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]]

Revision as of 09:26, 27 March 2021

The archytas clan tempers out the Archytas comma, 64/63. This means that four stacked 3/2 fifths equal a 9/7 major third. (Note the similarity in function to 81/80 in meantone, where four stacked 3/2 fifths equal a 5/4 major third.) This leads to tunings with 3s and 7s quite sharp, such as those of 22edo.

Adding 50/49 to the list of commas gives pajara, 36/35 gives dominant, 16/15 gives mother, 126/125 gives augene, 28/27 gives blacksmith, 245/243 gives superpyth, 250/243 gives porcupine, 686/675 gives beatles, 360/343 gives schism, 3125/3087 gives passion, 2430/2401 gives quasisuper, and 4375/4374 gives modus.

Discussed under their respective 5-limit families are mother, dominant, augene, porcupine, pajara, catalan, modus, and immunized. The rest are considered below.

Archy

Subgroup: 2.3.7

Comma list: 64/63

Sval mapping: [⟨1 0 6], ⟨0 1 -2]]

Sval mapping generators: ~2, ~3

Gencom mapping: [⟨1 1 0 4], ⟨0 1 0 -2]]

Gencom: [2 3/2; 64/63]

POTE generator: ~3/2 = 709.321

Template:Val list

Scales: archy5, archy7, archy12

Supra

Subgroup: 2.3.7.11

Comma list: 64/63, 99/98

Sval mapping: [⟨1 0 6 13], ⟨0 1 -2 -6]]

Sval mapping generators: ~2, ~3

Gencom mapping: [⟨1 1 0 4 7], ⟨0 1 0 -2 -6]]

Gencom: [2 3/2; 64/63 99/98]

POTE generator: ~3/2 = 707.192

Template:Val list

Scales: supra7, supra12

Supraphon

Subgroup: 2.3.7.11.13

Comma list: 64/63, 78/77, 99/98

Sval mapping: [⟨1 0 6 13 18], ⟨0 1 -2 -6 -9]]

Sval mapping generators: ~2, ~3

Gencom mapping: [⟨1 1 0 4 7 9], ⟨0 1 0 -2 -6 -9]]

Gencom: [2 3/2; 64/63 78/77 99/98]

POTE generator: ~3/2 = 706.137

Template:Val list

Scales: supra7, supra12

Suhajira

Subgroup: 2.3.7.11

Comma list: 64/63, 243/242

Sval mapping: [⟨1 1 4 2], ⟨0 2 -4 5]]

Sval mapping generators: ~2, ~3

Gencom mapping: [⟨1 1 0 4 2], ⟨0 1 0 -4 5]]

Gencom: [2 3/2; 64/63 99/98]

POTE generator: ~11/9 = 353.958

Template:Val list

Scales: suhajira7, suhajira10, suhajira17

2.3.7.11.13

Subgroup: 2.3.7.11.13

Comma list: 64/63, 78/77, 144/143

Sval mapping: [⟨1 1 4 2 4], ⟨0 2 -4 5 -1]]

Sval mapping generators: ~2, ~3

Gencom mapping: [⟨1 1 0 4 2 4], ⟨0 1 0 -4 5 -1]]

Gencom: [2 3/2; 64/63 78/77 99/98]

POTE generator: ~11/9 = 353.775

Template:Val list

Scales: suhajira7, suhajira10, suhajira17

Superpyth

Main article: Superpyth

Subgroup: 2.3.5.7

Comma list: 64/63, 245/243

Mapping: [⟨1 0 -12 6], ⟨0 1 9 -2]]

Wedgie: ⟨⟨ 1 9 -2 12 -6 -30 ]]

POTE generator: ~3/2 = 710.291

Template:Val list

Badness: 0.0323

11-limit

Subgroup: 2.3.5.7.11

Comma list: 64/63, 100/99, 245/243

Mapping: [⟨1 0 -12 6 -22], ⟨0 1 9 -2 16]]

POTE generator: ~3/2 = 710.175

Template:Val list

Badness: 0.0250

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 64/63, 78/77, 91/90, 100/99

Mapping: [⟨1 0 -12 6 -22 -17], ⟨0 1 9 -2 16 13]]

POTE generator: ~3/2 = 710.479

Template:Val list

Badness: 0.0247

Suprapyth

Subgroup: 2.3.5.7.11

Comma list: 55/54, 64/63, 99/98

Mapping: [⟨1 0 -12 6 13], ⟨0 1 9 -2 -6]]

POTE generator: ~3/2 = 709.495

Template:Val list

Badness: 0.0328

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 55/54, 64/63, 65/63, 99/98

Mapping: [⟨1 0 -12 6 13 18], ⟨0 1 9 -2 -6 -9]]

POTE generator: ~3/2 = 708.703

Template:Val list

Badness: 0.0363

Quasisuper

Subgroup: 2.3.5.7

Comma list: 64/63, 2430/2401

Mapping: [⟨1 0 23 6], ⟨0 1 -13 -2]]

Wedgie: ⟨⟨ 1 -13 -2 -23 -2 -6 32 ]]

POTE generator: ~3/2 = 708.328

Template:Val list

Badness: 0.0638

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).

