: 0.0309
Badness: 0.0309
</div></div>


= Beatles =
= Beatles =
== 5-limit ==
== 5-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~512/405 = 355.930
EDO generators: [[10edo|6\10]], [[17edo|10\17]], [[27edo|16\27]], [[37edo|22\37]]
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">


Subgroup: 2.3.5
Subgroup: 2.3.5
Line 662: Line 384:


Mapping: [{{val| 1 1 5 }}, {{val| 0 2 -9 }}]
Mapping: [{{val| 1 1 5 }}, {{val| 0 2 -9 }}]
POTE generator: ~512/405 = 355.930


{{Val list|legend=1| 10, 17c, 27, 64b, 91bc, 118bc }}
{{Val list|legend=1| 10, 17c, 27, 64b, 91bc, 118bc }}


Badness: 0.3585
Badness: 0.3585
</div></div>


== 7-limit ==
== 7-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~49/40 = 355.904
EDO generators: [[10edo|6\10]], [[17edo|10\17]], [[27edo|16\27]], [[37edo|22\37]]
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">


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 689: Line 399:
Mapping: [{{val| 1 1 5 4 }}, {{val| 0 2 -9 -4 }}]
Mapping: [{{val| 1 1 5 4 }}, {{val| 0 2 -9 -4 }}]


Wedgie: {{wedgie| 2 -9 -4 -19 -12 16 }}
{{Multival|legend=1| 2 -9 -4 -19 -12 16 }}
 
POTE generator: ~49/40 = 355.904


{{Val list|legend=1| 10, 17c, 27, 64b, 91bcd, 118bcd }}
{{Val list|legend=1| 10, 17c, 27, 64b, 91bcd, 118bcd }}


Badness: 0.0459
Badness: 0.0459
</div></div>


; Music
; Music
Line 701: Line 411:


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~49/40 = 356.140
EDO generators: [[27edo|16\27]], [[37edo|22\37]]
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">


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 719: Line 417:


Mapping: [{{val| 1 1 5 4 10 }}, {{val| 0 2 -9 -4 -22 }}]
Mapping: [{{val| 1 1 5 4 10 }}, {{val| 0 2 -9 -4 -22 }}]
POTE generator: ~49/40 = 356.140


{{Val list|legend=1| 27e, 37, 64be, 91bcde }}
{{Val list|legend=1| 27e, 37, 64be, 91bcde }}


Badness: 0.0456
Badness: 0.0456
</div></div>


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generator: ~16/13 = 356.229
EDO generators: [[27edo|16\27]], [[37edo|22\37]]
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">


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
Line 745: Line 431:


Mapping: [{{val| 1 1 5 4 10 4 }}, {{val| 0 2 -9 -4 -22 -1 }}]
Mapping: [{{val| 1 1 5 4 10 4 }}, {{val| 0 2 -9 -4 -22 -1 }}]
POTE generator: ~16/13 = 356.229


{{Val list|legend=1| 27e, 37, 64be }}
{{Val list|legend=1| 27e, 37, 64be }}


Badness: 0.0302
Badness: 0.0302
</div></div>


== Ringo ==
== Ringo ==
Period: 1\1
Optimal ([[POTE]]) generator: ~11/9 = 355.419
EDO generators: [[10edo|6\10]], [[17edo|10\17]], [[27edo|16\27]]
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">


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 771: Line 445:


Mapping: [{{val| 1 1 5 4 2 }}, {{val| 0 2 -9 -4 5 }}]
Mapping: [{{val| 1 1 5 4 2 }}, {{val| 0 2 -9 -4 5 }}]
POTE generator: ~11/9 = 355.419


{{Val list|legend=1| 10, 17c, 27e }}
{{Val list|legend=1| 10, 17c, 27e }}


Badness: 0.0329
Badness: 0.0329
</div></div>


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generator: ~11/9 = 355.456
EDO generators: [[10edo|6\10]], [[17edo|10\17]], [[27edo|16\27]]
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">


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
Line 797: Line 459:


Mapping: [{{val| 1 1 5 4 2 4 }}, {{val| 0 2 -9 -4 5 -1 }}]
Mapping: [{{val| 1 1 5 4 2 4 }}, {{val| 0 2 -9 -4 5 -1 }}]
POTE generator: ~11/9 = 355.456


{{Val list|legend=1| 10, 17c, 27e }}
{{Val list|legend=1| 10, 17c, 27e }}


Badness: 0.0226
Badness: 0.0226
</div></div>


= Passion =
= Passion =
== 5-limit ==
== 5-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~16/15 = 98.670
EDO generators: [[25edo|2\25]], [[37edo|3\37]], [[49edo|4\49]]
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">


Subgroup: 2.3.5
Subgroup: 2.3.5
Line 826: Line 476:


Mapping generators: 2, 16/15
Mapping generators: 2, 16/15
POTE generator: ~16/15 = 98.670


