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Marvel temperaments: Difference between revisions

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* [[Orwell]] → [[Semicomma family #Orwell|Semicomma family]] (+1728/1715, twelfth sliced in seven)
* [[Orwell]] → [[Semicomma family #Orwell|Semicomma family]] (+1728/1715, twelfth sliced in seven)
* ''[[Snipes]]''  → [[Wesley family #Snipes|Wesley family]] (+6125/5832, two octaves and a fourth sliced in seven)
* ''[[Snipes]]''  → [[Wesley family #Snipes|Wesley family]] (+6125/5832, two octaves and a fourth sliced in seven)
* ''[[Escapist]]'' → [[Escapade family #Escapade|Escapade family]] (+65625/65536, fourth sliced in nine)
* ''[[Submajor]]'' → [[Buzzardsmic clan #Submajor|Buzzardsmic clan]] (+65536/64827, two octaves and a fourth sliced in eight)
* ''[[Escapist]]'' → [[Escapade family #Escapist|Escapade family]] (+65625/65536, fourth sliced in nine)
* ''[[Decic]]'' → [[Cloudy clan #Decic|Cloudy clan]] (+16807/16384, generated by the fifth with a 1/10-octave period)
* ''[[Decic]]'' → [[Cloudy clan #Decic|Cloudy clan]] (+16807/16384, generated by the fifth with a 1/10-octave period)
* ''[[Amavil]]'' → [[Mabila family #Amavil|Mabila family]] (+17496/16807, four octaves and a fourth sliced in ten)
* ''[[Amavil]]'' → [[Mabila family #Amavil|Mabila family]] (+17496/16807, four octaves and a fourth sliced in ten)
* ''[[Betic]]'' → [[Sycamore family #Betic|Sycamore family]] (+1071875/1062882, fifth sliced in eleven)
* ''[[Betic]]'' → [[Sycamore family #Betic|Sycamore family]] (+1071875/1062882, fifth sliced in eleven)
* ''[[Hendeca]]'' → [[11th-octave temperaments #Hendeca|11th-octave temperaments]] (+122880/117649, generated by the fifth with a 1/11-octave period)
* ''[[Compton]]'' → [[Compton family #Compton|Compton family]] (+250047/250000, generated by the classical major third with a 1/12-octave period)
* ''[[Compton]]'' → [[Compton family #Compton|Compton family]] (+250047/250000, generated by the classical major third with a 1/12-octave period)
* ''[[Raccoon]]'' → [[Vavoom family #Raccoon|Vavoom family]] (+41943040/40353607, twelfth sliced in seventeen)
* ''[[Raccoon]]'' → [[Vavoom family #Raccoon|Vavoom family]] (+41943040/40353607, twelfth sliced in seventeen)
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* ''[[Gammy]]'' → [[Gammic family #Gammy|Gammic family]] (+94143178827/91913281250, fifth sliced in twenty)
* ''[[Gammy]]'' → [[Gammic family #Gammy|Gammic family]] (+94143178827/91913281250, fifth sliced in twenty)


Considered below are wizard, tritonic, septimin, slender, triton, merman, marvolo, amavil, enneaportent, submajor, alphorn, tertiosec, gwazy, and gracecordial.  
Considered below are wizard, tritonic, septimin, slender, triton, merman, marvolo, amavil, enneaportent, alphorn, tertiosec, gwazy, and gracecordial.  


Since {{nowrap|(5/4)<sup>2</sup> {{=}} 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.
Since {{nowrap|(5/4)<sup>2</sup> {{=}} 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.
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: mapping generators: ~1225/864, ~245/216
: mapping generators: ~1225/864, ~245/216
{{Multival|legend=1| 12 -2 20 -31 -2 52 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
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== Tritonic ==
== Tritonic ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Tritonic]].''
: ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Tritonic]].''