Subgroup: 2.3.5.7.11

Comma list: 64/63, 99/98, 121/120

Mapping: [⟨1 2 -3 2 1], ⟨0 -1 13 2 6]]

POTE generator: ~3/2 = 708.205

Template:Val list

Badness: 0.0322

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 64/63, 78/77, 91/90, 121/120

Mapping: [⟨1 0 23 6 13 18], ⟨0 1 -13 -2 -6 -9]]

POTE generator: ~3/2 = 708.004

Template:Val list

Badness: 0.0302

Quasisoup

Subgroup: 2.3.5.7.11

Comma list: 55/54, 64/63, 2430/2401

Mapping: [⟨1 0 23 6 -22], ⟨0 1 -13 -2 16]]

POTE generator: ~3/2 = 709.021

Template:Val list

Badness: 0.0835

Schism

See also: Schismatic family § Schism

Subgroup: 2.3.5.7

Comma list: 64/63, 360/343

Mapping: [⟨1 0 15 6], ⟨0 1 -8 -2]]

Wedgie: ⟨⟨ 1 -8 -2 -15 -6 18 ]]

POTE generator: ~3/2 = 701.556

Template:Val list

Badness: 0.0566

11-limit

Subgroup: 2.3.5.7.11

Comma list: 45/44, 64/63, 99/98

Mapping: [⟨1 0 15 6 13], ⟨0 1 -8 -2 -6]]

POTE generator: ~3/2 = 702.136

Template:Val list

Badness: 0.0375

Blacksmith

blacksmith10.jpg
Lattice of blacksmith

5-limit (blackwood)

Subgroup: 2.3.5

Comma list: 256/243

Mapping: [⟨5 8 0], ⟨0 0 1]]

Mapping generators: ~9/8, ~5

POTE generator: ~5/4 = 399.594

Template:Val list

Badness: 0.0638

7-limit

Subgroup: 2.3.5.7

Comma list: 28/27, 49/48

Mapping: [⟨5 8 0 14], ⟨0 0 1 0]]

Mapping generators: ~7/6, ~5

Wedgie: ⟨⟨ 0 5 0 8 0 -14 ]]

POTE generator: ~5/4 = 392.767

Template:Val list

Badness: 0.0256

11-limit

Subgroup: 2.3.5.7.11

Comma list: 28/27, 49/48, 55/54

Mapping: [⟨5 8 0 14 29], ⟨0 0 1 0 -1]]

POTE generator: ~5/4 = 394.948

Template:Val list

Badness: 0.0246

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 28/27, 40/39, 49/48, 55/54

Mapping: [⟨5 8 0 14 29 7], ⟨0 0 1 0 -1 1]]

POTE generator: ~5/4 = 391.0367

Template:Val list

Badness: 0.0205

Farrier

Subgroup: 2.3.5.7.11

Comma list: 28/27, 49/48, 77/75

Mapping: [⟨5 8 0 14 -6], ⟨0 0 1 0 2]]

POTE generator: ~5/4 = 398.070

Template:Val list

Badness: 0.0292

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 28/27, 40/39, 49/48, 66/65

Mapping: [⟨5 8 0 14 -6 7], ⟨0 0 1 0 2 1]]

POTE generator: ~5/4 = 396.812

Template:Val list

Badness: 0.0223

Ferrum

Subgroup: 2.3.5.7.11

Comma list: 28/27, 35/33, 49/48

Mapping: [⟨5 8 0 14 6], ⟨0 0 1 0 1]]

POTE generator: ~5/4 = 374.763

Template:Val list

Badness: 0.0309

Beatles

5-limit

Subgroup: 2.3.5

Comma list: 524288/492075

Mapping: [⟨1 1 5], ⟨0 2 -9]]

POTE generator: ~512/405 = 355.930

Template:Val list

Badness: 0.3585

7-limit

Subgroup: 2.3.5.7

Comma list: 64/63, 686/675

Mapping: [⟨1 1 5 4], ⟨0 2 -9 -4]]

Wedgie: ⟨⟨ 2 -9 -4 -19 -12 16 ]]

POTE generator: ~49/40 = 355.904

Template:Val list

Badness: 0.0459

Music

11-limit

Subgroup: 2.3.5.7.11

Comma list: 64/63, 100/99, 686/675

Mapping: [⟨1 1 5 4 10], ⟨0 2 -9 -4 -22]]

POTE generator: ~49/40 = 356.140

Template:Val list

Badness: 0.0456

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 64/63, 91/90, 100/99, 169/168

Mapping: [⟨1 1 5 4 10 4], ⟨0 2 -9 -4 -22 -1]]

