Marvel temperaments: Difference between revisions

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Line 244: Line 244:
[[POTE generator]]: ~16/15 = 98.809
[[POTE generator]]: ~16/15 = 98.809


{{Val list|legend=1| 12, 49dd }}
{{Val list|legend=1| 1, 11, 12, 49dd }}


[[Badness]]: 0.0751
[[Badness]]: 0.075055


= 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]].''
{{See also|Wizard}}
{{See also|Wizard}}
Line 267: Line 266:
{{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]]: 0.040846


Scales: [[wizard22]]
Scales: [[wizard22]]


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 283: Line 281:
POTE generator: ~5/4 = 383.232
POTE generator: ~5/4 = 383.232


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


Badness: 0.0185
Badness: 0.018539


Scales: [[wizard22]]
Scales: [[wizard22]]


=== Lizard ===
=== Lizard ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 301: Line 298:
POTE generator: ~5/4 = 383.389
POTE generator: ~5/4 = 383.389


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


Badness: 0.0218
Badness: 0.021781


==== 17-limit ====
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 317: Line 313:
POTE generator: ~5/4 = 383.381
POTE generator: ~5/4 = 383.381


{{Val list|legend=1| 22, 50, 72, 122g, 194dfg }}
Vals: {{Val list| 22, 50, 72, 122g, 194dfg }}
 
Badness: 0.0145


</div></div>
Badness: 0.014536


==== 19-limit ====
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Line 335: Line 328:
POTE generator: ~5/4 = 383.477
POTE generator: ~5/4 = 383.477


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


Badness: 0.0157
Badness: 0.015702
 
</div></div>


=== Gizzard ===
=== Gizzard ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 353: Line 343:
POTE generator: ~5/4 = 383.170
POTE generator: ~5/4 = 383.170


{{Val list|legend=1| 72, 166, 238cf }}
Vals: {{Val list| 72, 166, 238cf }}


Badness: 0.0203
Badness: 0.020252
 
</div></div>


==== 17-limit ====
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Line 371: Line 358:
POTE generator: ~5/4 = 383.175
POTE generator: ~5/4 = 383.175


{{Val list|legend=1| 72, 166g, 238cfg }}
Vals: {{Val list| 72, 166g, 238cfg }}


Badness: 0.0136
Badness: 0.013624


</div></div>


==== 19-limit ====
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Line 389: Line 374:
POTE generator: ~5/4 = 383.138
POTE generator: ~5/4 = 383.138


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


Badness: 0.0148
Badness: 0.014810


== Mage ==
== Mage ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 405: Line 389:
POTE generator: ~5/4 = 383.124
POTE generator: ~5/4 = 383.124


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


Badness: 0.0578
Badness: 0.057799


= Triton =
= Triton =
: ''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]].''


Line 423: Line 406:
[[POTE generator]]: ~7/5 = 568.865
[[POTE generator]]: ~7/5 = 568.865


{{Val list|legend=1| 19, 78bd, 97bd }}
{{Val list|legend=1| 2, 17d, 19, 78bd, 97bd }}


[[Badness]]: 0.0592
[[Badness]]: 0.059245


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 437: Line 419:
POTE generator: ~7/5 = 569.144
POTE generator: ~7/5 = 569.144


{{Val list|legend=1| 19, 59bde, 78bde, 97bde }}
Vals: {{Val list| 2, 17d, 19, 59bde, 78bde, 97bde }}


Badness: 0.0457
Badness: 0.045675


= Tritonic =
= Tritonic =
: ''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]].''


Line 456: Line 437:


{{Val list|legend=1| 29, 31, 60, 91, 122, 213bcd }}
{{Val list|legend=1| 29, 31, 60, 91, 122, 213bcd }}
[[Badness]]: 0.047578


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 467: Line 449:
POTE generator: ~7/5 = 580.267
POTE generator: ~7/5 = 580.267


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


Badness: 0.0237
Badness: 0.023659


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 481: Line 462:
POTE generator: ~7/5 = 580.108
POTE generator: ~7/5 = 580.108


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


Badness: 0.0230
Badness: 0.022993


== Tritoni ==
== Tritoni ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 495: Line 475:
POTE generator: ~7/5 = 580.389
POTE generator: ~7/5 = 580.389


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


Badness: 0.0455
Badness: 0.045456


= Merman =
= Merman =
: ''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]].''


