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Archytas clan: Difference between revisions

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Move blacksmith below schism for being weak extension
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</div></div>
</div></div>


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


[[File:blacksmith10.jpg|alt=blacksmith10.jpg|thumb|Lattice of blacksmith]]
Period: 1\1


== 5-limit (blackwood) ==
Optimal ([[POTE]]) generator: ~3/2 = 710.291


Period: 1\5
EDO generators: [[17edo|10\17]], [[22edo|13\22]], [[27edo|16\27]], [[49edo|29\49]]
 
Optimal ([[POTE]]) generator: ~5/4 = 399.594
 
EDO generators: [[10edo|3\10]], [[15edo|4\15]]


Scales (Scala files):  
Scales (Scala files):  
Line 173: Line 170:
<div class="mw-collapsible-content">
<div class="mw-collapsible-content">


Subgroup: 2.3.5
Subgroup: 2.3.5.7


Comma list: 256/243
Comma list: 64/63, 245/243


Mapping: [{{val| 5 8 0 }}, {{val| 0 0 1 }}]
Mapping: [{{val| 1 0 -12 6 }}, {{val| 0 1 9 -2 }}]


Mapping generators: ~9/8, ~5
Wedgie: {{wedgie| 1 9 -2 12 -6 -30 }}


{{Val list|legend=1| 5, 10, 15 }}
{{Val list|legend=1| 5, 17, 22, 27, 49 }}


Badness: 0.0638
Badness: 0.0323


</div></div>
</div></div>


== 7-limit ==
== 11-limit ==


Period: 1\5
Period: 1\1


Optimal ([[POTE]]) generator: ~5/4 = 392.767
Optimal ([[POTE]]) generator: ~3/2 = 710.175


EDO generators: [[10edo|3\10]], [[15edo|4\15]]
EDO generators: [[22edo|13\22]], [[27edo|16\27]], [[49edo|29\49]]


Scales (Scala files):  
Scales (Scala files):  
Line 201: Line 198:
<div class="mw-collapsible-content">
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7.11


Comma list: 28/27, 49/48
Comma list: 64/63, 100/99, 245/243


Mapping: [{{val| 5 8 0 14 }}, {{val| 0 0 1 0 }}]
Mapping: [{{val| 1 0 -12 6 -22 }}, {{val| 0 1 9 -2 16 }}]


Mapping generators: ~7/6, ~5
{{Val list|legend=1| 22, 27e, 49 }}


Wedgie: {{wedgie| 0 5 0 8 0 -14 }}
Badness: 0.0250
 
{{Val list|legend=1| 5, 10, 15, 40b, 55b }}
 
Badness: 0.0256


</div></div>
</div></div>


== 11-limit ==
=== 13-limit ===


Period: 1\5
Period: 1\1


Optimal ([[POTE]]) generator: ~5/4 = 394.948
Optimal ([[POTE]]) generator: ~3/2 = 710.479


EDO generators: [[10edo|3\10]], [[15edo|4\15]]
EDO generators: [[22edo|13\22]], [[27edo|16\27]], [[49edo|29\49]]


Scales (Scala files):  
Scales (Scala files):  
Line 231: Line 224:
<div class="mw-collapsible-content">
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11.13


Comma list: 28/27, 49/48, 55/54
Comma list: 64/63, 78/77, 91/90, 100/99


Mapping: [{{val| 5 8 0 14 29 }}, {{val| 0 0 1 0 -1 }}]
Mapping: [{{val| 1 0 -12 6 -22 -17 }}, {{val| 0 1 9 -2 16 13 }}]


{{Val list|legend=1| 5, 10, 15, 40be, 55be, 70bde, 85bcde}}
{{Val list|legend=1| 22, 27e, 49, 76bcde }}


Badness: 0.0246
Badness: 0.0247


</div></div>
</div></div>


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


Period: 1\5
Period: 1\1


Optimal ([[POTE]]) generator: ~5/4 = 391.0367
Optimal ([[POTE]]) generator: ~3/2 = 709.495


