Marvel temperaments: Difference between revisions

Xenllium (talk | contribs)
→Decic: added nice range and strict range
Tags: Mobile edit Mobile web edit
Revert databoxes
Line 13: Line 13:


== 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]]