Marvel temperaments: Difference between revisions

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== 5-limit ==
== 5-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~16/15 = 125.7549
EDO generators: [[9edo|1\9]], [[10edo|1\10]], [[19edo|2\19]]
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 31: Line 20:
[[Mapping]]: [{{val| 1 2 2 }}, {{val| 0 -4 3 }}]
[[Mapping]]: [{{val| 1 2 2 }}, {{val| 0 -4 3 }}]


[[Wedgie]]: {{wedgie| 4 -3 -14 }}
{{Multival|legend=1| 4 -3 -14 }}
 
[[POTE generator]]: ~16/15 = 125.7549


{{Val list|legend=1| 9, 10, 19, 67c, 86c, 105c }}
{{Val list|legend=1| 9, 10, 19, 67c, 86c, 105c }}
</div></div>


== 7-limit ==
== 7-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~15/14 = 125.608
EDO generators: [[9edo|1\9]], [[10edo|1\10]], [[19edo|2\19]]
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 56: Line 34:
[[Mapping]]: [{{val| 1 2 2 3 }}, {{val| 0 -4 3 -2 }}]
[[Mapping]]: [{{val| 1 2 2 3 }}, {{val| 0 -4 3 -2 }}]


[[Wedgie]]: {{wedgie| 4 -3 2 -14 -8 13 }}
{{Multival|legend=1| 4 -3 2 -14 -8 13 }}
 
[[POTE generator]]: ~15/14 = 125.608


{{Val list|legend=1| 9, 10, 19, 48d, 67cdd, 86cdd }}
{{Val list|legend=1| 9, 10, 19, 48d, 67cdd, 86cdd }}
</div></div>


=== Negra ===
=== Negra ===
This is the 2.3.5.7.13 extension of negri.  
This is the 2.3.5.7.13 extension of negri.  
Period: 1\1
Optimal (POTE) generator: ~14/13 = 125.567
EDO generators: [[9edo|1\9]], [[10edo|1\10]], [[19edo|2\19]]
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: 2.3.5.7.13
Subgroup: 2.3.5.7.13
Line 81: Line 47:
[[Comma list]]: 49/48, 65/64, 91/90
[[Comma list]]: 49/48, 65/64, 91/90


[[Mapping]]: [{{val| 1 2 2 3 4 }}, {{val| 0 -4 3 -2 -3 }}]
[[Sval]] [[Mapping]]: [{{val| 1 2 2 3 4 }}, {{val| 0 -4 3 -2 -3 }}]
 
Gencom mapping: [{{val| 1 2 2 3 0 4 }}, {{val| 0 -4 3 -2 0 -3 }}]


Gencom map: [{{val| 1 2 2 3 0 4 }}, {{val| 0 -4 3 -2 0 -3 }}]
[[Gencom]]: [2 14/13; 49/48 65/64 91/90]


Gencom: [2 14/13; 49/48 65/64 91/90]
POTE generator: ~14/13 = 125.567


{{Val list|legend=1| 9, 10, 19, 48df, 67cddf, 86cddff }}
{{Val list|legend=1| 9, 10, 19, 48df, 67cddf, 86cddff }}
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~15/14 = 126.474
EDO generators: [[9edo|1\9]], [[10edo|1\10]], [[19edo|2\19]]
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 109: Line 64:


Mapping: [{{val| 1 2 2 3 4 }}, {{val| 0 -4 3 -2 -5 }}]
Mapping: [{{val| 1 2 2 3 4 }}, {{val| 0 -4 3 -2 -5 }}]
POTE generator: ~15/14 = 126.474


{{Val list|legend=1| 9, 10, 19 }}
{{Val list|legend=1| 9, 10, 19 }}


[[Badness]]: 0.0262
Badness: 0.0262


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


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generator: ~14/13 = 126.431
EDO generators: [[9edo|1\9]], [[10edo|1\10]], [[19edo|2\19]]
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 133: Line 79:
Comma list: 45/44, 49/48, 56/55, 78/77
Comma list: 45/44, 49/48, 56/55, 78/77


[[POTE generator]]: ~14/13 = 126.431
Mapping: [{{val| 1 2 2 3 4 4 }}, {{val| 0 -4 3 -2 -5 -3 }}]


Mapping: [{{val| 1 2 2 3 4 4 }}, {{val| 0 -4 3 -2 -5 -3 }}]
POTE generator: ~14/13 = 126.431


{{Val list|legend=1| 9, 10, 19 }}
{{Val list|legend=1| 9, 10, 19 }}
</div></div>


== Negril ==
== Negril ==
Period: 1\1
Optimal ([[POTE]]) generator: ~15/14 = 124.767
EDO generators: [[19edo|2\19]], [[29edo|3\29]]
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 159: Line 92:


Mapping: [{{val| 1 2 2 3 2 }}, {{val| 0 -4 3 -2 14 }}]
Mapping: [{{val| 1 2 2 3 2 }}, {{val| 0 -4 3 -2 14 }}]
POTE generator: ~15/14 = 124.767


{{Val list|legend=1| 19, 29, 48d, 77cdd }}
{{Val list|legend=1| 19, 29, 48d, 77cdd }}


Badness: 0.0387
Badness: 0.0387
</div></div>


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generator: ~14/13 = 124.716
EDO generators: [[19edo|2\19]], [[29edo|3\29]]
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 184: Line 106:


Mapping: [{{val| 1 2 2 3 2 4 }}, {{val| 0 -4 3 -2 14 -3 }}]
Mapping: [{{val| 1 2 2 3 2 4 }}, {{val| 0 -4 3 -2 14 -3 }}]
POTE generator: ~14/13 = 124.716


{{Val list|legend=1| 19, 29, 48df, 77cddf }}
{{Val list|legend=1| 19, 29, 48df, 77cddf }}


Badness: 0.0244
Badness: 0.0244
</div></div>


== Negric ==
== Negric ==
Period: 1\1
Optimal ([[POTE]]) generator: ~15/14 = 127.039
EDO generators: [[9edo|1\9]], [[19edo|2\19]]
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 209: Line 120:


Mapping: [{{val| 1 2 2 3 3 }}, {{val| 0 -4 3 -2 4 }}]
Mapping: [{{val| 1 2 2 3 3 }}, {{val| 0 -4 3 -2 4 }}]
POTE generator: ~15/14 = 127.039


{{Val list|legend=1| 9, 19e, 47…, 66…, 85… }}
{{Val list|legend=1| 9, 19e, 47…, 66…, 85… }}


Badness: 0.0306
Badness: 0.0306
</div></div>


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generator: ~14/13 = 127.039
EDO generators: [[9edo|1\9]], [[19edo|2\19]]
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 234: Line 134:


Mapping: [{{val| 1 2 2 3 3 4 }}, {{val| 0 -4 3 -2 4 -3 }}]
Mapping: [{{val| 1 2 2 3 3 4 }}, {{val| 0 -4 3 -2 4 -3 }}]
POTE generator: ~14/13 = 127.039


{{Val list|legend=1| 9, 19e, 47…, 66…, 85… }}
{{Val list|legend=1| 9, 19e, 47…, 66…, 85… }}


Badness: 0.0202
Badness: 0.0202
</div></div>


== Negroni ==
== Negroni ==
Period: 1\1
Optimal ([[POTE]]) generator: ~15/14 = 124.539
EDO generators: [[10edo|1\10]], [[19edo|2\19]], [[29edo|3\29]]
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 259: Line 148:


Mapping: [{{val| 1 2 2 3 5 }}, {{val| 0 -4 3 -2 -15 }}]
Mapping: [{{val| 1 2 2 3 5 }}, {{val| 0 -4 3 -2 -15 }}]
POTE generator: ~15/14 = 124.539


{{Val list|legend=1| 10, 19e, 29, 77cddee }}
{{Val list|legend=1| 10, 19e, 29, 77cddee }}


Badness: 0.0353
Badness: 0.0353
</div></div>


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generator: ~14/13 = 124.545
EDO generators: [[10edo|1\10]], [[19edo|2\19]], [[29edo|3\29]]
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 284: Line 162:


Mapping: [{{val| 1 2 2 3 5 4 }}, {{val| 0 -4 3 -2 -15 -3 }}]
Mapping: [{{val| 1 2 2 3 5 4 }}, {{val| 0 -4 3 -2 -15 -3 }}]
POTE generator: ~14/13 = 124.545


{{Val list|legend=1| 10, 19e, 29, 77cddeef }}
{{Val list|legend=1| 10, 19e, 29, 77cddeef }}


Badness: 0.0216
Badness: 0.0216
</div></div>


== Wilsec ==
== Wilsec ==
Period: 1\1
Optimal ([[POTE]]) generator: ~11/8 = 537.186
EDO generators: [[29edo|13\29]], [[38edo|17\38]]
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 309: Line 176:


Mapping: [{{val| 1 6 -1 5 4 }}, {{val| 0 -8 6 -4 -1 }}]
Mapping: [{{val| 1 6 -1 5 4 }}, {{val| 0 -8 6 -4 -1 }}]
POTE generator: ~11/8 = 537.186


{{Val list|legend=1| 9, 20, 29, 38d, 67cdde }}
{{Val list|legend=1| 9, 20, 29, 38d, 67cdde }}


Badness: 0.0419
Badness: 0.0419
</div></div>


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generator: ~11/8 = 537.208
EDO generators: [[29edo|13\29]], [[38edo|17\38]]
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 334: Line 190:


Mapping: [{{val| 1 6 -1 5 4 7 }}, {{val| 0 -8 6 -4 -1 -6 }}]
Mapping: [{{val| 1 6 -1 5 4 7 }}, {{val| 0 -8 6 -4 -1 -6 }}]
POTE generator: ~11/8 = 537.208


{{Val list|legend=1| 9, 20, 29, 38df, 67cddef }}
{{Val list|legend=1| 9, 20, 29, 38df, 67cddef }}


Badness: 0.0252
Badness: 0.0252
</div></div>


=== 17-limit ===
=== 17-limit ===
Period: 1\1
Optimal ([[POTE]]) generator: ~11/8 = 537.230
EDO generators: [[29edo|13\29]], [[38edo|17\38]]
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: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17
Line 359: Line 204:


Mapping: [{{val| 1 6 -1 5 4 7 -2 }}, {{val| 0 -8 6 -4 -1 -6 11 }}]
Mapping: [{{val| 1 6 -1 5 4 7 -2 }}, {{val| 0 -8 6 -4 -1 -6 11 }}]
POTE generator: ~11/8 = 537.230


{{Val list|legend=1| 9, 20g, 29g, 38df, 67cddefg }}
{{Val list|legend=1| 9, 20g, 29g, 38df, 67cddefg }}


Badness: 0.0218
Badness: 0.0218
</div></div>


=== 19-limit ===
=== 19-limit ===
Period: 1\1
Optimal ([[POTE]]) generator: ~11/8 = 537.214
EDO generators: [[29edo|13\29]], [[38edo|17\38]]
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: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19
Line 384: Line 218:


Mapping: [{{val| 1 6 -1 5 4 7 -2 7 }}, {{val| 0 -8 6 -4 -1 -6 11 -5 }}]
Mapping: [{{val| 1 6 -1 5 4 7 -2 7 }}, {{val| 0 -8 6 -4 -1 -6 11 -5 }}]
POTE generator: ~11/8 = 537.214


{{Val list|legend=1| 9, 20g, 29g, 38df, 67cddefgh }}
{{Val list|legend=1| 9, 20g, 29g, 38df, 67cddefgh }}


Badness: 0.0168
Badness: 0.0168
</div></div>


= Passive =
= Passive =
{{see also | Archytas clan #Passion }}
{{see also | Archytas clan #Passion }}


Period: 1\1
Subgroup: 2.3.5.7
 
Optimal ([[POTE]]) generator: ~16/15 = 98.809
 
EDO generators: [[12edo|1\12]], [[13edo|1\13]]
 
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]]: 225/224, 256/245


Comma list: 225/224, 256/245
[[Mapping]]: [{{val| 1 2 2 3 }}, {{val| 0 -5 4 -2 }}]


Mapping: [{{val| 1 2 2 3 }}, {{val| 0 -5 4 -2 }}]
[[POTE generator]]: ~16/15 = 98.809


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


Badness: 0.0751
[[Badness]]: 0.0751
 
</div></div>


= Wizard =
= Wizard =


: ''For the 5-limit version of this temperament, see [[High badness temperaments #Wizard]].''
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Wizard]].''
Period: 1\2
Optimal ([[POTE]]) generator: ~5/4 = 383.256
EDO generators: [[22edo|7\22]], [[50edo|16\50]], [[72edo|23\72]], [[94edo|30\94]]
Scales (Scala files): [[wizard22]]
<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


Comma list: 225/224, 118098/117649
[[Comma list]]: 225/224, 118098/117649


Mapping: [{{val| 2 1 5 2 }}, {{val| 0 6 -1 10 }}]
[[Mapping]]: [{{val| 2 1 5 2 }}, {{val| 0 6 -1 10 }}]


Mapping generators: ~1225/864, ~245/216
Mapping generators: ~1225/864, ~245/216


Wedgie: {{wedgie| 12 -2 20 -31 -2 52 }}
[[POTE generator]]: ~5/4 = 383.256
 
{{Multival|legend=1| 12 -2 20 -31 -2 52 }}


{{Val list|legend=1| 22, 50, 72, 166, 238c, 310c, 382c }}
{{Val list|legend=1| 22, 50, 72, 166, 238c, 310c, 382c }}


Badness: 0.0408
[[Badness]]: 0.0408


</div></div>
Scales: [[wizard22]]


== 11-limit ==
== 11-limit ==
Period: 1\2
Optimal ([[POTE]]) generator: ~5/4 = 383.232
EDO generators: [[22edo|7\22]], [[50edo|16\50]], [[72edo|23\72]], [[94edo|30\94]]
Scales (Scala files): [[wizard22]]
<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 471: Line 271:


Mapping generators: ~99/70, ~25/22
Mapping generators: ~99/70, ~25/22
POTE generator: ~5/4 = 383.232


{{Val list|legend=1| 22, 50, 72, 166, 238c, 310c }}
{{Val list|legend=1| 22, 50, 72, 166, 238c, 310c }}
Line 476: Line 278:
Badness: 0.0185
Badness: 0.0185


</div></div>
Scales: [[wizard22]]


=== Lizard ===
=== Lizard ===
Period: 1\2
Optimal ([[POTE]]) generator: ~5/4 = 383.389
EDO generators: [[50edo|16\50]], [[72edo|23\72]]
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 499: Line 289:


Mapping generators: ~99/70, ~25/22
Mapping generators: ~99/70, ~25/22
POTE generator: ~5/4 = 383.389


{{Val list|legend=1| 22, 50, 72, 122, 194df }}
{{Val list|legend=1| 22, 50, 72, 122, 194df }}


Badness: 0.0218
Badness: 0.0218
</div></div>


==== 17-limit ====
==== 17-limit ====
Period: 1\2
Optimal ([[POTE]]) generator: ~5/4 = 383.381
EDO generators: [[50edo|16\50]], [[72edo|23\72]]
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: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17
Line 527: Line 305:


Mapping generators: ~17/12, ~17/15
Mapping generators: ~17/12, ~17/15
POTE generator: ~5/4 = 383.381


{{Val list|legend=1| 22, 50, 72, 122g, 194dfg }}
{{Val list|legend=1| 22, 50, 72, 122g, 194dfg }}
Line 535: Line 315:


==== 19-limit ====
==== 19-limit ====
Period: 1\2
Optimal ([[POTE]]) generator: ~5/4 = 383.477
EDO generators: [[50edo|16\50]], [[72edo|23\72]]
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: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19
Line 555: Line 323:


Mapping generators: ~17/12, ~17/15
Mapping generators: ~17/12, ~17/15
POTE generator: ~5/4 = 383.477


{{Val list|legend=1| 22h, 50, 72, 122g, 194dfg }}
{{Val list|legend=1| 22h, 50, 72, 122g, 194dfg }}
Line 563: Line 333:


=== Gizzard ===
=== Gizzard ===
Period: 1\2
Optimal ([[POTE]]) generator: ~5/4 = 383.170
EDO generators: [[72edo|23\72]], [[94edo|30\94]]
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 583: Line 341:


Mapping generators: ~99/70, ~25/22
Mapping generators: ~99/70, ~25/22
POTE generator: ~5/4 = 383.170


{{Val list|legend=1| 72, 166, 238cf }}
{{Val list|legend=1| 72, 166, 238cf }}
Line 591: Line 351:


==== 17-limit ====
==== 17-limit ====
Period: 1\2
Optimal ([[POTE]]) generator: ~5/4 = 383.175
EDO generators: [[72edo|23\72]], [[94edo|30\94]]
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: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17
Line 611: Line 359:


Mapping generators: ~17/12, ~17/15
Mapping generators: ~17/12, ~17/15
POTE generator: ~5/4 = 383.175


{{Val list|legend=1| 72, 166g, 238cfg }}
{{Val list|legend=1| 72, 166g, 238cfg }}
Line 619: Line 369:


==== 19-limit ====
==== 19-limit ====
Period: 1\2
Optimal ([[POTE]]) generator: ~5/4 = 383.138
EDO generators: [[72edo|23\72]], [[94edo|30\94]]
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: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19
Line 639: Line 377:


Mapping generators: ~17/12, ~17/15
Mapping generators: ~17/12, ~17/15
POTE generator: ~5/4 = 383.138


{{Val list|legend=1| 72, 94, 166g }}
{{Val list|legend=1| 72, 94, 166g }}


Badness: 0.0148
Badness: 0.0148
</div></div>


== Mage ==
== Mage ==
Period: 1\2
Optimal ([[POTE]]) generator: ~5/4 = 383.124
EDO generators: [[22edo|7\22]], [[50edo|16\50]], [[72edo|23\72]], [[94edo|30\94]]
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 667: Line 393:


Mapping generators: ~77/54, ~55/48
Mapping generators: ~77/54, ~55/48
POTE generator: ~5/4 = 383.124


{{Val list|legend=1| 22, 50e, 72ee, 94ee }}
{{Val list|legend=1| 22, 50e, 72ee, 94ee }}


Badness: 0.0578
Badness: 0.0578
</div></div>


= Triton =
= Triton =
Line 678: Line 404:
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Stump]].''
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Stump]].''