POTE generator: ~16/13 = 356.229

Template:Val list

Badness: 0.0302

Ringo

Subgroup: 2.3.5.7.11

Comma list: 56/55, 64/63, 540/539

Mapping: [⟨1 1 5 4 2], ⟨0 2 -9 -4 5]]

POTE generator: ~11/9 = 355.419

Template:Val list

Badness: 0.0329

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 56/55, 64/63, 78/77, 91/90

Mapping: [⟨1 1 5 4 2 4], ⟨0 2 -9 -4 5 -1]]

POTE generator: ~11/9 = 355.456

Template:Val list

Badness: 0.0226

Passion

5-limit

Subgroup: 2.3.5

Comma list: 262144/253125

Mapping: [⟨1 2 2], ⟨0 -5 4]]

Mapping generators: 2, 16/15

POTE generator: ~16/15 = 98.670

Template:Val list

Badness: 0.1686

7-limit

Subgroup: 2.3.5.7

Comma list: 64/63, 3125/3087

Mapping: [⟨1 2 2 2], ⟨0 -5 4 10]]

Mapping generators: 2, 16/15

Wedgie: ⟨⟨ 5 -4 -10 -18 -30 -12 ]]

POTE generator: ~16/15 = 98.153

Template:Val list

Badness: 0.0623

11-limit

Subgroup: 2.3.5.7.11

Comma list: 64/63, 100/99, 1375/1372

Mapping: [⟨1 2 2 2 2], ⟨0 -5 4 10 18]]

POTE generator: ~16/15 = 98.019

Template:Val list

Badness: 0.0408

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 64/63, 100/99, 196/195, 275/273

Mapping: [⟨1 2 2 2 2 2], ⟨0 -5 4 10 18 21]]

POTE generator: ~16/15 = 97.910

Template:Val list

Badness: 0.0309

Fervor

5-limit

Subgroup: 2.3.5

Comma list: 67108864/61509375

Mapping: [⟨1 4 -2], ⟨0 -5 9]]

POTE generator: ~64/45 = 577.705

Template:Val list

Badness: 0.8526

7-limit

Subgroup: 2.3.5.7

Comma list: 64/63, 9604/9375

Mapping: [⟨1 4 -2 -2], ⟨0 -5 9 10]]

Wedgie: ⟨⟨ 5 -9 -10 -26 -30 2 ]]

POTE generator: ~7/5 = 577.777

Template:Val list

Badness: 0.1085

11-limit

Subgroup: 2.3.5.7.11

Comma list: 56/55, 64/63, 1350/1331

Mapping: [⟨1 4 -2 -2 3], ⟨0 -5 9 10 1]]

POTE generator: ~7/5 = 577.850

Template:Val list

Badness: 0.0521

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 56/55, 64/63, 78/77, 507/500

Mapping: [⟨1 4 -2 -2 3 -4], ⟨0 -5 9 10 1 16]]

POTE generator: ~7/5 = 578.060

Template:Val list

Badness: 0.0397

Progress

5-limit

Subgroup: 2.3.5

Comma list: 32768/30375

Mapping: [⟨1 0 5], ⟨0 3 -5]]

POTE generator: ~64/45 = 561.264

Template:Val list

Badness: 0.2461

7-limit

Subgroup: 2.3.5.7

Comma list: 64/63, 392/375

Mapping: [⟨1 0 5 6], ⟨0 3 -5 -6]]

Wedgie: ⟨⟨ 3 -5 -6 -15 -18 0 ]]

POTE generator: ~7/5 = 562.122

Template:Val list

Badness: 0.0664

11-limit

Subgroup: 2.3.5.7.11

Comma list: 56/55, 64/63, 77/75

Mapping: [⟨1 0 5 6 4], ⟨0 3 -5 -6 -1]]

POTE generator: ~7/5 = 562.085

Template:Val list

Badness: 0.0310

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 56/55, 64/63, 66/65, 77/75

Mapping: [⟨1 0 5 6 4 0], ⟨0 3 -5 -6 -1 7]]

POTE generator: ~7/5 = 562.365

Template:Val list

Badness: 0.0262

Progressive

Subgroup: 2.3.5.7.11.13

Comma list: 26/25, 56/55, 64/63, 77/75

Mapping: [⟨1 0 5 6 4 9], ⟨0 3 -5 -6 -1 -10]]

POTE generator: ~7/5 = 563.239

Template:Val list

Badness: 0.0327

Sixix

5-limit

Subgroup: 2.3.5

Comma list: 3125/2916

Mapping: [⟨1 3 4], ⟨0 -5 -6]]

POTE generator: ~6/5 = 338.365

Template:Val list

Badness: 0.1531

7-limit

Subgroup: 2.3.5.7

Comma list: 64/63, 3125/2916

Mapping: [⟨1 3 4 0], ⟨0 -5 -6 10]]

POTE generator: ~6/5 = 337.4419

Template:Val list

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