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
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{{Mapping|legend=1| 1 4 -3 -3 | 0 -5 11 12 }}
{{Mapping|legend=1| 1 4 -3 -3 | 0 -5 11 12 }}


{{Multival|legend=1| 5 -11 -12 -29 -33 3 }}
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~7/5 = 580.286
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/5 = 580.286


{{Optimal ET sequence|legend=1| 29, 31, 60, 91, 122, 213bcd }}
{{Optimal ET sequence|legend=1| 29, 31, 60, 91, 122, 213bcd }}
Line 209: Line 207:
Mapping: {{mapping| 1 4 -3 -3 2 | 0 -5 11 12 3 }}
Mapping: {{mapping| 1 4 -3 -3 2 | 0 -5 11 12 3 }}


{{Multival|legend=1| 5 -11 -12 -3 -29 -33 -22 3 31 33 }}
Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 580.267
 
Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 580.267


{{Optimal ET sequence|legend=1| 29, 31, 60e }}
{{Optimal ET sequence|legend=1| 29, 31, 60e }}
Line 224: Line 220:
Mapping: {{mapping| 1 4 -3 -3 2 -5 | 0 -5 11 12 3 18 }}
Mapping: {{mapping| 1 4 -3 -3 2 -5 | 0 -5 11 12 3 18 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 580.108
Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 580.108


{{Optimal ET sequence|legend=1| 29, 31, 60e }}
{{Optimal ET sequence|legend=1| 29, 31, 60e }}
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Mapping: {{mapping| 1 4 -3 -3 2 -5 -8 | 0 -5 11 12 3 18 25 }}
Mapping: {{mapping| 1 4 -3 -3 2 -5 -8 | 0 -5 11 12 3 18 25 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 580.055
Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 580.055


{{Optimal ET sequence|legend=1| 29g, 31, 60e }}
{{Optimal ET sequence|legend=1| 29g, 31, 60e }}


Badness: ?
Badness: 0.019093


==== 19-limit ====
==== 19-limit ====
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Mapping: {{mapping| 1 4 -3 -3 2 -5 -8 -3 | 0 -5 11 12 3 18 25 15 }}
Mapping: {{mapping| 1 4 -3 -3 2 -5 -8 -3 | 0 -5 11 12 3 18 25 15 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 580.026
Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 580.026


{{Optimal ET sequence|legend=1| 29g, 31, 60e }}
{{Optimal ET sequence|legend=1| 29g, 31, 60e }}


Badness: ?
Badness: 0.017010


==== 23-limit ====
==== 23-limit ====
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Mapping: {{mapping| 1 4 -3 -3 2 -5 -8 -3 5 | 0 -5 11 12 3 18 25 15 -1 }}
Mapping: {{mapping| 1 4 -3 -3 2 -5 -8 -3 5 | 0 -5 11 12 3 18 25 15 -1 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 580.009
Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 580.009


{{Optimal ET sequence|legend=1| 29g, 31, 60e }}
{{Optimal ET sequence|legend=1| 29g, 31, 60e }}


Badness: ?
Badness: 0.014471


=== Tritoni ===
=== Tritoni ===
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Mapping: {{mapping| 1 4 -3 -3 17 | 0 -5 11 12 -28 }}
Mapping: {{mapping| 1 4 -3 -3 17 | 0 -5 11 12 -28 }}


{{Multival|legend=1| 5 -11 -12 28 -29 -33 27 3 103 120 }}
Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 580.389
 
Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 580.389


{{Optimal ET sequence|legend=1| 31, 91, 122, 153d }}
{{Optimal ET sequence|legend=1| 31, 91, 122, 153d }}
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== Septimin ==
== Septimin ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Septimin]].''
: ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Septimin]].''


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
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{{Mapping|legend=1| 1 4 1 5 | 0 -11 6 -10 }}
{{Mapping|legend=1| 1 4 1 5 | 0 -11 6 -10 }}


{{Multival|legend=1| 11 -6 10 -35 -15 40 }}
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~7/6 = 263.632
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/6 = 263.632


{{Optimal ET sequence|legend=1| 41, 91, 132d }}
{{Optimal ET sequence|legend=1| 41, 91, 132d }}
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Mapping: {{mapping| 1 4 1 5 5 | 0 -11 6 -10 -7 }}
Mapping: {{mapping| 1 4 1 5 5 | 0 -11 6 -10 -7 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 263.634
Optimal tuning (POTE): ~2 = 1200.000, ~7/6 = 263.634


{{Optimal ET sequence|legend=1| 41, 91, 223cdef }}
{{Optimal ET sequence|legend=1| 41, 91, 223cdef }}
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Mapping: {{mapping| 1 4 1 5 5 7 | 0 -11 6 -10 -7 -15 }}
Mapping: {{mapping| 1 4 1 5 5 7 | 0 -11 6 -10 -7 -15 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 263.700
Optimal tuning (POTE): ~2 = 1200.000, ~7/6 = 263.700


{{Optimal ET sequence|legend=1| 41, 91 }}
{{Optimal ET sequence|legend=1| 41, 91 }}
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== Merman ==
== Merman ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Merman]].''
: ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Merman]].''