Period: 1\1
Subgroup: 2.3.5.7
 
Optimal ([[POTE]]) generator: ~7/5 = 568.865
 
EDO generators: [[19edo|9\19]], [[21edo|10\21]]


Scales (Scala files):  
[[Comma list]]: 225/224, 1029/1000


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
[[Mapping]]: [{{val| 1 0 6 7 }}, {{val| 0 3 -7 -8 }}]
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7
{{Multival|legend=1| 3 -7 -8 -18 -21 1 }}


Comma list: 225/224, 1029/1000
[[POTE generator]]: ~7/5 = 568.865
 
Mapping: [{{val| 1 0 6 7 }}, {{val| 0 3 -7 -8 }}]
 
Wedgie: {{wedgie| 3 -7 -8 -18 -21 1 }}


{{Val list|legend=1| 19, 78bd, 97bd }}
{{Val list|legend=1| 19, 78bd, 97bd }}


Badness: 0.0592
[[Badness]]: 0.0592
 
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~7/5 = 569.144
EDO generators: [[19edo|9\19]], [[21edo|10\21]]
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 723: Line 425:


Mapping: [{{val| 1 0 6 7 4 }}, {{val| 0 3 -7 -8 -1 }}]
Mapping: [{{val| 1 0 6 7 4 }}, {{val| 0 3 -7 -8 -1 }}]
POTE generator: ~7/5 = 569.144


{{Val list|legend=1| 19, 59bde, 78bde, 97bde }}
{{Val list|legend=1| 19, 59bde, 78bde, 97bde }}


Badness: 0.0457
Badness: 0.0457
</div></div>


= Tritonic =
= Tritonic =
Line 734: Line 436:
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Tritonic]].''
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Tritonic]].''


Period: 1\1
Subgroup: 2.3.5.7
 
Optimal ([[POTE]]) generator: ~7/5 = 580.286


EDO generators: [[29edo|14\29]], [[31edo|15\31]], [[60edo|29\60]]
[[Comma list]]: 225/224, 50421/50000
 
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: 225/224, 50421/50000
[[Mapping]]: [{{val| 1 4 -3 -3 }}, {{val| 0 -5 11 12 }}]


Mapping: [{{val| 1 4 -3 -3 }}, {{val| 0 -5 11 12 }}]
{{Multival|legend=1| 5 -11 -12 -29 -33 3 }}


Wedgie: {{wedgie| 5 -11 -12 -29 -33 3 }}
[[POTE generator]]: ~7/5 = 580.286


{{Val list|legend=1| 29, 31, 60, 91, 122, 213bcd }}
{{Val list|legend=1| 29, 31, 60, 91, 122, 213bcd }}
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~7/5 = 580.267
EDO generators: [[29edo|14\29]], [[31edo|15\31]], [[60edo|29\60]]
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 777: Line 455:


Mapping: [{{val| 1 4 -3 -3 2 }}, {{val| 0 -5 11 12 3 }}]
Mapping: [{{val| 1 4 -3 -3 2 }}, {{val| 0 -5 11 12 3 }}]
POTE generator: ~7/5 = 580.267


{{Val list|legend=1| 29, 31, 60e }}
{{Val list|legend=1| 29, 31, 60e }}


Badness: 0.0237
Badness: 0.0237
</div></div>


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generator: ~7/5 = 580.108
EDO generators: [[29edo|14\29]], [[31edo|15\31]], [[60edo|29\60]]
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 803: Line 469:


Mapping: [{{val| 1 4 -3 -3 2 -5 }}, {{val| 0 -5 11 12 3 18 }}]
Mapping: [{{val| 1 4 -3 -3 2 -5 }}, {{val| 0 -5 11 12 3 18 }}]
POTE generator: ~7/5 = 580.108


{{Val list|legend=1| 29, 31, 60e, 151cde }}
{{Val list|legend=1| 29, 31, 60e, 151cde }}


Badness: 0.0230
Badness: 0.0230
</div></div>


== Tritoni ==
== Tritoni ==
Period: 1\1
Optimal ([[POTE]]) generator: ~7/5 = 580.389
EDO generators: [[31edo|15\31]], [[91edo|44\91]], [[122edo|59\122]]
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 829: Line 483:


Mapping: [{{val| 1 4 -3 -3 17 }}, {{val| 0 -5 11 12 -28 }}]
Mapping: [{{val| 1 4 -3 -3 17 }}, {{val| 0 -5 11 12 -28 }}]
POTE generator: ~7/5 = 580.389


{{Val list|legend=1| 31, 91, 122, 153d }}
{{Val list|legend=1| 31, 91, 122, 153d }}


Badness: 0.0455
Badness: 0.0455
</div></div>


= Merman =
= Merman =
Line 840: Line 494:
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Merman]].''
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Merman]].''


Period: 1\1
Subgroup: 2.3.5.7
 
Optimal ([[POTE]]) generator: ~7/5 = 585.585
 
EDO generators: [[41edo|20\41]], [[43edo|21\43]], [[84edo|41\84]]
 
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]]: 225/224, 2500000/2470629


Comma list: 225/224, 2500000/2470629
[[Mapping]]: [{{val| 1 5 -5 -5 }}, {{val| 0 -7 15 16 }}]


Mapping: [{{val| 1 5 -5 -5 }}, {{val| 0 -7 15 16 }}]
{{Multival|legend=1| 7 -15 -16 -40 -45 5 }}


Wedgie: {{wedgie| 7 -15 -16 -40 -45 5 }}
[[POTE generator]]: ~7/5 = 585.585


{{Val list|legend=1| 41, 84, 125 }}
{{Val list|legend=1| 41, 84, 125 }}


Badness: 0.0551
[[Badness]]: 0.0551
 
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~7/5 = 585.606
EDO generators: [[41edo|20\41]], [[43edo|21\43]], [[84edo|41\84]]
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 885: Line 515:


Mapping: [{{val| 1 5 -5 -5 2 }}, {{val| 0 -7 15 16 3 }}]
Mapping: [{{val| 1 5 -5 -5 2 }}, {{val| 0 -7 15 16 3 }}]
POTE generator: ~7/5 = 585.606


{{Val list|legend=1| 41, 84, 125e }}
{{Val list|legend=1| 41, 84, 125e }}


Badness: 0.0364
Badness: 0.0364
</div></div>


== 13-limit ==
== 13-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~7/5 = 585.657
EDO generators: [[41edo|20\41]], [[43edo|21\43]], [[84edo|41\84]]
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 911: Line 529:


Mapping: [{{val| 1 5 -5 -5 2 12 }}, {{val| 0 -7 15 16 3 -17 }}]
Mapping: [{{val| 1 5 -5 -5 2 12 }}, {{val| 0 -7 15 16 3 -17 }}]
POTE generator: ~7/5 = 585.657


{{Val list|legend=1| 41, 84, 125e, 209ef, 293ef }}
{{Val list|legend=1| 41, 84, 125e, 209ef, 293ef }}


Badness: 0.0275
Badness: 0.0275
</div></div>


= Septimin =
= Septimin =
Line 922: Line 540:
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Septimin]].''
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Septimin]].''