EDO generators: [[10edo|3\10]], [[15edo|4\15]]
EDO generators: [[17edo|10\17]], [[22edo|13\22]]


Scales (Scala files):  
Scales (Scala files):  
Line 257: Line 250:
<div class="mw-collapsible-content">
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11


Comma list: 28/27, 40/39, 49/48, 55/54
Comma list: 55/54, 64/63, 99/98


Mapping: [{{val| 5 8 0 14 29 7 }}, {{val| 0 0 1 0 -1 1 }}]
Mapping: [{{val| 1 0 -12 6 13 }}, {{val| 0 1 9 -2 -6 }}]


{{Val list|legend=1| 5, 10, 15, 25e, 40bef}}
{{Val list|legend=1| 17, 22 }}


Badness: 0.0205
Badness: 0.0328


</div></div>
</div></div>


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


Period: 1\5
Period: 1\1


Optimal ([[POTE]]) generator: ~5/4 = 398.070
Optimal ([[POTE]]) generator: ~3/2 = 708.703


EDO generators: [[10edo|3\10]], [[15edo|4\15]]
EDO generators: [[17edo|10\17]], [[22edo|13\22]]


Scales (Scala files):  
Scales (Scala files):  
Line 283: Line 276:
<div class="mw-collapsible-content">
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11.13


Comma list: 28/27, 49/48, 77/75
Comma list: 55/54, 64/63, 65/63, 99/98


Mapping: [{{val| 5 8 0 14 -6 }}, {{val| 0 0 1 0 2 }}]
Mapping: [{{val| 1 0 -12 6 13 18 }}, {{val| 0 1 9 -2 -6 -9 }}]


{{Val list|legend=1| 5e, 10e, 15 }}
{{Val list|legend=1| 17, 22, 83cdf }}


Badness: 0.0292
Badness: 0.0363


</div></div>
</div></div>


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


Period: 1\5
Period: 1\1


Optimal ([[POTE]]) generator: ~5/4 = 396.812
Optimal ([[POTE]]) generator: ~3/2 = 708.328


EDO generators: [[10edo|3\10]], [[15edo|4\15]]
EDO generators: [[17edo|10\17]], [[22edo|13\22]], [[39edo|23\39]], [[61edo|36\61]]


Scales (Scala files):  
Scales (Scala files):  
Line 309: Line 302:
<div class="mw-collapsible-content">
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7
 
Comma list: 64/63, 2430/2401


Comma list: 28/27, 40/39, 49/48, 66/65
Mapping: [{{val| 1 0 23 6 }}, {{val| 0 1 -13 -2 }}]


Mapping: [{{val| 5 8 0 14 -6 7 }}, {{val| 0 0 1 0 2 1 }}]
Wedgie: {{wedgie| 1 -13 -2 -23 -2 -6 32 }}


{{Val list|legend=1| 5e, 10e, 15 }}
{{Val list|legend=1| 17c, 22, 61d }}


Badness: 0.0223
Badness: 0.0638


</div></div>
</div></div>


== Ferrum ==
== 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).


Period: 1\5
Period: 1\1


Optimal ([[POTE]]) generator: ~5/4 = 374.763
Optimal ([[POTE]]) generator: ~3/2 = 708.205


EDO generators: [[10edo|3\10]]
EDO generators: [[17edo|10\17]], [[22edo|13\22]], [[39edo|23\39]], [[61edo|36\61]]


Scales (Scala files):  
Scales (Scala files):  
Line 337: Line 333:
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 28/27, 35/33, 49/48
Comma list: 64/63, 99/98, 121/120


Mapping: [{{val| 5 8 0 14 6 }}, {{val| 0 0 1 0 1 }}]
Mapping: [{{val| 1 2 -3 2 1 }}, {{val| 0 -1 13 2 6 }}]


{{Val list|legend=1| 5e, 10 }}
{{Val list|legend=1| 17c, 22, 39d, 61d }}


Badness: 0.0309
Badness: 0.0322


</div></div>
</div></div>


= Superpyth =
=== 13-limit ===
{{main| Superpyth }}


Period: 1\1
Period: 1\1


Optimal ([[POTE]]) generator: ~3/2 = 710.291
Optimal ([[POTE]]) generator: ~3/2 = 708.004