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
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{{Mapping|legend=1| 1 5 -5 -5 | 0 -7 15 16 }}
{{Mapping|legend=1| 1 5 -5 -5 | 0 -7 15 16 }}


{{Multival|legend=1| 7 -15 -16 -40 -45 5 }}
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~7/5 = 585.585
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/5 = 585.585


{{Optimal ET sequence|legend=1| 41, 84, 125 }}
{{Optimal ET sequence|legend=1| 41, 84, 125 }}
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Mapping: {{mapping| 1 5 -5 -5 2 | 0 -7 15 16 3 }}
Mapping: {{mapping| 1 5 -5 -5 2 | 0 -7 15 16 3 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.606
Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 585.606


{{Optimal ET sequence|legend=1| 41, 84, 125e }}
{{Optimal ET sequence|legend=1| 41, 84, 125e }}
Line 364: Line 354:
Mapping: {{mapping| 1 5 -5 -5 2 12 | 0 -7 15 16 3 -17 }}
Mapping: {{mapping| 1 5 -5 -5 2 12 | 0 -7 15 16 3 -17 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.657
Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 585.657


{{Optimal ET sequence|legend=1| 41, 84, 125e, 209ef, 293ef }}
{{Optimal ET sequence|legend=1| 41, 84, 125e, 209ef, 293ef }}
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{{Mapping|legend=1| 1 2 2 3 | 0 -13 10 -6 }}
{{Mapping|legend=1| 1 2 2 3 | 0 -13 10 -6 }}


{{Multival|legend=1| 13 -10 6 -46 -27 42 }}
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~49/48 = 38.413
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/48 = 38.413


{{Optimal ET sequence|legend=1| 31, 94, 125 }}
{{Optimal ET sequence|legend=1| 31, 94, 125 }}
Line 394: Line 382:
Mapping: {{mapping| 1 2 2 3 4 | 0 -13 10 -6 -17 }}
Mapping: {{mapping| 1 2 2 3 4 | 0 -13 10 -6 -17 }}


Optimal tuning (POTE): ~2 = 1\1, ~49/48 = 38.387
Optimal tuning (POTE): ~2 = 1200.000, ~49/48 = 38.387


{{Optimal ET sequence|legend=1| 31, 63, 94, 125 }}
{{Optimal ET sequence|legend=1| 31, 63, 94, 125 }}
Line 407: Line 395:
Mapping: {{mapping| 1 2 2 3 4 3 | 0 -13 10 -6 -17 22 }}
Mapping: {{mapping| 1 2 2 3 4 3 | 0 -13 10 -6 -17 22 }}


Optimal tuning (POTE): ~2 = 1\1, ~49/48 = 38.314
Optimal tuning (POTE): ~2 = 1200.000, ~49/48 = 38.314


{{Optimal ET sequence|legend=1| 31, 63, 94 }}
{{Optimal ET sequence|legend=1| 31, 63, 94 }}
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== Triton ==
== Triton ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Stump]].''
: ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Stump]].''


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
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{{Mapping|legend=1| 1 0 6 7 | 0 3 -7 -8 }}
{{Mapping|legend=1| 1 0 6 7 | 0 3 -7 -8 }}


{{Multival|legend=1| 3 -7 -8 -18 -21 1 }}
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~7/5 = 568.865
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/5 = 568.865


{{Optimal ET sequence|legend=1| 2, 17d, 19, 78bd, 97bd }}
{{Optimal ET sequence|legend=1| 2, 17d, 19, 78bd, 97bd }}
Line 437: Line 423:
Mapping: {{mapping| 1 0 6 7 4 | 0 3 -7 -8 -1 }}
Mapping: {{mapping| 1 0 6 7 4 | 0 3 -7 -8 -1 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 569.144
Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 569.144


{{Optimal ET sequence|legend=1| 2, 17d, 19, 59bde, 78bde, 97bde }}
{{Optimal ET sequence|legend=1| 2, 17d, 19, 59bde, 78bde, 97bde }}