Period: 1\1
Subgroup: 2.3.5.7
 
Optimal ([[POTE]]) generator: ~7/6 = 263.632
 
EDO generators: [[41edo|9\41]], [[50edo|11\50]], [[91edo|20\91]]
 
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]]: 225/224, 84035/82944


Comma list: 225/224, 84035/82944
[[Mapping]]: [{{val| 1 4 1 5 }}, {{val| 0 -11 6 -10 }}]


Mapping: [{{val| 1 4 1 5 }}, {{val| 0 -11 6 -10 }}]
{{Multival|legend=1| 11 -6 10 -35 -15 40 }}


Wedgie: {{wedgie| 11 -6 10 -35 -15 40 }}
[[POTE generator]]: ~7/6 = 263.632


{{Val list|legend=1| 41, 91, 132 }}
{{Val list|legend=1| 41, 91, 132 }}
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~7/6 = 263.634
EDO generators: [[41edo|9\41]], [[50edo|11\50]], [[91edo|20\91]]
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 965: Line 559:


Mapping: [{{val| 1 4 1 5 5 }}, {{val| 0 -11 6 -10 -7 }}]
Mapping: [{{val| 1 4 1 5 5 }}, {{val| 0 -11 6 -10 -7 }}]
POTE generator: ~7/6 = 263.634


{{Val list|legend=1| 41, 91, 223cdef }}
{{Val list|legend=1| 41, 91, 223cdef }}
</div></div>


== 13-limit ==
== 13-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~7/6 = 263.700
EDO generators: [[41edo|9\41]], [[50edo|11\50]], [[91edo|20\91]]
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 989: Line 571:


Mapping: [{{val| 1 4 1 5 5 7 }}, {{val| 0 -11 6 -10 -7 -15 }}]
Mapping: [{{val| 1 4 1 5 5 7 }}, {{val| 0 -11 6 -10 -7 -15 }}]
POTE generator: ~7/6 = 263.700


{{Val list|legend=1| 41, 91 }}
{{Val list|legend=1| 41, 91 }}
</div></div>


= Slender =
= Slender =


Period: 1\1
Subgroup: 2.3.5.7


Optimal ([[POTE]]) generator: ~49/48 = 38.413
[[Comma list]]: 225/224, 589824/588245


EDO generators: [[31edo|1\31]], [[32edo|1\32]], [[63edo|2\63]], [[94edo|3\94]]
[[Mapping]]: [{{val| 1 2 2 3 }}, {{val| 0 -13 10 -6 }}]


Scales (Scala files):
{{Multival|legend=1| 13 -10 6 -46 -27 42 }}


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
[[POTE generator]]: ~49/48 = 38.413
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
Subgroup: 2.3.5.7
 
Comma list: 225/224, 589824/588245
 
Mapping: [{{val| 1 2 2 3 }}, {{val| 0 -13 10 -6 }}]
 
Wedgie: {{wedgie| 13 -10 6 -46 -27 42 }}


{{Val list|legend=1| 31, 94, 125 }}
{{Val list|legend=1| 31, 94, 125 }}


Badness: 0.0569
[[Badness]]: 0.0569
 
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~49/48 = 38.387
EDO generators: [[31edo|1\31]], [[32edo|1\32]], [[63edo|2\63]], [[94edo|3\94]]
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 1,041: Line 599:


Mapping: [{{val| 1 2 2 3 4 }}, {{val| 0 -13 10 -6 -17 }}]
Mapping: [{{val| 1 2 2 3 4 }}, {{val| 0 -13 10 -6 -17 }}]
POTE generator: ~49/48 = 38.387


{{Val list|legend=1| 31, 63, 94, 125 }}
{{Val list|legend=1| 31, 63, 94, 125 }}


Badness: 0.02534
Badness: 0.02534
</div></div>


== 13-limit ==
== 13-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~49/48 = 38.314
EDO generators: [[31edo|1\31]], [[32edo|1\32]], [[63edo|2\63]], [[94edo|3\94]]
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 1,067: Line 613:


Mapping: [{{val| 1 2 2 3 4 3 }}, {{val| 0 -13 10 -6 -17 22 }}]
Mapping: [{{val| 1 2 2 3 4 3 }}, {{val| 0 -13 10 -6 -17 22 }}]
POTE generator: ~49/48 = 38.314


{{Val list|legend=1| 31, 63, 94 }}
{{Val list|legend=1| 31, 63, 94 }}


Badness: 0.02591
Badness: 0.02591
</div></div>


= Marvo =
= Marvo =
{{see also| Gravity family }}
{{see also| Gravity family }}
Period: 1\1
Optimal ([[POTE]]) generator: ~27/20 = 516.694
EDO generators: [[65edo|28\65]], [[72edo|31\72]], [[137edo|59\137]]
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 1,095: Line 629:
Mapping: [{{val| 1 5 12 29 }}, {{val| 0 -6 -17 -46 }}]
Mapping: [{{val| 1 5 12 29 }}, {{val| 0 -6 -17 -46 }}]


Wedgie: {{wedgie| 6 17 46 13 56 59 }}
{{Multival|legend=1| 6 17 46 13 56 59 }}
 
POTE generator: ~27/20 = 516.694


{{Val list|legend=1| 65d, 72, 137, 209, 281, 569bcc }}
{{Val list|legend=1| 65d, 72, 137, 209, 281, 569bcc }}


Badness: 0.0976
Badness: 0.0976
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~27/20 = 516.699
EDO generators: [[65edo|28\65]], [[72edo|31\72]], [[137edo|59\137]]
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 1,122: Line 644:


Mapping: [{{val| 1 5 12 29 12 }}, {{val| 0 -6 -17 -46 -15 }}]
Mapping: [{{val| 1 5 12 29 12 }}, {{val| 0 -6 -17 -46 -15 }}]
POTE generator: ~27/20 = 516.699


{{Val list|legend=1| 65d, 72, 281, 353c, 425bc, 497bc }}
{{Val list|legend=1| 65d, 72, 281, 353c, 425bc, 497bc }}


Badness: 0.0317
Badness: 0.0317
</div></div>


== 13-limit ==
== 13-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~27/20 = 516.730
EDO generators: [[65edo|28\65]], [[72edo|31\72]], [[137edo|59\137]]
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 658:


Mapping: [{{val| 1 5 12 29 12 39 }}, {{val| 0 -6 -17 -46 -15 -62 }}]
Mapping: [{{val| 1 5 12 29 12 39 }}, {{val| 0 -6 -17 -46 -15 -62 }}]
POTE generator: ~27/20 = 516.730


{{Val list|legend=1| 65d, 72, 137, 209, 281f, 490bcf }}
{{Val list|legend=1| 65d, 72, 137, 209, 281f, 490bcf }}


Badness: 0.0269
Badness: 0.0269
</div></div>


= Marvolo =
= Marvolo =


Period: 1\1
Subgroup: 2.3.5.7
 
Optimal ([[POTE]]) generator: ~21/20 = 83.348
 
EDO generators: [[29edo|2\29]], [[43edo|3\43]], [[72edo|5\72]]
 
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]]: 225/224, 156250000/155649627


Comma list: 225/224, 156250000/155649627
[[Mapping]]: [{{val| 1 2 1 1 }}, {{val| 0 -6 19 26 }}]


Mapping: [{{val| 1 2 1 1 }}, {{val| 0 -6 19 26 }}]
{{Multival|legend=1| 6 -19 -26 -44 -58 -7 }}


Wedgie: {{wedgie| 6 -19 -26 -44 -58 -7 }}
[[POTE generator]]: ~21/20 = 83.348


{{Val list|legend=1| 29, 43, 72, 619bcd, 691bcd }}
{{Val list|legend=1| 29, 43, 72, 619bcd, 691bcd }}


Badness: 0.0833
[[Badness]]: 0.0833
 
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~21/20 = 83.340
EDO generators: [[29edo|2\29]], [[43edo|3\43]], [[72edo|5\72]]
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 1,202: Line 688:


Mapping: [{{val| 1 2 1 1 2 }}, {{val| 0 -6 19 26 21 }}]
Mapping: [{{val| 1 2 1 1 2 }}, {{val| 0 -6 19 26 21 }}]
POTE generator: ~21/20 = 83.340


{{Val list|legend=1| 29, 43, 72 }}
{{Val list|legend=1| 29, 43, 72 }}
Line 1,210: Line 698:


== 13-limit ==
== 13-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~21/20 = 83.330
EDO generators: [[29edo|2\29]], [[43edo|3\43]], [[72edo|5\72]]
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 1,228: Line 704:


Mapping: [{{val| 1 2 1 1 2 3 }}, {{val| 0 -6 19 26 21 10 }}]
Mapping: [{{val| 1 2 1 1 2 3 }}, {{val| 0 -6 19 26 21 10 }}]
POTE generator: ~21/20 = 83.330


{{Val list|legend=1| 29, 43, 72, 115f }}
{{Val list|legend=1| 29, 43, 72, 115f }}
Line 1,238: Line 716:
== 5-limit (mabila) ==
== 5-limit (mabila) ==


Period: 1\1
Subgroup: 2.3.5


Optimal ([[POTE]]) generator: ~512/375 = 529.6849
[[Comma list]]: 268435456/263671875


EDO generators: [[34edo|15\34]], [[43edo|19\43]], [[77edo|34\77]], [[111edo|49\111]]
[[Mapping]]: [{{val| 1 6 1 }}, {{val| 0 -10 3 }}]