EDO generators: [[17edo|10\17]], [[22edo|13\22]], [[27edo|16\27]], [[49edo|29\49]]
EDO generators: [[17edo|10\17]], [[22edo|13\22]], [[39edo|23\39]], [[61edo|36\61]]


Scales (Scala files):  
Scales (Scala files):  
Line 362: Line 357:
<div class="mw-collapsible-content">
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7.11.13


Comma list: 64/63, 245/243
Comma list: 64/63, 78/77, 91/90, 121/120


Mapping: [{{val| 1 0 -12 6 }}, {{val| 0 1 9 -2 }}]
Mapping: [{{val| 1 0 23 6 13 18 }}, {{val| 0 1 -13 -2 -6 -9 }}]


Wedgie: {{wedgie| 1 9 -2 12 -6 -30 }}
{{Val list|legend=1| 17c, 22, 39d, 61df, 100bcdf }}


{{Val list|legend=1| 5, 17, 22, 27, 49 }}
Badness: 0.0302
 
Badness: 0.0323


</div></div>
</div></div>


== 11-limit ==
== Quasisoup ==


Period: 1\1
Period: 1\1


Optimal ([[POTE]]) generator: ~3/2 = 710.175
Optimal ([[POTE]]) generator: ~3/2 = 709.021


EDO generators: [[22edo|13\22]], [[27edo|16\27]], [[49edo|29\49]]
EDO generators: [[22edo|13\22]]


Scales (Scala files):  
Scales (Scala files):  
Line 392: Line 385:
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 64/63, 100/99, 245/243
Comma list: 55/54, 64/63, 2430/2401


Mapping: [{{val| 1 0 -12 6 -22 }}, {{val| 0 1 9 -2 16 }}]
Mapping: [{{val| 1 0 23 6 -22 }}, {{val| 0 1 -13 -2 16 }}]


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


Badness: 0.0250
Badness: 0.0835


</div></div>
</div></div>


=== 13-limit ===
= Schism =
{{see also|Schismatic family #Schism}}


Period: 1\1
Period: 1\1


Optimal ([[POTE]]) generator: ~3/2 = 710.479
Optimal ([[POTE]]) generator: ~3/2 = 701.556


EDO generators: [[22edo|13\22]], [[27edo|16\27]], [[49edo|29\49]]
EDO generators: [[12edo|7\12]], [[17edo|10\17]]


Scales (Scala files):  
Scales (Scala files):  
Line 416: Line 410:
<div class="mw-collapsible-content">
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7
 
Comma list: 64/63, 360/343


Comma list: 64/63, 78/77, 91/90, 100/99
Mapping: [{{val| 1 0 15 6 }}, {{val| 0 1 -8 -2 }}]


Mapping: [{{val| 1 0 -12 6 -22 -17 }}, {{val| 0 1 9 -2 16 13 }}]
Wedgie: {{wedgie| 1 -8 -2 -15 -6 18 }}


{{Val list|legend=1| 22, 27e, 49, 76bcde }}
{{Val list|legend=1| 12, 41d, 53d }}


Badness: 0.0247
Badness: 0.0566


</div></div>
</div></div>


== Suprapyth ==
== 11-limit ==


Period: 1\1
Period: 1\1


Optimal ([[POTE]]) generator: ~3/2 = 709.495
Optimal ([[POTE]]) generator: ~3/2 = 702.136


EDO generators: [[17edo|10\17]], [[22edo|13\22]]
EDO generators: [[12edo|7\12]], [[17edo|10\17]]


Scales (Scala files):  
Scales (Scala files):  
Line 444: Line 440:
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 55/54, 64/63, 99/98
Comma list: 45/44, 64/63, 99/98