Badness: 0.045675
Badness: 0.045675
== Submajor ==
[[Subgroup]]: 2.3.5
[[Comma list]]: 69198046875/68719476736
{{Mapping|legend=1| 1 4 -1 | 0 -8 11 }}
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10125/8192 = 362.321
{{Optimal ET sequence|legend=1| 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc }}
[[Badness]]: 0.130236
=== 7-limit ===
[[Subgroup]]: 2.3.5.7
[[Comma list]]: 225/224, 51200/50421
{{Mapping|legend=1| 1 4 -1 1 | 0 -8 11 6 }}
{{Multival|legend=1| 8 -11 -6 -36 -32 17 }}
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/40 = 362.255
{{Optimal ET sequence|legend=1| 10, 33, 43, 53 }}
[[Badness]]: 0.060533
==== 2.3.5.7.13 subgroup ====
{{ See also | Greater tendoneutralic }}
This temperament naturally comes about from a structure in EDOs like [[43edo|43]] and [[53edo|53]] where two flattened ~[[13/8]] intervals reach the [[No-fives subgroup temperaments#Buzzard|buzzard]] generator of ~[[21/16]], two of which produce a semitritave (that can here be equated to [[26/15]], providing a mapping of 5 significantly less complex than the [[vulture]] mapping), and two of those finally reach [[3/1]].
Subgroup: 2.3.5.7.13
Comma list: 169/168, 225/224, 640/637
Mapping: {{mapping| 1 4 -1 1 4 | 0 -8 11 6 -1 }}
Optimal tuning (CTE): ~2 = 1\1, ~16/13 = 362.242
Badness (Dirichlet): 0.847
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 6655/6561
Mapping: {{mapping| 1 4 -1 1 11 | 0 -8 11 6 -25 }}
Optimal tuning (POTE): ~2 = 1\1, ~27/22 = 362.101
{{Optimal ET sequence|legend=1| 10, 43e, 53, 116, 169de, 285cde }}
Badness: 0.050582
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 225/224, 275/273, 385/384
Mapping: {{mapping| 1 4 -1 1 11 4 | 0 -8 11 6 -25 -1 }}
Optimal tuning (POTE): ~2 = 1\1, ~16/13 = 362.105
{{Optimal ET sequence|legend=1| 10, 43e, 53, 116, 169de, 285cdef }}
Badness: 0.027689
=== Interpental ===
Subgroup: 2.3.5.7.11
Comma list: 99/98, 176/175, 51200/50421
Mapping: {{mapping| 1 4 -1 1 -5 | 0 -8 11 6 28 }}
Optimal tuning (POTE): ~2 = 1\1, ~49/40 = 362.418
{{Optimal ET sequence|legend=1| 43, 53, 96, 149d }}
Badness: 0.051806
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 169/168, 176/175, 640/637
Mapping: {{mapping| 1 4 -1 1 -5 4 | 0 -8 11 6 28 -1 }}
Optimal tuning (POTE): ~2 = 1\1, ~16/13 = 362.402
{{Optimal ET sequence|legend=1| 43, 53, 96, 149d }}
Badness: 0.029680


== Marvolo ==
== Marvolo ==
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{{Mapping|legend=1| 1 2 1 1 | 0 -6 19 26 }}
{{Mapping|legend=1| 1 2 1 1 | 0 -6 19 26 }}


{{Multival|legend=1| 6 -19 -26 -44 -58 -7 }}
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~21/20 = 83.348
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~21/20 = 83.348


{{Optimal ET sequence|legend=1| 29, 43, 72, 619bcd, 691bcd }}
{{Optimal ET sequence|legend=1| 29, 43, 72, 619bcd, 691bcd }}
Line 560: Line 449:
Mapping: {{mapping| 1 2 1 1 2 | 0 -6 19 26 21 }}
Mapping: {{mapping| 1 2 1 1 2 | 0 -6 19 26 21 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 83.340
Optimal tuning (POTE): ~2 = 1200.000, ~21/20 = 83.340


{{Optimal ET sequence|legend=1| 29, 43, 72 }}
{{Optimal ET sequence|legend=1| 29, 43, 72 }}
Line 573: Line 462:
Mapping: {{mapping| 1 2 1 1 2 3 | 0 -6 19 26 21 10 }}
Mapping: {{mapping| 1 2 1 1 2 3 | 0 -6 19 26 21 10 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 83.330
Optimal tuning (POTE): ~2 = 1200.000, ~21/20 = 83.330