Scales (Scala files):
[[POTE generator]]: ~512/375 = 529.6849
 
<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
 
Comma list: 268435456/263671875
 
Mapping: [{{val| 1 6 1 }}, {{val| 0 -10 3 }}]


{{Val list|legend=1| 9, 25, 34, 77, 111, 145, 256c }}
{{Val list|legend=1| 9, 25, 34, 77, 111, 145, 256c }}


Badness: 0.2325
[[Badness]]: 0.2325
 
</div></div>


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


Period: 1\1
Subgroup: 2.3.5.7
 
Optimal ([[POTE]]) generator: ~48/35 = 529.979
 
EDO generators: [[34edo|15\34]], [[43edo|19\43]]
 
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]]: 225/224, 17496/16807


Comma list: 225/224, 17496/16807
[[Mapping]]: [{{val| 1 6 1 9 }}, {{val| 0 -10 3 -14 }}]


Mapping: [{{val| 1 6 1 9 }}, {{val| 0 -10 3 -14 }}]
{{Multival|legend=1| 10 -3 14 -28 -6 41 }}


Wedgie: {{wedgie| 10 -3 14 -28 -6 41 }}
[[POTE generator]]: ~48/35 = 529.979


{{Val list|legend=1| 9, 25d, 34d, 43, 77d }}
{{Val list|legend=1| 9, 25d, 34d, 43, 77d }}


Badness: 0.1096
[[Badness]]: 0.1096
 
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~15/11 = 529.974
EDO generators: [[34edo|15\34]], [[43edo|19\43]]
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 1,309: Line 751:


Mapping: [{{val| 1 6 1 9 7 }}, {{val| 0 -10 3 -14 -8 }}]
Mapping: [{{val| 1 6 1 9 7 }}, {{val| 0 -10 3 -14 -8 }}]
POTE generator: ~15/11 = 529.974


{{Val list|legend=1| 9, 34d, 43, 77de }}
{{Val list|legend=1| 9, 34d, 43, 77de }}


Badness: 0.0426
Badness: 0.0426
</div></div>


== 13-limit ==
== 13-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~15/11 = 529.951
EDO generators: [[34edo|15\34]], [[43edo|19\43]]
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 1,335: Line 765:


Mapping: [{{val| 1 6 1 9 7 9 }}, {{val| 0 -10 3 -14 -8 -12 }}]
Mapping: [{{val| 1 6 1 9 7 9 }}, {{val| 0 -10 3 -14 -8 -12 }}]
POTE generator: ~15/11 = 529.951


{{Val list|legend=1| 9, 34d, 43, 77de }}
{{Val list|legend=1| 9, 34d, 43, 77de }}


Badness: 0.0258
Badness: 0.0258
</div></div>


= Enneaportent =
= Enneaportent =


Period: 1\9
Subgroup: 2.3.5.7
 
Optimal ([[POTE]]) generator: ~5/4 = 383.165
 
EDO generators: [[63edo|20\63]], [[72edo|23\72]], [[81edo|26\81]]


Scales (Scala files):  
[[Comma list]]: 225/224, 40353607/40310784


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
[[Mapping]]: [{{val| 9 0 28 11 }}, {{val| 0 2 -1 2 }}]
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7
{{Multival|legend=1| 18 -9 18 -56 -22 67 }}


Comma list: 225/224, 40353607/40310784
[[POTE generator]]: ~5/4 = 383.165
 
Mapping: [{{val| 9 0 28 11 }}, {{val| 0 2 -1 2 }}]
 
Wedgie: {{wedgie| 18 -9 18 -56 -22 67 }}


{{Val list|legend=1| 63, 72, 495bcd }}
{{Val list|legend=1| 63, 72, 495bcd }}


Badness: 0.0937
[[Badness]]: 0.0937
 
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\9
Optimal ([[POTE]]) generator: ~5/4 = 383.146
EDO generators: [[63edo|20\63]], [[72edo|23\72]], [[81edo|26\81]]
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 1,389: Line 795:


Mapping: [{{val| 9 0 28 11 24 }}, {{val| 0 2 -1 2 1 }}]
Mapping: [{{val| 9 0 28 11 24 }}, {{val| 0 2 -1 2 1 }}]
POTE generator: ~5/4 = 383.146


{{Val list|legend=1| 63, 72, 423cd, 495bcd }}
{{Val list|legend=1| 63, 72, 423cd, 495bcd }}
Line 1,397: Line 805:


== 13-limit ==
== 13-limit ==
Period: 1\9
Optimal ([[POTE]]) generator: ~5/4 = 383.047
EDO generators: [[63edo|20\63]], [[72edo|23\72]], [[81edo|26\81]]
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 1,415: Line 811:


Mapping: [{{val| 9 0 28 11 24 19 }}, {{val| 0 2 -1 2 1 2 }}]
Mapping: [{{val| 9 0 28 11 24 19 }}, {{val| 0 2 -1 2 1 2 }}]
POTE generator: ~5/4 = 383.047


{{Val list|legend=1| 63, 72, 279cf }}
{{Val list|legend=1| 63, 72, 279cf }}
Line 1,425: Line 823:
== 5-limit ==
== 5-limit ==


Period: 1\1
Subgroup: 2.3.5
 
Optimal ([[POTE]]) generator: ~10125/8192 = 362.321
 
EDO generators: [[43edo|13\43]], [[53edo|16\53]], [[63edo|19\63]], [[96edo|29\96]], [[116edo|35\116]]
 
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
[[Comma list]]: 69198046875/68719476736


Comma list: 69198046875/68719476736
[[Mapping]]: [{{val| 1 4 -1 }}, {{val| 0 -8 11 }}]


Mapping: [{{val| 1 4 -1 }}, {{val| 0 -8 11 }}]
[[POTE generator]]: ~10125/8192 = 362.321


{{Val list|legend=1| 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc}}
{{Val list|legend=1| 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc}}


Badness: 0.1302
[[Badness]]: 0.1302
 
</div></div>


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


Period: 1\1
Subgroup: 2.3.5.7


Optimal ([[POTE]]) generator: ~49/40 = 362.255
[[Comma list]]: 225/224, 51200/50421


EDO generators: [[43edo|13\43]], [[53edo|16\53]], [[63edo|19\63]], [[96edo|29\96]], [[116edo|35\116]]
[[Mapping]]: [{{val| 1 4 -1 1 }}, {{val| 0 -8 11 6 }}]


Scales (Scala files):
{{Multival|legend=1| 8 -11 -6 -36 -32 17 }}


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
[[POTE generator]]: ~49/40 = 362.255
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
Subgroup: 2.3.5.7
 
Comma list: 225/224, 51200/50421
 
Mapping: [{{val| 1 4 -1 1 }}, {{val| 0 -8 11 6 }}]
 
Wedgie: {{wedgie| 8 -11 -6 -36 -32 17 }}


{{Val list|legend=1| 10, 33, 43, 53 }}
{{Val list|legend=1| 10, 33, 43, 53 }}


Badness: 0.0605
[[Badness]]: 0.0605
 
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~27/22 = 362.101
EDO generators: [[53edo|16\53]], [[63edo|19\63]], [[116edo|35\116]]
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 1,496: Line 858:


Mapping: [{{val| 1 4 -1 1 11 }}, {{val| 0 -8 11 6 -25 }}]
Mapping: [{{val| 1 4 -1 1 11 }}, {{val| 0 -8 11 6 -25 }}]
POTE generator: ~27/22 = 362.101


{{Val list|legend=1| 53, 116, 169de, 285cde }}
{{Val list|legend=1| 53, 116, 169de, 285cde }}


Badness: 0.0506
Badness: 0.0506
</div></div>


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generator: ~16/13 = 362.105
EDO generators: [[53edo|16\53]], [[63edo|19\63]], [[116edo|35\116]]
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 1,522: Line 872:


Mapping: [{{val| 1 4 -1 1 11 4 }}, {{val| 0 -8 11 6 -25 -1 }}]
Mapping: [{{val| 1 4 -1 1 11 4 }}, {{val| 0 -8 11 6 -25 -1 }}]
POTE generator: ~16/13 = 362.105


{{Val list|legend=1| 53, 116, 169de, 285cdef }}
{{Val list|legend=1| 53, 116, 169de, 285cdef }}
Line 1,530: Line 882:


== Interpental ==
== Interpental ==
Period: 1\1
Optimal ([[POTE]]) generator: ~49/40 = 362.418
EDO generators: [[43edo|13\43]], [[53edo|16\53]], [[96edo|29\96]]
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 1,550: Line 890:


Mapping: [{{val| 1 4 -1 1 -5 }}, {{val| 0 -8 11 6 28 }}]
Mapping: [{{val| 1 4 -1 1 -5 }}, {{val| 0 -8 11 6 28 }}]
POTE generator: ~49/40 = 362.418