Line 515: Line 494:
{{Val list|legend=1| 41, 84, 125 }}
{{Val list|legend=1| 41, 84, 125 }}


[[Badness]]: 0.0551
[[Badness]]: 0.055078


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 527: Line 505:
POTE generator: ~7/5 = 585.606
POTE generator: ~7/5 = 585.606


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


Badness: 0.0364
Badness: 0.036383


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 541: Line 518:
POTE generator: ~7/5 = 585.657
POTE generator: ~7/5 = 585.657


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


Badness: 0.0275
Badness: 0.027544


= Septimin =
= Septimin =
Line 558: Line 535:
[[POTE generator]]: ~7/6 = 263.632
[[POTE generator]]: ~7/6 = 263.632


{{Val list|legend=1| 41, 91, 132 }}
{{Val list|legend=1| 41, 91, 132d }}


[[Badness]]: 0.054502
[[Badness]]: 0.054502
Line 589: Line 566:


= Slender =
= Slender =
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 602: Line 578:
{{Val list|legend=1| 31, 94, 125 }}
{{Val list|legend=1| 31, 94, 125 }}


[[Badness]]: 0.0569
[[Badness]]: 0.056934


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 614: Line 589:
POTE generator: ~49/48 = 38.387
POTE generator: ~49/48 = 38.387


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


Badness: 0.02534
Badness: 0.025342


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 628: Line 602:
POTE generator: ~49/48 = 38.314
POTE generator: ~49/48 = 38.314


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


Badness: 0.02591
Badness: 0.025913


= Marvo =
= Marvo =
Line 637: Line 611:
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Comma list: 225/224, 78125000/78121827
[[Comma list]]: 225/224, 78125000/78121827


Mapping: [{{val| 1 5 12 29 }}, {{val| 0 -6 -17 -46 }}]
[[Mapping]]: [{{val| 1 5 12 29 }}, {{val| 0 -6 -17 -46 }}]


{{Multival|legend=1| 6 17 46 13 56 59 }}
{{Multival|legend=1| 6 17 46 13 56 59 }}


POTE generator: ~27/20 = 516.694
[[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]]: 0.097627


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 659: Line 632:
POTE generator: ~27/20 = 516.699
POTE generator: ~27/20 = 516.699


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


Badness: 0.0317
Badness: 0.031685


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 673: Line 645:
POTE generator: ~27/20 = 516.730
POTE generator: ~27/20 = 516.730


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


Badness: 0.0269
Badness: 0.026882


= Marvolo =
= Marvolo =
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 691: Line 662:
{{Val list|legend=1| 29, 43, 72, 619bcd, 691bcd }}
{{Val list|legend=1| 29, 43, 72, 619bcd, 691bcd }}


[[Badness]]: 0.0833
[[Badness]]: 0.083338


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 703: Line 673:
POTE generator: ~21/20 = 83.340
POTE generator: ~21/20 = 83.340


{{Val list|legend=1| 29, 43, 72 }}
Vals: {{Val list| 29, 43, 72 }}


Badness: 0.0290
Badness: 0.028965
 
</div></div>


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 719: Line 686:
POTE generator: ~21/20 = 83.330
POTE generator: ~21/20 = 83.330


{{Val list|legend=1| 29, 43, 72, 115f }}
Vals: {{Val list| 29, 43, 72, 115f }}


Badness: 0.0215
Badness: 0.021470
 
</div></div>


= Amavil =
= Amavil =
== 5-limit (mabila) ==
== 5-limit (Mabila) ==
 
Subgroup: 2.3.5
Subgroup: 2.3.5


Line 738: Line 702:
{{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]]: 0.232481


== 7-limit ==
== 7-limit ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 754: Line 717:
{{Val list|legend=1| 9, 25d, 34d, 43, 77d }}
{{Val list|legend=1| 9, 25d, 34d, 43, 77d }}


[[Badness]]: 0.1096
[[Badness]]: 0.109625


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 766: Line 728:
POTE generator: ~15/11 = 529.974
POTE generator: ~15/11 = 529.974


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


Badness: 0.0426
Badness: 0.042649


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 780: Line 741:
POTE generator: ~15/11 = 529.951
POTE generator: ~15/11 = 529.951


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


Badness: 0.0258
Badness: 0.025791


= Enneaportent =
= Enneaportent =
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 796: Line 756:
[[POTE generator]]: ~5/4 = 383.165
[[POTE generator]]: ~5/4 = 383.165


{{Val list|legend=1| 63, 72, 495bcd }}
{{Val list|legend=1| 9, 63, 72, 495bcd }}


[[Badness]]: 0.0937
[[Badness]]: 0.093679


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 810: Line 769:
POTE generator: ~5/4 = 383.146
POTE generator: ~5/4 = 383.146


{{Val list|legend=1| 63, 72, 423cd, 495bcd }}
Vals: {{Val list| 9, 63, 72, 423cd, 495bcd }}
 
Badness: 0.0304


</div></div>
Badness: 0.030426


== 13-limit ==
== 13-limit ==
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 826: Line 782:
POTE generator: ~5/4 = 383.047
POTE generator: ~5/4 = 383.047