{{Optimal ET sequence|legend=1| 29, 43, 72, 115f }}
{{Optimal ET sequence|legend=1| 29, 43, 72, 115f }}
Line 586: Line 475:
Mapping: {{mapping| 1 2 1 1 2 3 2 | 0 -6 19 26 21 10 30 }}
Mapping: {{mapping| 1 2 1 1 2 3 2 | 0 -6 19 26 21 10 30 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 83.330
Optimal tuning (POTE): ~2 = 1200.000, ~21/20 = 83.330


{{Optimal ET sequence|legend=1| 29g, 43, 72 }}
{{Optimal ET sequence|legend=1| 29g, 43, 72 }}
Badness: 0.014924


=== 19-limit ===
=== 19-limit ===
Line 597: Line 488:
Mapping: {{mapping| 1 2 1 1 2 3 2 3 | 0 -6 19 26 21 10 30 18 }}
Mapping: {{mapping| 1 2 1 1 2 3 2 3 | 0 -6 19 26 21 10 30 18 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 83.330
Optimal tuning (POTE): ~2 = 1200.000, ~21/20 = 83.330


{{Optimal ET sequence|legend=1| 29g, 43, 72 }}
{{Optimal ET sequence|legend=1| 29g, 43, 72 }}
Badness: 0.014722


== Enneaportent ==
== Enneaportent ==
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{{Mapping|legend=1| 9 0 28 11 | 0 2 -1 2 }}
{{Mapping|legend=1| 9 0 28 11 | 0 2 -1 2 }}


: mapping generators: ~2592/2401, ~12005/6912
: Mapping generators: ~2592/2401, ~12005/6912


{{Multival|legend=1| 18 -9 18 -56 -22 67 }}
[[Optimal tuning]] ([[POTE]]): ~2592/2401 = 133.3333, ~12005/6912 = 950.1680 (~1728/1715 = 16.8347)
 
[[Optimal tuning]] ([[POTE]]): ~2592/2401 = 1\9, ~12005/6912 = 950.1680 (~1728/1715 = 16.8347)


{{Optimal ET sequence|legend=1| 9, 63, 72, 495bcd }}
{{Optimal ET sequence|legend=1| 9, 63, 72, 495bcd }}
Line 625: Line 516:
Mapping: {{mapping| 9 0 28 11 24 | 0 2 -1 2 1 }}
Mapping: {{mapping| 9 0 28 11 24 | 0 2 -1 2 1 }}


Optimal tuning (POTE): ~121/112 = 1\9, ~210/121 = 950.1873 (~99/98 = 16.8540)
Optimal tuning (POTE): ~121/112 = 133.3333, ~210/121 = 950.1873 (~99/98 = 16.8540)


{{Optimal ET sequence|legend=1| 9, 63, 72, 423cd, 495bcd }}
{{Optimal ET sequence|legend=1| 9, 63, 72, 423cd, 495bcd }}
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Mapping: {{mapping| 9 0 28 11 24 19 | 0 2 -1 2 1 2 }}
Mapping: {{mapping| 9 0 28 11 24 19 | 0 2 -1 2 1 2 }}


Optimal tuning (POTE): ~14/13 = 1\9, ~26/15 = 950.2867 (~105/104 = 16.9534)
Optimal tuning (POTE): ~14/13 = 133.3333, ~26/15 = 950.2867 (~105/104 = 16.9534)


{{Optimal ET sequence|legend=1| 9, 63, 72, 279cf }}
{{Optimal ET sequence|legend=1| 9, 63, 72, 279cf }}
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== Gracecordial ==
== Gracecordial ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Gracecordial]].''
: ''For the 5-limit version of this temperament, see [[Schismic–Pythagorean equivalence continuum #Gracecordial]].''


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
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{{Mapping|legend=1| 1 0 34 63 | 0 1 -20 -38 }}
{{Mapping|legend=1| 1 0 34 63 | 0 1 -20 -38 }}


{{Multival|legend=1| 1 -20 -38 -34 -63 -32 }}
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~3/2 = 700.824
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 700.824


{{Optimal ET sequence|legend=1| 12, 113, 125, 238c, 363c }}
{{Optimal ET sequence|legend=1| 12, 113, 125, 238c, 363c }}
Line 668: Line 557:
Mapping: {{mapping| 1 0 34 63 -90 | 0 1 -20 -38 59 }}
Mapping: {{mapping| 1 0 34 63 -90 | 0 1 -20 -38 59 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.834
Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.834


{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125, 238c }}
{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125, 238c }}
Line 681: Line 570:
Mapping: {{mapping| 1 0 34 63 -90 -66 | 0 1 -20 -38 59 44 }}
Mapping: {{mapping| 1 0 34 63 -90 -66 | 0 1 -20 -38 59 44 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.841
Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.841