{{Val list|legend=1| 43, 53, 96, 149d }}
{{Val list|legend=1| 43, 53, 96, 149d }}
Line 1,558: Line 900:


=== 13-limit ===
=== 13-limit ===
Period: 1\1
Optimal ([[POTE]]) generator: ~16/13 = 362.402
EDO generators: [[43edo|13\43]], [[53edo|16\53]], [[96edo|29\96]]
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 1,578: Line 908:


Mapping: [{{val| 1 4 -1 1 -5 4 }}, {{val| 0 -8 11 6 28 -1 }}]
Mapping: [{{val| 1 4 -1 1 -5 4 }}, {{val| 0 -8 11 6 28 -1 }}]
POTE generator: ~16/13 = 362.402


{{Val list|legend=1| 43, 53, 96, 149d }}
{{Val list|legend=1| 43, 53, 96, 149d }}
Line 1,586: Line 918:


= Alphorn =
= Alphorn =
Period: 1\1


Optimal ([[POTE]]) generator: ~48/35 = 556.221
Subgroup: 2.3.5.7
 
EDO generators: [[28edo|13\28]], [[41edo|19\41]]
 
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]]: 225/224, 5764801/5668704


Comma list: 225/224, 5764801/5668704
[[Mapping]]: [{{val| 1 9 0 13 }}, {{val| 0 -16 5 -22 }}]


Mapping: [{{val| 1 9 0 13 }}, {{val| 0 -16 5 -22 }}]
{{Multival|legend=1| 16 -5 22 -45 -10 65 }}


Wedgie: {{wedgie| 16 -5 22 -45 -10 65 }}
[[POTE generator]]: ~48/35 = 556.221


{{Val list|legend=1| 28d, 41, 151cd, 192cd, 233cd }}
{{Val list|legend=1| 28d, 41, 151cd, 192cd, 233cd }}


Badness: 0.1293
[[Badness]]: 0.1293
 
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\1
Optimal ([[POTE]]) generator: ~11/8 = 556.144
EDO generators: [[28edo|13\28]], [[41edo|19\41]]
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 1,630: Line 940:


Mapping: [{{val| 1 9 0 13 3 }}, {{val| 0 -16 5 -22 1 }}]
Mapping: [{{val| 1 9 0 13 3 }}, {{val| 0 -16 5 -22 1 }}]
POTE generator: ~11/8 = 556.144


{{Val list|legend=1| 28d, 41, 315cde }}
{{Val list|legend=1| 28d, 41, 315cde }}


Badness: 0.0735
Badness: 0.0735
</div></div>


= Decic =
= Decic =
The ''decic'' temperament (10&amp;50, named by [[User:Xenllium|Xenllium]]) tempers out the [[cloudy comma]], 16807/16384 and the [[225/224|marvel comma]], 225/224 in the 7-limit. It can be extended naturally to the 11-, 13-, and 17-limit by adding 385/384, 105/104, and 170/169 to the comma list in this order.
The ''decic'' temperament (10&amp;50, named by [[User:Xenllium|Xenllium]]) tempers out the [[cloudy comma]], 16807/16384 and the [[225/224|marvel comma]], 225/224 in the 7-limit. It can be extended naturally to the 11-, 13-, and 17-limit by adding 385/384, 105/104, and 170/169 to the comma list in this order.
== 7-limit ==
Period: 1\10
Optimal ([[POTE]]) generator: ~3/2 = 698.696
EDO generators: [[50edo|1\50]], [[60edo|1\60]]
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 1,662: Line 959:


{{Multival|legend=1| 10 -10 0 -39 -28 28 }}
{{Multival|legend=1| 10 -10 0 -39 -28 28 }}
[[POTE generator]]: ~3/2 = 698.696


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 1,671: Line 970:


[[Badness]]: 0.089135
[[Badness]]: 0.089135
</div></div>


== 11-limit ==
== 11-limit ==
Period: 1\10
Optimal (POTE) generator: ~3/2 = 696.791
EDO generators: [[50edo|1\50]], [[60edo|1\60]]
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 1,696: Line 981:
Mapping generators: ~15/14, ~3
Mapping generators: ~15/14, ~3


[[Tuning ranges]]:  
POTE generator: ~3/2 = 696.791
 
Tuning ranges:  
* valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
* valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
* nice range: ~3/2 = [689.363, 702.512]
* nice range: ~3/2 = [689.363, 702.512]
Line 1,704: Line 991:


Badness: 0.063900
Badness: 0.063900
</div></div>


== 13-limit ==
== 13-limit ==
Period: 1\10
Optimal (POTE) generator: ~3/2 = 696.993
EDO generators: [[50edo|1\50]], [[60edo|1\60]]
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 1,728: Line 1,002:
Mapping generators: ~14/13, ~3
Mapping generators: ~14/13, ~3


[[Tuning ranges]]:  
POTE generator: ~3/2 = 696.993
 
Tuning ranges:  
* valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
* valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
* nice range: ~3/2 = [689.363, 702.512]
* nice range: ~3/2 = [689.363, 702.512]
Line 1,736: Line 1,012:


Badness: 0.036880
Badness: 0.036880
</div></div>


== 17-limit ==
== 17-limit ==
Period: 1\10
Optimal (POTE) generator: ~3/2 = 697.085
EDO generators: [[50edo|1\50]], [[60edo|1\60]]
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: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17
Line 1,760: Line 1,023:
Mapping generators: ~14/13, ~3
Mapping generators: ~14/13, ~3


[[Tuning ranges]]:  
POTE generator: ~3/2 = 697.085
 
Tuning ranges:  
* valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
* valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
* nice range: ~3/2 = [689.363, 704.955]
* nice range: ~3/2 = [689.363, 704.955]
Line 1,768: Line 1,033:


Badness: 0.025064
Badness: 0.025064
</div></div>


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

Revision as of 11:38, 27 March 2021

This page discusses some of the temperaments tempering out [-5 2 2 -1⟩ = 225/224, the marvel comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton, merman and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp, escapade and mavila.

Since (5/4)2 = 225/224 × 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess a version of the augmented triad where each third approximates either 5/4 or 9/7. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.

The melodic signature of marvel temperaments is that 16/15 and 15/14 are tempered to be equal. Hence 8/7 can be divided into two equal parts.

Marvel tempering allows for a tritone substitution whereby the dominant seventh chord formed by adding 16/9 above the root shares its tritone with a 4:5:6:7 tetrad. (The tritone of the dominant seventh is (16/9)/(5/4) = 64/45. Setting this equal to 10/7 gives (10/7)/(64/45) = 225/224.)

Negri

Main article: Negri

Negri tempers out the negri comma in the 5-limit, 49/48 and 225/224 in the 7-limit. It can be extended naturally to the 2.3.5.7.13 subgroup by adding 91/90 to the comma list; this will be discussed below under the title of negra.

5-limit

Subgroup: 2.3.5

Comma list: 16875/16384

Mapping: [⟨1 2 2], ⟨0 -4 3]]

Wedgie: ⟨⟨ 4 -3 -14 ]]

POTE generator: ~16/15 = 125.7549

Template:Val list

7-limit

Subgroup: 2.3.5.7

Comma list: 49/48, 225/224

Mapping: [⟨1 2 2 3], ⟨0 -4 3 -2]]

Wedgie: ⟨⟨ 4 -3 2 -14 -8 13 ]]

POTE generator: ~15/14 = 125.608

Template:Val list

Negra

This is the 2.3.5.7.13 extension of negri.

