Marvel temperaments: Difference between revisions
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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.) | 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 = | == Negri == | ||
{{main| Negri }} | {{main| Negri }} | ||
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[[Badness]]: 0.086856 | [[Badness]]: 0.086856 | ||
== 7-limit == | === 7-limit === | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 62: | Line 62: | ||
[[Badness]]: 0.026483 | [[Badness]]: 0.026483 | ||
=== Negra === | ==== Negra ==== | ||
This is the 2.3.5.7.13 extension of negri. | This is the 2.3.5.7.13 extension of negri. | ||
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[[Comma list]]: 49/48, 65/64, 91/90 | [[Comma list]]: 49/48, 65/64, 91/90 | ||
[[Sval]] [[ | [[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]] [[mapping]]: [{{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 | [[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 }} | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 92: | Line 92: | ||
Badness: 0.026190 | Badness: 0.026190 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.017833 | Badness: 0.017833 | ||
== Negril == | === Negril === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Badness: 0.038679 | Badness: 0.038679 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.024383 | Badness: 0.024383 | ||
== Negric == | === Negric === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 144: | Line 144: | ||
Badness: 0.030617 | Badness: 0.030617 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 157: | Line 157: | ||
Badness: 0.020205 | Badness: 0.020205 | ||
== Negroni == | === Negroni === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Badness: 0.035296 | Badness: 0.035296 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.021559 | Badness: 0.021559 | ||
== Wilsec == | === Wilsec === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Badness: 0.041886 | Badness: 0.041886 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.025192 | Badness: 0.025192 | ||
=== 17-limit === | ==== 17-limit ==== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 222: | Line 222: | ||
Badness: 0.021778 | Badness: 0.021778 | ||
=== 19-limit === | ==== 19-limit ==== | ||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
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Badness: 0.016828 | Badness: 0.016828 | ||
= Passive = | == Passive == | ||
Passive (1&11) tempers out the same 5-limit comma as the [[Archytas clan #Passion|passion temperament]] (12&49), but with the marvel (126/125) rather than 64/63 tempered out. | |||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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[[Badness]]: 0.075055 | [[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}} | ||
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Scales: [[wizard22]] | Scales: [[wizard22]] | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Scales: [[wizard22]] | Scales: [[wizard22]] | ||
=== Lizard === | ==== Lizard ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.021781 | Badness: 0.021781 | ||
==== 17-limit ==== | ===== 17-limit ===== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
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Badness: 0.014536 | 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 | ||
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Badness: 0.015702 | Badness: 0.015702 | ||
=== Gizzard === | ==== Gizzard ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.020252 | Badness: 0.020252 | ||
==== 17-limit ==== | ===== 17-limit ===== | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
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Badness: 0.013624 | Badness: 0.013624 | ||
===== 19-limit ===== | |||
==== 19-limit ==== | |||
Subgroup: 2.3.5.7.11.13.17.19 | Subgroup: 2.3.5.7.11.13.17.19 | ||
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Badness: 0.014810 | Badness: 0.014810 | ||
== Mage == | === Mage === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Badness: 0.057799 | 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]].'' | ||
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[[Badness]]: 0.059245 | [[Badness]]: 0.059245 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Badness: 0.045675 | 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]].'' | ||
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[[Badness]]: 0.047578 | [[Badness]]: 0.047578 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Badness: 0.023659 | Badness: 0.023659 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.022993 | Badness: 0.022993 | ||
== Tritoni == | === Tritoni === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Badness: 0.045456 | 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]].'' | ||
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[[Badness]]: 0.055078 | [[Badness]]: 0.055078 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 511: | Line 510: | ||
Badness: 0.036383 | Badness: 0.036383 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 524: | Line 523: | ||
Badness: 0.027544 | Badness: 0.027544 | ||
= Septimin = | == Septimin == | ||
: ''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]].'' | ||
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[[Badness]]: 0.054502 | [[Badness]]: 0.054502 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 554: | Line 553: | ||
Badness: 0.031309 | Badness: 0.031309 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.023117 | Badness: 0.023117 | ||
= Slender = | == Slender == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 582: | Line 581: | ||
[[Badness]]: 0.056934 | [[Badness]]: 0.056934 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 595: | Line 594: | ||
Badness: 0.025342 | Badness: 0.025342 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 608: | Line 607: | ||
Badness: 0.025913 | Badness: 0.025913 | ||
= Marvo = | == Marvo == | ||
{{see also| Gravity family }} | {{see also| Gravity family }} | ||
| Line 625: | Line 624: | ||
[[Badness]]: 0.097627 | [[Badness]]: 0.097627 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 638: | Line 637: | ||
Badness: 0.031685 | Badness: 0.031685 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 651: | Line 650: | ||
Badness: 0.026882 | Badness: 0.026882 | ||
= Marvolo = | == Marvolo == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 666: | Line 665: | ||
[[Badness]]: 0.083338 | [[Badness]]: 0.083338 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 679: | Line 678: | ||
Badness: 0.028965 | Badness: 0.028965 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 692: | Line 691: | ||
Badness: 0.021470 | Badness: 0.021470 | ||
= Amavil = | == Amavil == | ||
== 5-limit (Mabila) == | === 5-limit (Mabila) === | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 706: | Line 705: | ||
[[Badness]]: 0.232481 | [[Badness]]: 0.232481 | ||
== 7-limit == | === 7-limit === | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 721: | Line 720: | ||
[[Badness]]: 0.109625 | [[Badness]]: 0.109625 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 734: | Line 733: | ||
Badness: 0.042649 | Badness: 0.042649 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 747: | Line 746: | ||
Badness: 0.025791 | Badness: 0.025791 | ||
= Enneaportent = | == Enneaportent == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 762: | Line 761: | ||
[[Badness]]: 0.093679 | [[Badness]]: 0.093679 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 775: | Line 774: | ||
Badness: 0.030426 | Badness: 0.030426 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 788: | Line 787: | ||
Badness: 0.022322 | Badness: 0.022322 | ||
= Submajor = | == Submajor == | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 801: | Line 800: | ||
[[Badness]]: 0.130236 | [[Badness]]: 0.130236 | ||
== 7-limit == | === 7-limit === | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 816: | Line 815: | ||
[[Badness]]: 0.060533 | [[Badness]]: 0.060533 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 829: | Line 828: | ||
Badness: 0.050582 | Badness: 0.050582 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 842: | Line 841: | ||
Badness: 0.027689 | Badness: 0.027689 | ||
== Interpental == | === Interpental === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 857: | Line 856: | ||
Badness: 0.051806 | Badness: 0.051806 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 872: | Line 871: | ||
Badness: 0.029680 | Badness: 0.029680 | ||
= Alphorn = | == Alphorn == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 887: | Line 886: | ||
[[Badness]]: 0.129258 | [[Badness]]: 0.129258 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 900: | Line 899: | ||
Badness: 0.073459 | Badness: 0.073459 | ||
= Tertiosec = | == Tertiosec == | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 913: | Line 912: | ||
[[Badness]]: 0.851003 | [[Badness]]: 0.851003 | ||
== 7-limit == | === 7-limit === | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 928: | Line 927: | ||
[[Badness]]: 0.431636 | [[Badness]]: 0.431636 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||