{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125f, 238cf }}
{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125f, 238cf }}
Line 694: Line 583:
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 | 0 1 -20 -38 59 44 7 }}
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 | 0 1 -20 -38 59 44 7 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.841
Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.841


{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125f, 238cf }}
{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125f, 238cf }}
Line 707: Line 596:
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 | 0 1 -20 -38 59 44 7 -3 }}
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 | 0 1 -20 -38 59 44 7 -3 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.842
Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.842


{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125f, 238cf }}
{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125f, 238cf }}
Line 720: Line 609:
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 | 0 1 -20 -38 59 44 7 -3 30 }}
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 | 0 1 -20 -38 59 44 7 -3 30 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.843
Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.843


{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 238cfi }}
{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 238cfi }}
Line 733: Line 622:
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 | 0 1 -20 -38 59 44 7 -3 30 34 }}
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 | 0 1 -20 -38 59 44 7 -3 30 34 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.842
Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.842


{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125f, 238cfi }}
{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125f, 238cfi }}
Line 746: Line 635:
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 -79 | 0 1 -20 -38 59 44 7 -3 30 34 53 }}
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 -79 | 0 1 -20 -38 59 44 7 -3 30 34 53 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.838
Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.838


{{Optimal ET sequence|legend=1| 12e, 101cdek, 113, 125f, 238cfi }}
{{Optimal ET sequence|legend=1| 12e, 101cdek, 113, 125f, 238cfi }}
Line 759: Line 648:
Mapping: {{mapping| 1 0 34 63 89 | 0 1 -20 -38 -54 }}
Mapping: {{mapping| 1 0 34 63 89 | 0 1 -20 -38 -54 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.885
Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.885


{{Optimal ET sequence|legend=1| 12, 101cd, 113 }}
{{Optimal ET sequence|legend=1| 12, 101cd, 113 }}
Line 772: Line 661:
Mapping: {{mapping| 1 0 34 63 89 113 | 0 1 -20 -38 -54 -69 }}
Mapping: {{mapping| 1 0 34 63 89 113 | 0 1 -20 -38 -54 -69 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.890
Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.890


{{Optimal ET sequence|legend=1| 12f, 101cdf, 113 }}
{{Optimal ET sequence|legend=1| 12f, 101cdf, 113 }}
Line 785: Line 674:
Mapping: {{mapping| 1 0 34 63 89 113 -7 | 0 1 -20 -38 -54 -69 7 }}
Mapping: {{mapping| 1 0 34 63 89 113 -7 | 0 1 -20 -38 -54 -69 7 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.870
Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.870


{{Optimal ET sequence|legend=1| 12f, 101cdf, 113 }}
{{Optimal ET sequence|legend=1| 12f, 101cdf, 113 }}
Line 798: Line 687:
Mapping: {{mapping| 1 0 34 63 89 113 -7 9 | 0 1 -20 -38 -54 -69 7 -3 }}
Mapping: {{mapping| 1 0 34 63 89 113 -7 9 | 0 1 -20 -38 -54 -69 7 -3 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 700.866
Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.866


{{Optimal ET sequence|legend=1| 12f, 101cdf, 113 }}
{{Optimal ET sequence|legend=1| 12f, 101cdf, 113 }}
Line 811: Line 700:
{{Mapping|legend=1| 1 9 0 13 | 0 -16 5 -22 }}
{{Mapping|legend=1| 1 9 0 13 | 0 -16 5 -22 }}


{{Multival|legend=1| 16 -5 22 -45 -10 65 }}
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~48/35 = 556.221
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~48/35 = 556.221


{{Optimal ET sequence|legend=1| 28d, 41, 151cd, 192cd, 233cd }}
{{Optimal ET sequence|legend=1| 28d, 41, 151cd, 192cd, 233cd }}
Line 826: Line 713:
Mapping: {{mapping| 1 9 0 13 3 | 0 -16 5 -22 1 }}
Mapping: {{mapping| 1 9 0 13 3 | 0 -16 5 -22 1 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/8 = 556.144
Optimal tuning (POTE): ~2 = 1200.000, ~11/8 = 556.144


{{Optimal ET sequence|legend=1| 28d, 41, 315cde }}
{{Optimal ET sequence|legend=1| 28d, 41, 315cde }}
Line 833: Line 720:


== Misneb ==
== Misneb ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Misneb]].''
: ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Misneb]].''