Subgroup: 2.3.5.7.13

Comma list: 49/48, 65/64, 91/90

Sval Mapping: [⟨1 2 2 3 4], ⟨0 -4 3 -2 -3]]

Gencom mapping: [⟨1 2 2 3 0 4], ⟨0 -4 3 -2 0 -3]]

Gencom: [2 14/13; 49/48 65/64 91/90]

POTE generator: ~14/13 = 125.567

Template:Val list

11-limit

Subgroup: 2.3.5.7.11

Comma list: 45/44, 49/48, 56/55

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

POTE generator: ~15/14 = 126.474

Template:Val list

Badness: 0.0262

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 45/44, 49/48, 56/55, 78/77

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

POTE generator: ~14/13 = 126.431

Template:Val list

Negril

Subgroup: 2.3.5.7.11

Comma list: 49/48, 100/99, 225/224

Mapping: [⟨1 2 2 3 2], ⟨0 -4 3 -2 14]]

POTE generator: ~15/14 = 124.767

Template:Val list

Badness: 0.0387

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 65/64, 91/90, 875/858

Mapping: [⟨1 2 2 3 2 4], ⟨0 -4 3 -2 14 -3]]

POTE generator: ~14/13 = 124.716

Template:Val list

Badness: 0.0244

Negric

Subgroup: 2.3.5.7.11

Comma list: 33/32, 49/48, 77/75

Mapping: [⟨1 2 2 3 3], ⟨0 -4 3 -2 4]]

POTE generator: ~15/14 = 127.039

Template:Val list

Badness: 0.0306

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 33/32, 49/48, 65/64, 91/90

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

POTE generator: ~14/13 = 127.039

Template:Val list

Badness: 0.0202

Negroni

Subgroup: 2.3.5.7.11

Comma list: 49/48, 55/54, 225/224

Mapping: [⟨1 2 2 3 5], ⟨0 -4 3 -2 -15]]

POTE generator: ~15/14 = 124.539

Template:Val list

Badness: 0.0353

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 55/54, 65/64, 91/90

Mapping: [⟨1 2 2 3 5 4], ⟨0 -4 3 -2 -15 -3]]

POTE generator: ~14/13 = 124.545

Template:Val list

Badness: 0.0216

Wilsec

Subgroup: 2.3.5.7.11

Comma list: 49/48, 121/120, 225/224

Mapping: [⟨1 6 -1 5 4], ⟨0 -8 6 -4 -1]]

POTE generator: ~11/8 = 537.186

Template:Val list

Badness: 0.0419

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 65/64, 91/90, 121/120

Mapping: [⟨1 6 -1 5 4 7], ⟨0 -8 6 -4 -1 -6]]

POTE generator: ~11/8 = 537.208

Template:Val list

Badness: 0.0252

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 49/48, 65/64, 91/90, 121/120, 154/153

Mapping: [⟨1 6 -1 5 4 7 -2], ⟨0 -8 6 -4 -1 -6 11]]

POTE generator: ~11/8 = 537.230

Template:Val list

Badness: 0.0218

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 49/48, 65/64, 77/76, 91/90, 121/120, 154/153

Mapping: [⟨1 6 -1 5 4 7 -2 7], ⟨0 -8 6 -4 -1 -6 11 -5]]

POTE generator: ~11/8 = 537.214

Template:Val list

Badness: 0.0168

Passive

See also: Archytas clan § Passion

Subgroup: 2.3.5.7

Comma list: 225/224, 256/245

Mapping: [⟨1 2 2 3], ⟨0 -5 4 -2]]

POTE generator: ~16/15 = 98.809

Template:Val list

Badness: 0.0751

Wizard

For the 5-limit version of this temperament, see High badness temperaments #Wizard.

Subgroup: 2.3.5.7

Comma list: 225/224, 118098/117649

Mapping: [⟨2 1 5 2], ⟨0 6 -1 10]]

Mapping generators: ~1225/864, ~245/216

POTE generator: ~5/4 = 383.256

Wedgie: ⟨⟨ 12 -2 20 -31 -2 52 ]]

Template:Val list

Badness: 0.0408

Scales: wizard22

11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 4000/3993

Mapping: [⟨2 1 5 2 8], ⟨0 6 -1 10 -3]]

Mapping generators: ~99/70, ~25/22

POTE generator: ~5/4 = 383.232

Template:Val list

Badness: 0.0185

Scales: wizard22

Lizard

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 351/350, 364/363, 385/384

Mapping: [⟨2 1 5 2 8 11], ⟨0 6 -1 10 -3 -10]]

Mapping generators: ~99/70, ~25/22

POTE generator: ~5/4 = 383.389

Template:Val list

Badness: 0.0218

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 221/220, 273/272, 289/288, 351/350, 375/374

Mapping: [⟨2 1 5 2 8 11 6], ⟨0 6 -1 10 -3 -10 6]]

Mapping generators: ~17/12, ~17/15

POTE generator: ~5/4 = 383.381

Template:Val list

Badness: 0.0145

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342

Mapping: [⟨2 1 5 2 8 11 6 2], ⟨0 6 -1 10 -3 -10 6 18]]

Mapping generators: ~17/12, ~17/15

POTE generator: ~5/4 = 383.477

Template:Val list

Badness: 0.0157

Gizzard

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 325/324, 385/384, 1573/1568

Mapping: [⟨2 1 5 2 8 -2], ⟨0 6 -1 10 -3 26]]

Mapping generators: ~99/70, ~25/22

POTE generator: ~5/4 = 383.170

Template:Val list

Badness: 0.0203

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 225/224, 289/288, 325/324, 375/374, 385/384

Mapping: [⟨2 1 5 2 8 -2 6], ⟨0 6 -1 10 -3 26 6]]

Mapping generators: ~17/12, ~17/15

POTE generator: ~5/4 = 383.175

Template:Val list

Badness: 0.0136

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 225/224, 325/324, 375/374, 385/384, 400/399, 595/594

Mapping: [⟨2 1 5 2 8 -2 6 15], ⟨0 6 -1 10 -3 26 6 -18]]

Mapping generators: ~17/12, ~17/15

POTE generator: ~5/4 = 383.138

Template:Val list

Badness: 0.0148

Mage

Subgroup: 2.3.5.7.11

Comma list: 99/98, 176/175, 1331/1296

Mapping: [⟨2 1 5 2 4], ⟨0 6 -1 10 8]]

Mapping generators: ~77/54, ~55/48

POTE generator: ~5/4 = 383.124

Template:Val list

Badness: 0.0578

Triton

For the 5-limit version of this temperament, see High badness temperaments #Stump.

Subgroup: 2.3.5.7

Comma list: 225/224, 1029/1000

Mapping: [⟨1 0 6 7], ⟨0 3 -7 -8]]

Wedgie: ⟨⟨ 3 -7 -8 -18 -21 1 ]]

POTE generator: ~7/5 = 568.865

Template:Val list

Badness: 0.0592

11-limit

Subgroup: 2.3.5.7.11

Comma list: 45/44, 56/55, 1029/1000

Mapping: [⟨1 0 6 7 4], ⟨0 3 -7 -8 -1]]

POTE generator: ~7/5 = 569.144

Template:Val list

Badness: 0.0457

Tritonic

For the 5-limit version of this temperament, see High badness temperaments #Tritonic.

Subgroup: 2.3.5.7

Comma list: 225/224, 50421/50000

Mapping: [⟨1 4 -3 -3], ⟨0 -5 11 12]]

Wedgie: ⟨⟨ 5 -11 -12 -29 -33 3 ]]

POTE generator: ~7/5 = 580.286

Template:Val list

11-limit

Subgroup: 2.3.5.7.11

Comma list: 121/120, 225/224, 441/440

Mapping: [⟨1 4 -3 -3 2], ⟨0 -5 11 12 3]]

POTE generator: ~7/5 = 580.267

Template:Val list

Badness: 0.0237

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 121/120, 196/195, 275/273

Mapping: [⟨1 4 -3 -3 2 -5], ⟨0 -5 11 12 3 18]]

POTE generator: ~7/5 = 580.108

Template:Val list

Badness: 0.0230

Tritoni

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 27783/27500

Mapping: [⟨1 4 -3 -3 17], ⟨0 -5 11 12 -28]]

POTE generator: ~7/5 = 580.389

Template:Val list

Badness: 0.0455

Merman

For the 5-limit version of this temperament, see High badness temperaments #Merman.

Subgroup: 2.3.5.7

Comma list: 225/224, 2500000/2470629

Mapping: [⟨1 5 -5 -5], ⟨0 -7 15 16]]

Wedgie: ⟨⟨ 7 -15 -16 -40 -45 5 ]]

POTE generator: ~7/5 = 585.585

Template:Val list

Badness: 0.0551

11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 441/440, 1344/1331

Mapping: [⟨1 5 -5 -5 2], ⟨0 -7 15 16 3]]

POTE generator: ~7/5 = 585.606

Template:Val list

Badness: 0.0364

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 144/143, 225/224, 364/363, 441/440

Mapping: [⟨1 5 -5 -5 2 12], ⟨0 -7 15 16 3 -17]]

POTE generator: ~7/5 = 585.657

Template:Val list

Badness: 0.0275

Septimin

For the 5-limit version of this temperament, see High badness temperaments #Septimin.