{{Val list|legend=1| 12, 49, 61, 73 }}
{{Val list|legend=1| 12, 49, 61, 73 }}


Badness: 0.1686
Badness: 0.1686
</div></div>


== 7-limit ==
== 7-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~16/15 = 98.153
EDO generators: [[25edo|2\25]], [[37edo|3\37]], [[49edo|4\49]]
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">


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 855: Line 493:
Mapping generators: 2, 16/15
Mapping generators: 2, 16/15


Wedgie: {{wedgie| 5 -4 -10 -18 -30 -12 }}
{{Multival|legend=1| 5 -4 -10 -18 -30 -12 }}
 
POTE generator: ~16/15 = 98.153


{{Val list|legend=1| 12, 37, 49, 110bcd }}
{{Val list|legend=1| 12, 37, 49, 110bcd }}


Badness: 0.0623
Badness: 0.0623
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~16/15 = 98.019
EDO generators: [[25edo|2\25]], [[37edo|3\37]], [[49edo|4\49]]
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">


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 882: Line 508:


Mapping: [{{val| 1 2 2 2 2 }}, {{val| 0 -5 4 10 18 }}]
Mapping: [{{val| 1 2 2 2 2 }}, {{val| 0 -5 4 10 18 }}]
POTE generator: ~16/15 = 98.019


{{Val list|legend=1| 12, 37, 49 }}
{{Val list|legend=1| 12, 37, 49 }}


Badness: 0.0408
Badness: 0.0408
</div></div>


== 13-limit ==
== 13-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~16/15 = 97.910
EDO generators: [[25edo|2\25]], [[37edo|3\37]], [[49edo|4\49]]
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">


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
Line 908: Line 522:


Mapping: [{{val| 1 2 2 2 2 2 }}, {{val| 0 -5 4 10 18 21 }}]
Mapping: [{{val| 1 2 2 2 2 2 }}, {{val| 0 -5 4 10 18 21 }}]
POTE generator: ~16/15 = 97.910


{{Val list|legend=1| 12f, 25f, 37, 49f }}
{{Val list|legend=1| 12f, 25f, 37, 49f }}


Badness: 0.0309
Badness: 0.0309
</div></div>


= Fervor =
= Fervor =
== 5-limit ==
== 5-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~64/45 = 577.705
EDO generators: [[25edo|12\25]], [[27edo|13\27]]
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">


Subgroup: 2.3.5
Subgroup: 2.3.5
Line 935: Line 537:


Mapping: [{{val| 1 4 -2 }}, {{val| 0 -5 9 }}]
Mapping: [{{val| 1 4 -2 }}, {{val| 0 -5 9 }}]
POTE generator: ~64/45 = 577.705


{{Val list|legend=1| 25, 27 }}
{{Val list|legend=1| 25, 27 }}


Badness: 0.8526
Badness: 0.8526
</div></div>


== 7-limit ==
== 7-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~7/5 = 577.777
EDO generators: [[25edo|12\25]], [[27edo|13\27]]
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">


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 962: Line 552:
Mapping: [{{val| 1 4 -2 -2 }}, {{val| 0 -5 9 10 }}]
Mapping: [{{val| 1 4 -2 -2 }}, {{val| 0 -5 9 10 }}]


Wedgie: {{wedgie| 5 -9 -10 -26 -30 2 }}
{{Multival|legend=1| 5 -9 -10 -26 -30 2 }}
 
POTE generator: ~7/5 = 577.777


{{Val list|legend=1| 25, 27 }}
{{Val list|legend=1| 25, 27 }}


Badness: 0.1085
Badness: 0.1085
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~7/5 = 577.850
EDO generators: [[25edo|12\25]], [[27edo|13\27]]
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">


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 989: Line 567:


Mapping: [{{val| 1 4 -2 -2 3 }}, {{val| 0 -5 9 10 1 }}]
Mapping: [{{val| 1 4 -2 -2 3 }}, {{val| 0 -5 9 10 1 }}]
POTE generator: ~7/5 = 577.850


{{Val list|legend=1| 25e, 27e }}
{{Val list|legend=1| 25e, 27e }}


Badness: 0.0521
Badness: 0.0521
</div></div>


== 13-limit ==
== 13-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~7/5 = 578.060
EDO generators: [[25edo|12\25]], [[27edo|13\27]]
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">


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
Line 1,015: Line 581:


Mapping: [{{val| 1 4 -2 -2 3 -4 }}, {{val| 0 -5 9 10 1 16 }}]
Mapping: [{{val| 1 4 -2 -2 3 -4 }}, {{val| 0 -5 9 10 1 16 }}]
POTE generator: ~7/5 = 578.060


{{Val list|legend=1| 27e }}
{{Val list|legend=1| 27e }}


Badness: 0.0397
Badness: 0.0397
</div></div>


= Progress =
= Progress =
== 5-limit ==
== 5-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~64/45 = 561.264
EDO generators: [[15edo|7\15]], [[17edo|8\17]]
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">