{{Val list|legend=1| 63, 72, 279cf }}
Vals: {{Val list| 9, 63, 72, 279cf }}


Badness: 0.0223
Badness: 0.022322
 
</div></div>


= Submajor =
= Submajor =
== 5-limit ==
Subgroup: 2.3.5
Subgroup: 2.3.5


Line 843: Line 795:
[[POTE generator]]: ~10125/8192 = 362.321
[[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]]: 0.130236


== 7-limit ==
== 7-limit ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 861: Line 812:
{{Val list|legend=1| 10, 33, 43, 53 }}
{{Val list|legend=1| 10, 33, 43, 53 }}


[[Badness]]: 0.0605
[[Badness]]: 0.060533


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 873: Line 823:
POTE generator: ~27/22 = 362.101
POTE generator: ~27/22 = 362.101


{{Val list|legend=1| 53, 116, 169de, 285cde }}
Vals: {{Val list| 10, 43e, 53, 116, 169de, 285cde }}


Badness: 0.0506
Badness: 0.050582


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 887: Line 836:
POTE generator: ~16/13 = 362.105
POTE generator: ~16/13 = 362.105


{{Val list|legend=1| 53, 116, 169de, 285cdef }}
Vals: {{Val list| 10, 43e, 53, 116, 169de, 285cdef }}


Badness: 0.0277
Badness: 0.027689
 
</div></div>


== Interpental ==
== Interpental ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 905: Line 851:
POTE generator: ~49/40 = 362.418
POTE generator: ~49/40 = 362.418


{{Val list|legend=1| 43, 53, 96, 149d }}
Vals: {{Val list| 43, 53, 96, 149d }}


Badness: 0.0518
Badness: 0.051806
 
</div></div>


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 923: Line 866:
POTE generator: ~16/13 = 362.402
POTE generator: ~16/13 = 362.402


{{Val list|legend=1| 43, 53, 96, 149d }}
Vals: {{Val list| 43, 53, 96, 149d }}


Badness: 0.0297
Badness: 0.029680
 
</div></div>


= Alphorn =
= Alphorn =
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 943: Line 883:
{{Val list|legend=1| 28d, 41, 151cd, 192cd, 233cd }}
{{Val list|legend=1| 28d, 41, 151cd, 192cd, 233cd }}


[[Badness]]: 0.1293
[[Badness]]: 0.129258


== 11-limit ==
== 11-limit ==
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 955: Line 894:
POTE generator: ~11/8 = 556.144
POTE generator: ~11/8 = 556.144


{{Val list|legend=1| 28d, 41, 315cde }}
Vals: {{Val list| 28d, 41, 315cde }}
 
Badness: 0.073459
 
= Tertiosec =
Subgroup: 2.3.5
 
[[Comma list]]: {{monzo| -89 21 24 }}
 
[[Mapping]]: [{{val| 3 7 5 }}, {{val| 0 -8 7 }}]
 
[[POTE generator]]: ~16/15 = 112.281
 
{{Val list|legend=1| 21, 54, 75, 96, 171 }}
 
[[Badness]]: 0.851003
 
== 7-limit ==
Subgroup: 2.3.5.7
 
[[Comma list]]: 225/224, 14495514624/13841287201
 
[[Mapping]]: [{{val| 3 7 5 9 }}, {{val| 0 -8 7 -2 }}]
 
{{Multival|legend=1| 24 -21 6 -89 -58 73 }}
 
[[POTE generator]]: ~15/14 = 112.283
 
{{Val list|legend=1| 21, 54, 75, 96, 171d }}
 
[[Badness]]: 0.431636
 
== 11-limit ==
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 3840/3773, 12005/11979
 
Mapping: [{{val| 3 7 5 9 9 }}, {{val| 0 -8 7 -2 5 }}]
 
POTE generator: ~15/14 = 112.171
 
Vals: {{Val list| 21, 54, 75e }}


Badness: 0.0735
Badness: 0.173485


[[Category:Regular temperament theory]]
[[Category:Regular temperament theory]]

Revision as of 11:15, 14 May 2021

This page discusses miscellaneous rank-2 temperaments tempering out [-5 2 2 -1⟩ = 225/224, the marvel comma or septimal kleisma.