Mapping: [{{val| 1 0 -12 6 13 }}, {{val| 0 1 9 -2 -6 }}]
Mapping: [{{val| 1 0 15 6 13 }}, {{val| 0 1 -8 -2 -6 }}]


{{Val list|legend=1| 17, 22 }}
{{Val list|legend=1| 12, 29de, 41de }}


Badness: 0.0328
Badness: 0.0375


</div></div>
</div></div>


=== 13-limit ===
= Blacksmith =
 
[[File:blacksmith10.jpg|alt=blacksmith10.jpg|thumb|Lattice of blacksmith]]
 
== 5-limit (blackwood) ==


Period: 1\1
Period: 1\5


Optimal ([[POTE]]) generator: ~3/2 = 708.703
Optimal ([[POTE]]) generator: ~5/4 = 399.594


EDO generators: [[17edo|10\17]], [[22edo|13\22]]
EDO generators: [[10edo|3\10]], [[15edo|4\15]]


Scales (Scala files):  
Scales (Scala files):  
Line 468: Line 468:
<div class="mw-collapsible-content">
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5
 
Comma list: 256/243


Comma list: 55/54, 64/63, 65/63, 99/98
Mapping: [{{val| 5 8 0 }}, {{val| 0 0 1 }}]


Mapping: [{{val| 1 0 -12 6 13 18 }}, {{val| 0 1 9 -2 -6 -9 }}]
Mapping generators: ~9/8, ~5


{{Val list|legend=1| 17, 22, 83cdf }}
{{Val list|legend=1| 5, 10, 15 }}


Badness: 0.0363
Badness: 0.0638


</div></div>
</div></div>


= Quasisuper =
== 7-limit ==


Period: 1\1
Period: 1\5


Optimal ([[POTE]]) generator: ~3/2 = 708.328
Optimal ([[POTE]]) generator: ~5/4 = 392.767


EDO generators: [[17edo|10\17]], [[22edo|13\22]], [[39edo|23\39]], [[61edo|36\61]]
EDO generators: [[10edo|3\10]], [[15edo|4\15]]


Scales (Scala files):  
Scales (Scala files):  
Line 496: Line 498:
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Comma list: 64/63, 2430/2401
Comma list: 28/27, 49/48
 
Mapping: [{{val| 5 8 0 14 }}, {{val| 0 0 1 0 }}]


Mapping: [{{val| 1 0 23 6 }}, {{val| 0 1 -13 -2 }}]
Mapping generators: ~7/6, ~5


Wedgie: {{wedgie| 1 -13 -2 -23 -2 -6 32 }}
Wedgie: {{wedgie| 0 5 0 8 0 -14 }}


{{Val list|legend=1| 17c, 22, 61d }}
{{Val list|legend=1| 5, 10, 15, 40b, 55b }}


Badness: 0.0638
Badness: 0.0256


</div></div>
</div></div>


== Quasisupra ==
== 11-limit ==
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
Period: 1\5


Optimal ([[POTE]]) generator: ~3/2 = 708.205
Optimal ([[POTE]]) generator: ~5/4 = 394.948


EDO generators: [[17edo|10\17]], [[22edo|13\22]], [[39edo|23\39]], [[61edo|36\61]]
EDO generators: [[10edo|3\10]], [[15edo|4\15]]


Scales (Scala files):  
Scales (Scala files):  
Line 525: Line 528:
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 64/63, 99/98, 121/120
Comma list: 28/27, 49/48, 55/54


Mapping: [{{val| 1 2 -3 2 1 }}, {{val| 0 -1 13 2 6 }}]
Mapping: [{{val| 5 8 0 14 29 }}, {{val| 0 0 1 0 -1 }}]


{{Val list|legend=1| 17c, 22, 39d, 61d }}
{{Val list|legend=1| 5, 10, 15, 40be, 55be, 70bde, 85bcde}}


Badness: 0.0322
Badness: 0.0246


</div></div>
</div></div>
Line 537: Line 540:
=== 13-limit ===
=== 13-limit ===


Period: 1\1
Period: 1\5


Optimal ([[POTE]]) generator: ~3/2 = 708.004
Optimal ([[POTE]]) generator: ~5/4 = 391.0367