Subgroup: 2.3.5.7

Comma list: 225/224, 84035/82944

Mapping: [⟨1 4 1 5], ⟨0 -11 6 -10]]

Wedgie: ⟨⟨ 11 -6 10 -35 -15 40 ]]

POTE generator: ~7/6 = 263.632

Template:Val list

11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 2401/2376

Mapping: [⟨1 4 1 5 5], ⟨0 -11 6 -10 -7]]

POTE generator: ~7/6 = 263.634

Template:Val list

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 144/143, 196/195, 245/242

Mapping: [⟨1 4 1 5 5 7], ⟨0 -11 6 -10 -7 -15]]

POTE generator: ~7/6 = 263.700

Template:Val list

Slender

Subgroup: 2.3.5.7

Comma list: 225/224, 589824/588245

Mapping: [⟨1 2 2 3], ⟨0 -13 10 -6]]

Wedgie: ⟨⟨ 13 -10 6 -46 -27 42 ]]

POTE generator: ~49/48 = 38.413

Template:Val list

Badness: 0.0569

11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 1331/1323

Mapping: [⟨1 2 2 3 4], ⟨0 -13 10 -6 -17]]

POTE generator: ~49/48 = 38.387

Template:Val list

Badness: 0.02534

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 275/273, 385/384, 1331/1323

Mapping: [⟨1 2 2 3 4 3], ⟨0 -13 10 -6 -17 22]]

POTE generator: ~49/48 = 38.314

Template:Val list

Badness: 0.02591

Marvo

See also: Gravity family

Subgroup: 2.3.5.7

Comma list: 225/224, 78125000/78121827

Mapping: [⟨1 5 12 29], ⟨0 -6 -17 -46]]

Wedgie: ⟨⟨ 6 17 46 13 56 59 ]]

POTE generator: ~27/20 = 516.694

Template:Val list

Badness: 0.0976

11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 243/242, 4000/3993

Mapping: [⟨1 5 12 29 12], ⟨0 -6 -17 -46 -15]]

POTE generator: ~27/20 = 516.699

Template:Val list

Badness: 0.0317

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 243/242, 351/350, 1625/1617

Mapping: [⟨1 5 12 29 12 39], ⟨0 -6 -17 -46 -15 -62]]

POTE generator: ~27/20 = 516.730

Template:Val list

Badness: 0.0269

Marvolo

Subgroup: 2.3.5.7

Comma list: 225/224, 156250000/155649627

Mapping: [⟨1 2 1 1], ⟨0 -6 19 26]]

Wedgie: ⟨⟨ 6 -19 -26 -44 -58 -7 ]]

POTE generator: ~21/20 = 83.348

Template:Val list

Badness: 0.0833

11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 441/440, 4000/3993

Mapping: [⟨1 2 1 1 2], ⟨0 -6 19 26 21]]

POTE generator: ~21/20 = 83.340

Template:Val list

Badness: 0.0290

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 225/224, 364/363, 441/440

Mapping: [⟨1 2 1 1 2 3], ⟨0 -6 19 26 21 10]]

POTE generator: ~21/20 = 83.330

Template:Val list

Badness: 0.0215

Amavil

5-limit (mabila)

Subgroup: 2.3.5

Comma list: 268435456/263671875

Mapping: [⟨1 6 1], ⟨0 -10 3]]

POTE generator: ~512/375 = 529.6849

Template:Val list

Badness: 0.2325

7-limit

Subgroup: 2.3.5.7

Comma list: 225/224, 17496/16807

Mapping: [⟨1 6 1 9], ⟨0 -10 3 -14]]

Wedgie: ⟨⟨ 10 -3 14 -28 -6 41 ]]

POTE generator: ~48/35 = 529.979

Template:Val list

Badness: 0.1096

11-limit

Subgroup: 2.3.5.7.11

Comma list: 99/98, 176/175, 864/847

Mapping: [⟨1 6 1 9 7], ⟨0 -10 3 -14 -8]]

POTE generator: ~15/11 = 529.974

Template:Val list

Badness: 0.0426

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 78/77, 99/98, 144/143, 176/175

Mapping: [⟨1 6 1 9 7 9], ⟨0 -10 3 -14 -8 -12]]

POTE generator: ~15/11 = 529.951

Template:Val list

Badness: 0.0258

Enneaportent

Subgroup: 2.3.5.7

Comma list: 225/224, 40353607/40310784

Mapping: [⟨9 0 28 11], ⟨0 2 -1 2]]

Wedgie: ⟨⟨ 18 -9 18 -56 -22 67 ]]

POTE generator: ~5/4 = 383.165

Template:Val list

Badness: 0.0937

11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 12005/11979

Mapping: [⟨9 0 28 11 24], ⟨0 2 -1 2 1]]

POTE generator: ~5/4 = 383.146

Template:Val list

Badness: 0.0304

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 225/224, 364/363, 1716/1715

Mapping: [⟨9 0 28 11 24 19], ⟨0 2 -1 2 1 2]]

POTE generator: ~5/4 = 383.047

Template:Val list

Badness: 0.0223

Submajor

5-limit

Subgroup: 2.3.5

Comma list: 69198046875/68719476736

Mapping: [⟨1 4 -1], ⟨0 -8 11]]

POTE generator: ~10125/8192 = 362.321

Template:Val list

Badness: 0.1302

7-limit

Subgroup: 2.3.5.7

Comma list: 225/224, 51200/50421

Mapping: [⟨1 4 -1 1], ⟨0 -8 11 6]]

Wedgie: ⟨⟨ 8 -11 -6 -36 -32 17 ]]

POTE generator: ~49/40 = 362.255

Template:Val list

Badness: 0.0605

11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 6655/6561

Mapping: [⟨1 4 -1 1 11], ⟨0 -8 11 6 -25]]

POTE generator: ~27/22 = 362.101

Template:Val list

Badness: 0.0506

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 225/224, 275/273, 385/384

Mapping: [⟨1 4 -1 1 11 4], ⟨0 -8 11 6 -25 -1]]

POTE generator: ~16/13 = 362.105

Template:Val list

Badness: 0.0277

Interpental

Subgroup: 2.3.5.7.11

Comma list: 99/98, 176/175, 51200/50421

POTE generator: ~49/40 = 362.418

Mapping: [⟨1 4 -1 1 -5], ⟨0 -8 11 6 28]]

POTE generator: ~49/40 = 362.418

Template:Val list

Badness: 0.0518

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 99/98, 169/168, 176/175, 640/637

POTE generator: ~16/13 = 362.402

Mapping: [⟨1 4 -1 1 -5 4], ⟨0 -8 11 6 28 -1]]

POTE generator: ~16/13 = 362.402

Template:Val list

Badness: 0.0297

Alphorn

Subgroup: 2.3.5.7

Comma list: 225/224, 5764801/5668704

Mapping: [⟨1 9 0 13], ⟨0 -16 5 -22]]

Wedgie: ⟨⟨ 16 -5 22 -45 -10 65 ]]

POTE generator: ~48/35 = 556.221

Template:Val list

Badness: 0.1293

11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 12250/11979

Mapping: [⟨1 9 0 13 3], ⟨0 -16 5 -22 1]]

POTE generator: ~11/8 = 556.144

Template:Val list

Badness: 0.0735

Decic

The decic temperament (10&50, named by Xenllium) tempers out the cloudy comma, 16807/16384 and the marvel comma, 225/224 in the 7-limit. It can be extended naturally to the 11-, 13-, and 17-limit by adding 385/384, 105/104, and 170/169 to the comma list in this order.

Subgroup: 2.3.5.7

Comma list: 225/224, 16807/16384

Mapping: [⟨10 0 39 28], ⟨0 1 -1 0]]

Mapping generators: ~15/14, ~3

Wedgie: ⟨⟨ 10 -10 0 -39 -28 28 ]]

POTE generator: ~3/2 = 698.696

Tuning ranges:

  • valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
  • nice range: ~3/2 = [693.129, 702.512]
  • strict range: ~3/2 = [696.000, 700.000]

Template:Val list

Badness: 0.089135

11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 385/384, 3087/3025

Mapping: [⟨10 0 39 28 3], ⟨0 1 -1 0 2]]

Mapping generators: ~15/14, ~3

POTE generator: ~3/2 = 696.791

Tuning ranges:

  • valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
  • nice range: ~3/2 = [689.363, 702.512]
  • strict range: ~3/2 = [696.000, 700.000]

Template:Val list

Badness: 0.063900

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 144/143, 196/195, 2200/2197

Mapping: [⟨10 0 39 28 3 37], ⟨0 1 -1 0 2 0]]

Mapping generators: ~14/13, ~3

POTE generator: ~3/2 = 696.993

Tuning ranges:

  • valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
  • nice range: ~3/2 = [689.363, 702.512]
  • strict range: ~3/2 = [696.000, 700.000]

Template:Val list

Badness: 0.036880

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 105/104, 144/143, 170/169, 196/195, 221/220

Mapping: [⟨10 0 39 28 3 37 25], ⟨0 1 -1 0 2 0 1]]

Mapping generators: ~14/13, ~3

POTE generator: ~3/2 = 697.085

Tuning ranges:

  • valid range: ~3/2 = [696.000, 700.000] (29\50 to 35\60)
  • nice range: ~3/2 = [689.363, 704.955]
  • strict range: ~3/2 = [696.000, 700.000]

Template:Val list

Badness: 0.025064

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