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 841: Line 728:
{{Mapping|legend=1| 1 3 1 3 | 0 -15 14 -2 }}
{{Mapping|legend=1| 1 3 1 3 | 0 -15 14 -2 }}


{{Multival|legend=1| 15 -14 2 -57 -39 44 }}
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~16/15 = 113.235
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~16/15 = 113.235


{{Optimal ET sequence|legend=1| 21, 32, 53 }}
{{Optimal ET sequence|legend=1| 21, 32, 53 }}
Line 856: Line 741:
Mapping: {{mapping| 1 3 1 3 1 | 0 -15 14 -2 26 }}
Mapping: {{mapping| 1 3 1 3 1 | 0 -15 14 -2 26 }}


Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 113.323
Optimal tuning (POTE): ~2 = 1200.000, ~16/15 = 113.323


{{Optimal ET sequence|legend=1| 21, 32e, 53, 127, 180de }}
{{Optimal ET sequence|legend=1| 21, 32e, 53, 127, 180de }}
Line 869: Line 754:
Mapping: {{mapping| 1 3 1 3 1 2 | 0 -15 14 -2 26 18 }}
Mapping: {{mapping| 1 3 1 3 1 2 | 0 -15 14 -2 26 18 }}


Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 113.323
Optimal tuning (POTE): ~2 = 1200.000, ~16/15 = 113.323


{{Optimal ET sequence|legend=1| 21, 32e, 53, 127, 180de }}
{{Optimal ET sequence|legend=1| 21, 32e, 53, 127, 180de }}
Line 882: Line 767:
Mapping: {{mapping| 1 3 1 3 6 | 0 -15 14 -2 -27 }}
Mapping: {{mapping| 1 3 1 3 6 | 0 -15 14 -2 -27 }}


Optimal tuning (POTE): ~2 = 1\1, ~16/15 = 113.142
Optimal tuning (POTE): ~2 = 1200.000, ~16/15 = 113.142


{{Optimal ET sequence|legend=1| 32, 53, 191de, 244cddee, 297cddee }}
{{Optimal ET sequence|legend=1| 32, 53, 191de, 244cddee, 297cddee }}
Line 889: Line 774:


== Untriton ==
== Untriton ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Untriton]].''
: ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Untriton]].''


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 897: Line 782:
{{Mapping|legend=1| 1 6 -7 -7 | 0 -9 19 20 }}
{{Mapping|legend=1| 1 6 -7 -7 | 0 -9 19 20 }}


{{Multival|legend=1| 9 -19 -20 -51 -57 7 }}
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~7/5 = 588.641
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/5 = 588.641


{{Optimal ET sequence|legend=1| 51, 53, 316cd, 369cdd, 422cdd }}
{{Optimal ET sequence|legend=1| 51, 53, 316cd, 369cdd, 422cdd }}
Line 912: Line 795:
Mapping: {{mapping| 1 6 -7 -7 1 | 0 -9 19 20 5 }}
Mapping: {{mapping| 1 6 -7 -7 1 | 0 -9 19 20 5 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 588.626
Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 588.626


{{Optimal ET sequence|legend=1| 51, 53 }}
{{Optimal ET sequence|legend=1| 51, 53 }}
Line 925: Line 808:
Mapping: {{mapping| 1 6 -7 -7 1 -12 | 0 -9 19 20 5 32 }}
Mapping: {{mapping| 1 6 -7 -7 1 -12 | 0 -9 19 20 5 32 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 588.654
Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 588.654


{{Optimal ET sequence|legend=1| 51f, 53 }}
{{Optimal ET sequence|legend=1| 51f, 53 }}
Line 938: Line 821:
{{Mapping|legend=1| 1 1 5 7 | 0 5 -23 -36 }}
{{Mapping|legend=1| 1 1 5 7 | 0 5 -23 -36 }}


{{Multival|legend=1| 5 -23 -36 -48 -71 -19 }}
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~10000/9261 = 139.838
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10000/9261 = 139.838


{{Optimal ET sequence|legend=1| 43, 60, 103, 266bcd, 369bcd }}
{{Optimal ET sequence|legend=1| 43, 60, 103, 266bcd, 369bcd }}
Line 953: Line 834:
Mapping: {{mapping| 1 1 5 7 8 | 0 5 -23 -36 -39 }}
Mapping: {{mapping| 1 1 5 7 8 | 0 5 -23 -36 -39 }}