EDO generators: [[17edo|10\17]], [[22edo|13\22]], [[39edo|23\39]], [[61edo|36\61]]
EDO generators: [[10edo|3\10]], [[15edo|4\15]]


Scales (Scala files):  
Scales (Scala files):  
Line 551: Line 554:
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 64/63, 78/77, 91/90, 121/120
Comma list: 28/27, 40/39, 49/48, 55/54


Mapping: [{{val| 1 0 23 6 13 18 }}, {{val| 0 1 -13 -2 -6 -9 }}]
Mapping: [{{val| 5 8 0 14 29 7 }}, {{val| 0 0 1 0 -1 1 }}]


{{Val list|legend=1| 17c, 22, 39d, 61df, 100bcdf }}
{{Val list|legend=1| 5, 10, 15, 25e, 40bef}}


Badness: 0.0302
Badness: 0.0205


</div></div>
</div></div>


== Quasisoup ==
== Farrier ==


Period: 1\1
Period: 1\5


Optimal ([[POTE]]) generator: ~3/2 = 709.021
Optimal ([[POTE]]) generator: ~5/4 = 398.070


EDO generators: [[22edo|13\22]]
EDO generators: [[10edo|3\10]], [[15edo|4\15]]


Scales (Scala files):  
Scales (Scala files):  
Line 577: Line 580:
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 55/54, 64/63, 2430/2401
Comma list: 28/27, 49/48, 77/75


Mapping: [{{val| 1 0 23 6 -22 }}, {{val| 0 1 -13 -2 16 }}]
Mapping: [{{val| 5 8 0 14 -6 }}, {{val| 0 0 1 0 2 }}]


{{Val list|legend=1| 22 }}
{{Val list|legend=1| 5e, 10e, 15 }}


Badness: 0.0835
Badness: 0.0292


</div></div>
</div></div>


= Schism =
=== 13-limit ===
{{see also|Schismatic family #Schism}}


Period: 1\1
Period: 1\5


Optimal ([[POTE]]) generator: ~3/2 = 701.556
Optimal ([[POTE]]) generator: ~5/4 = 396.812


EDO generators: [[12edo|7\12]], [[17edo|10\17]]
EDO generators: [[10edo|3\10]], [[15edo|4\15]]


Scales (Scala files):  
Scales (Scala files):  
Line 602: Line 604:
<div class="mw-collapsible-content">
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7.11.13


Comma list: 64/63, 360/343
Comma list: 28/27, 40/39, 49/48, 66/65


Mapping: [{{val| 1 0 15 6 }}, {{val| 0 1 -8 -2 }}]
Mapping: [{{val| 5 8 0 14 -6 7 }}, {{val| 0 0 1 0 2 1 }}]


Wedgie: {{wedgie| 1 -8 -2 -15 -6 18 }}
{{Val list|legend=1| 5e, 10e, 15 }}


{{Val list|legend=1| 12, 41d, 53d }}
Badness: 0.0223
 
Badness: 0.0566


</div></div>
</div></div>


== 11-limit ==
== Ferrum ==


Period: 1\1
Period: 1\5


Optimal ([[POTE]]) generator: ~3/2 = 702.136
Optimal ([[POTE]]) generator: ~5/4 = 374.763


EDO generators: [[12edo|7\12]], [[17edo|10\17]]
EDO generators: [[10edo|3\10]]


Scales (Scala files):  
Scales (Scala files):  
Line 632: Line 632:
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 45/44, 64/63, 99/98
Comma list: 28/27, 35/33, 49/48


Mapping: [{{val| 1 0 15 6 13 }}, {{val| 0 1 -8 -2 -6 }}]
Mapping: [{{val| 5 8 0 14 6 }}, {{val| 0 0 1 0 1 }}]


{{Val list|legend=1| 12, 29de, 41de }}
{{Val list|legend=1| 5e, 10 }}


Badness: 0.0375
Badness: 0.0309


</div></div>
</div></div>
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