Subgroup: 2.3.5
Subgroup: 2.3.5
Line 1,042: Line 596:


Mapping: [{{val| 1 0 5 }}, {{val| 0 3 -5 }}]
Mapping: [{{val| 1 0 5 }}, {{val| 0 3 -5 }}]
POTE generator: ~64/45 = 561.264


{{Val list|legend=1| 15, 32c, 47bc, 62bc }}
{{Val list|legend=1| 15, 32c, 47bc, 62bc }}


Badness: 0.2461
Badness: 0.2461
</div></div>


== 7-limit ==
== 7-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~7/5 = 562.122
EDO generators: [[15edo|7\15]], [[17edo|8\17]]
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">


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 1,069: Line 611:
Mapping: [{{val| 1 0 5 6 }}, {{val| 0 3 -5 -6 }}]
Mapping: [{{val| 1 0 5 6 }}, {{val| 0 3 -5 -6 }}]


Wedgie: {{wedgie| 3 -5 -6 -15 -18 0 }}
{{Multival|legend=1| 3 -5 -6 -15 -18 0 }}
 
POTE generator: ~7/5 = 562.122


{{Val list|legend=1| 15, 32c, 79bcc, 111bcc }}
{{Val list|legend=1| 15, 32c, 79bcc, 111bcc }}


Badness: 0.0664
Badness: 0.0664
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~7/5 = 562.085
EDO generators: [[15edo|7\15]], [[17edo|8\17]]
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">


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 1,096: Line 626:


Mapping: [{{val| 1 0 5 6 4 }}, {{val| 0 3 -5 -6 -1 }}]
Mapping: [{{val| 1 0 5 6 4 }}, {{val| 0 3 -5 -6 -1 }}]
POTE generator: ~7/5 = 562.085


{{Val list|legend=1| 15, 32c, 47bc, 79bcce }}
{{Val list|legend=1| 15, 32c, 47bc, 79bcce }}


Badness: 0.0310
Badness: 0.0310
</div></div>


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generator: ~7/5 = 562.365
EDO generators: [[15edo|7\15]], [[17edo|8\17]]
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">


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
Line 1,122: Line 640:


Mapping: [{{val| 1 0 5 6 4 0 }}, {{val| 0 3 -5 -6 -1 7 }}]
Mapping: [{{val| 1 0 5 6 4 0 }}, {{val| 0 3 -5 -6 -1 7 }}]
POTE generator: ~7/5 = 562.365


{{Val list|legend=1| 15, 17c, 32cf }}
{{Val list|legend=1| 15, 17c, 32cf }}


Badness: 0.0262
Badness: 0.0262
</div></div>


=== Progressive ===
=== Progressive ===
Period: 1\1
Optimal ([[POTE]]) generator: ~7/5 = 563.239
EDO generators: [[15edo|7\15]], [[17edo|8\17]]
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">


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
Line 1,148: Line 654:


Mapping: [{{val| 1 0 5 6 4 9 }}, {{val| 0 3 -5 -6 -1 -10 }}]
Mapping: [{{val| 1 0 5 6 4 9 }}, {{val| 0 3 -5 -6 -1 -10 }}]
POTE generator: ~7/5 = 563.239


{{Val list|legend=1| 15f, 17c, 32c, 49c }}
{{Val list|legend=1| 15f, 17c, 32c, 49c }}


Badness: 0.0327
Badness: 0.0327
</div></div>


= Sixix =
= Sixix =
== 5-limit ==
== 5-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~6/5 = 338.365
EDO generators: [[25edo|7\25]], [[32edo|9\32]]
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">


Subgroup: 2.3.5
Subgroup: 2.3.5
Line 1,175: Line 669:


Mapping: [{{val| 1 3 4 }}, {{val| 0 -5 -6 }}]
Mapping: [{{val| 1 3 4 }}, {{val| 0 -5 -6 }}]
POTE generator: ~6/5 = 338.365


{{Val list|legend=1| 7, 25, 32 }}
{{Val list|legend=1| 7, 25, 32 }}


Badness: 0.1531
Badness: 0.1531
</div></div>


== 7-limit ==
== 7-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~6/5 = 337.4419
EDO generators: [[25edo|7\25]], [[32edo|9\32]]
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">


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 1,201: Line 683:


Mapping: [{{val| 1 3 4 0 }}, {{val| 0 -5 -6 10 }}]
Mapping: [{{val| 1 3 4 0 }}, {{val| 0 -5 -6 10 }}]
POTE generator: ~6/5 = 337.4419


{{Val list|legend=1| 7, 25, 32 }}
{{Val list|legend=1| 7, 25, 32 }}
</div></div>


[[Category:Theory]]
[[Category:Theory]]
Retrieved from "https://en.xen.wiki/w/Archytas_clan"