Optimal tuning (POTE): ~2 = 1\1, ~320/297 = 139.827
Optimal tuning (POTE): ~2 = 1200.000, ~320/297 = 139.827


{{Optimal ET sequence|legend=1| 43, 60e, 103 }}
{{Optimal ET sequence|legend=1| 43, 60e, 103 }}
Line 966: Line 847:
Mapping: {{mapping| 1 1 5 7 8 3 | 0 5 -23 -36 -39 6 }}
Mapping: {{mapping| 1 1 5 7 8 3 | 0 5 -23 -36 -39 6 }}


Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 139.812
Optimal tuning (POTE): ~2 = 1200.000, ~13/12 = 139.812


{{Optimal ET sequence|legend=1| 43, 60e, 103 }}
{{Optimal ET sequence|legend=1| 43, 60e, 103 }}
Line 979: Line 860:
Mapping: {{mapping| 1 1 5 7 8 3 7 | 0 5 -23 -36 -39 6 -25 }}
Mapping: {{mapping| 1 1 5 7 8 3 7 | 0 5 -23 -36 -39 6 -25 }}


Optimal tuning (POTE): ~2 = 1\1, ~13/12 = 139.815
Optimal tuning (POTE): ~2 = 1200.000, ~13/12 = 139.815


{{Optimal ET sequence|legend=1| 43, 60e, 103 }}
{{Optimal ET sequence|legend=1| 43, 60e, 103 }}
Line 994: Line 875:
{{Mapping|legend=1| 2 1 6 4 | 0 8 -5 6 }}
{{Mapping|legend=1| 2 1 6 4 | 0 8 -5 6 }}


{{Multival|legend=1| 16 -10 12 -53 -26 56 }}
[[Optimal tuning]] ([[POTE]]): ~2401/1728 = 600.000, ~35/32 = 162.658
 
[[Optimal tuning]] ([[POTE]]): ~2401/1728 = 1\2, ~35/32 = 162.658


{{Optimal ET sequence|legend=1| 22, 74, 96, 118d }}
{{Optimal ET sequence|legend=1| 22, 74, 96, 118d }}
Line 1,009: Line 888:
Mapping: {{mapping| 2 1 6 4 8 | 0 8 -5 6 -4 }}
Mapping: {{mapping| 2 1 6 4 8 | 0 8 -5 6 -4 }}


Optimal tuning (POTE): ~363/256 = 1\2, ~11/10 = 162.592
Optimal tuning (POTE): ~363/256 = 600.000, ~11/10 = 162.592


{{Optimal ET sequence|legend=1| 22, 74, 96, 118d }}
{{Optimal ET sequence|legend=1| 22, 74, 96, 118d }}
Line 1,016: Line 895:


== Tertiosec ==
== Tertiosec ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Tertiosec]].''
: ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Tertiosec]].''


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 1,024: Line 903:
{{Mapping|legend=1| 3 7 5 9 | 0 -8 7 -2 }}
{{Mapping|legend=1| 3 7 5 9 | 0 -8 7 -2 }}


{{Multival|legend=1| 24 -21 6 -89 -58 73 }}
[[Optimal tuning]] ([[POTE]]): ~3072/2401 = 400.000, ~15/14 = 112.283
 
[[Optimal tuning]] ([[POTE]]): ~3072/2401 = 1\3, ~15/14 = 112.283


{{Optimal ET sequence|legend=1| 21, 54, 75, 96, 171d }}
{{Optimal ET sequence|legend=1| 21, 54, 75, 96, 171d }}
Line 1,039: Line 916:
Mapping: {{mapping| 3 7 5 9 9 | 0 -8 7 -2 5 }}
Mapping: {{mapping| 3 7 5 9 9 | 0 -8 7 -2 5 }}


Optimal tuning (POTE): ~44/35 = 1\3, ~15/14 = 112.171
Optimal tuning (POTE): ~44/35 = 400.000, ~15/14 = 112.171


{{Optimal ET sequence|legend=1| 21, 54, 75e }}
{{Optimal ET sequence|legend=1| 21, 54, 75e }}
Line 1,046: Line 923:


[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Pages with mostly numerical content]]
[[Category:Marvel temperaments| ]] <!-- main article -->
[[Category:Marvel temperaments| ]] <!-- main article -->
[[Category:Marvel| ]] <!-- key article -->
[[Category:Marvel| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Marvel_temperaments"