Temperaments considered in families and clans are:

  • sharp ({25/24, 28/27}, dicot family)
  • pelogic ({21/20, 135/128}, pelogic family)
  • august ({36/35, 128/125}, augmented family)
  • pajara ({50/49, 64/63}, diaschismic family / jubilismic clan / archytas clan)
  • meantone ({81/80, 126/125}, meantone family)
  • magic ({225/224, 245/243}, magic family)
  • miracle ({225/224, 1029/1024}, gamelismic clan)
  • orwell ({225/224, 1728/1715}, semicomma family)
  • garibaldi ({225/224, 3125/3087}, schismatic family)
  • catakleismic ({225/224, 4375/4374}, kleismic family)
  • decic ({225/224, 16807/16384}, cloudy clan)
  • escapade ({225/224, 65625/65536}, escapade family)
  • fog ({225/224, 156250/151263}, misty family)
  • compton ({225/224, 250047/250000}, pythagorean family)
  • qintosec ({225/224, 2560000/2470629}, qintosec family)

Considered below are negri, wizard, tritonic, septimin, slender, triton, merman, marvo, marvolo, amavil, enneaportent, submajor, and alphorn.

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.

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

Badness: 0.086856

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

Badness: 0.026483

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

Vals: Template:Val list

Badness: 0.026190

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

Vals: Template:Val list

Badness: 0.017833

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

Vals: Template:Val list

Badness: 0.038679

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

Vals: Template:Val list

Badness: 0.024383

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

Vals: Template:Val list

Badness: 0.030617

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

Vals: Template:Val list

Badness: 0.020205

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

Vals: Template:Val list

Badness: 0.035296

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

Vals: Template:Val list

Badness: 0.021559

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

Vals: Template:Val list

Badness: 0.041886

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

Vals: Template:Val list

Badness: 0.025192

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

Vals: Template:Val list

Badness: 0.021778

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

Vals: Template:Val list

Badness: 0.016828

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: 0.075055

Wizard

For the 5-limit version of this temperament, see High badness temperaments #Wizard.
See also: 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: 0.040846

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

Vals: Template:Val list

Badness: 0.018539

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

Vals: Template:Val list

Badness: 0.021781

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

Vals: Template:Val list

Badness: 0.014536

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

Vals: Template:Val list

Badness: 0.015702

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

Vals: Template:Val list

Badness: 0.020252

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

Vals: Template:Val list

Badness: 0.013624


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

Vals: Template:Val list

Badness: 0.014810

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

Vals: Template:Val list

Badness: 0.057799

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: 0.059245

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

Vals: Template:Val list

Badness: 0.045675

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

Badness: 0.047578

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

Vals: Template:Val list

Badness: 0.023659

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

Vals: Template:Val list

Badness: 0.022993

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

Vals: Template:Val list

Badness: 0.045456

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: 0.055078

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

Vals: Template:Val list

Badness: 0.036383

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

Vals: Template:Val list

Badness: 0.027544

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

Badness: 0.054502

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

Vals: Template:Val list

Badness: 0.031309

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

Vals: Template:Val list

Badness: 0.023117

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: 0.056934

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

Vals: Template:Val list

Badness: 0.025342

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

Vals: Template:Val list

Badness: 0.025913

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: 0.097627

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

Vals: Template:Val list

Badness: 0.031685

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

Vals: Template:Val list

Badness: 0.026882

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: 0.083338

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

Vals: Template:Val list

Badness: 0.028965

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

Vals: Template:Val list

Badness: 0.021470

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: 0.232481

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: 0.109625

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

Vals: Template:Val list

Badness: 0.042649

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

Vals: Template:Val list

Badness: 0.025791

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: 0.093679

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

Vals: Template:Val list

Badness: 0.030426

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

Vals: Template:Val list

Badness: 0.022322

Submajor

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: 0.130236

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: 0.060533

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

Vals: Template:Val list

Badness: 0.050582

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

Vals: Template:Val list

Badness: 0.027689

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

Vals: Template:Val list

Badness: 0.051806

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

Vals: Template:Val list

Badness: 0.029680

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: 0.129258

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

Vals: Template:Val list

Badness: 0.073459

Tertiosec

Subgroup: 2.3.5

Comma list: [-89 21 24⟩

Mapping: [⟨3 7 5], ⟨0 -8 7]]

POTE generator: ~16/15 = 112.281

Template:Val list

Badness: 0.851003

7-limit

Subgroup: 2.3.5.7

Comma list: 225/224, 14495514624/13841287201

Mapping: [⟨3 7 5 9], ⟨0 -8 7 -2]]

Wedgie: ⟨⟨ 24 -21 6 -89 -58 73 ]]

POTE generator: ~15/14 = 112.283

Template:Val list

Badness: 0.431636

11-limit

Subgroup: 2.3.5.7.11

Comma list: 225/224, 3840/3773, 12005/11979

Mapping: [⟨3 7 5 9 9], ⟨0 -8 7 -2 5]]

POTE generator: ~15/14 = 112.171

Vals: Template:Val list

Badness: 0.173485

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