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Marvel temperaments: Difference between revisions

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{{Technical data page}}
This page discusses miscellaneous rank-2 temperaments tempering out {{monzo|-5 2 2 -1}} = [[225/224]], the marvel comma or septimal kleisma.  
This page discusses miscellaneous rank-2 temperaments tempering out {{monzo|-5 2 2 -1}} = [[225/224]], the marvel comma or septimal kleisma.  


Temperaments considered in families and clans are:  
Temperaments considered in families and clans are:  
* ''[[Pelogic]]'' → [[Pelogic family #Pelogic|Pelogic family]] (+21/20 or 135/128, generated by the fifth with 5/4 mapped to the m3)
* ''[[Pelogic]]'' → [[Mavila family #Pelogic|Mavila family]] (+21/20 or 135/128, generated by the fifth with 5/4 mapped to the m3)
* [[Meantone]] → [[Meantone family #Septimal meantone|Meantone family]] (+81/80 or 126/125, generated by the fifth with 5/4 mapped to the M3)
* [[Meantone]] → [[Meantone family #Septimal meantone|Meantone family]] (+81/80 or 126/125, generated by the fifth with 5/4 mapped to the M3)
* [[Garibaldi temperament|Garibaldi]] → [[Schismatic family #Garibaldi|Schismatic family]] (+3125/3087, generated by the fifth with 5/4 mapped to the d4)
* [[Garibaldi]] → [[Schismatic family #Garibaldi|Schismatic family]] (+3125/3087, generated by the fifth with 5/4 mapped to the d4)
* [[Pajara]] → [[Diaschismic family #Pajara|Diaschismic family]] (+50/49 or 64/63, generated by the fifth with a semioctave period)
* [[Pajara]] → [[Diaschismic family #Pajara|Diaschismic family]] (+50/49 or 64/63, generated by the fifth with a semioctave period)
* ''[[Sharp]]'' → [[Dicot family #Sharp|Dicot family]] (+25/24 or 28/27, fifth sliced in two)
* ''[[Sharpie]]'' → [[Dicot family #Sharpie|Dicot family]] (+25/24 or 28/27, fifth sliced in two)
* ''[[Immune]]'' → [[Immunity family #Immune|Immunity family]] (+781250/750141, twelfth sliced in two)
* ''[[Immune]]'' → [[Immunity family #Immune|Immunity family]] (+781250/750141, twelfth sliced in two)
* ''[[August]]'' → [[Augmented family #August|Augmented family]] (+36/35 or 128/125, generated by the fifth with a 1/3-octave period)
* ''[[August]]'' → [[Augmented family #August|Augmented family]] (+36/35 or 128/125, generated by the fifth with a 1/3-octave period)
Line 21: Line 22:
* [[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)
* ''[[Escapade]]'' → [[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)
Line 30: Line 33:
* ''[[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 (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.


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.
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.)
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 {{nowrap|(16/9)/(5/4) {{=}} 64/45}}. Setting this equal to 10/7 gives {{nowrap|(10/7)/(64/45) {{=}} 225/224}}.)


== Wizard ==
== Wizard ==
{{Main| Wizard }}
{{Main| Wizard }}
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Wizard]].''
: ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Wizard]].''
 
Wizard has a semi-octave period and is generated by an interval that is best treated as ~17/15. The semi-octave complement of this interval is ~5/4. Wizard can be described as {{nowrap|22 &amp; 72}}. Its ploidacot is diploid alpha-hexacot, so six generator steps plus a semi-octave period gives the [[3/1|perfect twelfth]]. [[72edo]], [[94edo]], and especially [[166edo]] are good tunings for it.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 50: Line 55:
: mapping generators: ~1225/864, ~245/216
: mapping generators: ~1225/864, ~245/216


{{Multival|legend=1| 12 -2 20 -31 -2 52 }}
[[Optimal tuning]]s:
 
* [[CTE]]: ~1225/864 = 600.000, ~245/216 = 216.919
[[Optimal tuning]] ([[POTE]]): ~1225/864 = 1\2, ~5/4 = 383.256 (~245/216 = 216.744)
: [[error map]]: {{val| 0.000 -0.443 -3.232 +0.361 }}
* [[POTE]]: ~1225/864 = 600.000, ~245/216 = 216.744
: error map: {{val| 0.000 -1.492 -3.057 -1.388 }}


{{Optimal ET sequence|legend=1| 22, 50, 72, 166, 238c, 310c, 382c }}
{{Optimal ET sequence|legend=1| 22, 50, 72, 166, 238c, 310c, 382c }}


[[Badness]]: 0.040846
[[Badness]] (Smith): 0.040846
 
Scales: [[wizard22]]


=== 11-limit ===
=== 11-limit ===
Line 67: Line 72:
Mapping: {{mapping| 2 1 5 2 8 | 0 6 -1 10 -3 }}
Mapping: {{mapping| 2 1 5 2 8 | 0 6 -1 10 -3 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~5/4 = 383.232 (~25/22 = 216.768)
Optimal tunings:
 
* CTE: ~99/70 = 600.000, ~25/22 = 216.900
{{Optimal ET sequence|legend=1| 22, 50, 72, 166, 238c, 310c }}
* POTE: ~99/70 = 600.000, ~25/22 = 216.768


Badness: 0.018539
{{Optimal ET sequence|legend=0| 22, 50, 72, 166, 238c, 310c }}


Scales: [[wizard22]]
Badness (Smith): 0.018539


==== Lizard ====
==== Lizard ====
Line 82: Line 87:
Mapping: {{mapping| 2 1 5 2 8 11 | 0 6 -1 10 -3 -10 }}
Mapping: {{mapping| 2 1 5 2 8 11 | 0 6 -1 10 -3 -10 }}


Optimal tuning (POTE): ~55/39 = 1\2, ~5/4 = 383.389 (~25/22 = 216.711)
Optimal tunings:
* CTE: ~55/39 = 600.000, ~25/22 = 216.703
* POTE: ~55/39 = 600.000, ~25/22 = 216.711


{{Optimal ET sequence|legend=1| 22, 50, 72, 122, 194df }}
{{Optimal ET sequence|legend=0| 22, 50, 72, 122, 194df }}


Badness: 0.021781
Badness (Smith): 0.021781


===== 17-limit =====
===== 17-limit =====
Line 95: Line 102:
Mapping: {{mapping| 2 1 5 2 8 11 6 | 0 6 -1 10 -3 -10 6 }}
Mapping: {{mapping| 2 1 5 2 8 11 6 | 0 6 -1 10 -3 -10 6 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~5/4 = 383.381 (~17/15 = 216.619)
Optimal tunings:
* CTE: ~17/12 = 600.000, ~17/15 = 216.748
* POTE: ~17/12 = 600.000, ~17/15 = 216.619


{{Optimal ET sequence|legend=1| 22, 50, 72, 122g, 194dfg }}
{{Optimal ET sequence|legend=0| 22, 50, 72, 122g, 194dfg }}


Badness: 0.014536
Badness (Smith): 0.014536


===== 19-limit =====
===== 19-limit =====
Line 108: Line 117:
Mapping: {{mapping| 2 1 5 2 8 11 6 2 | 0 6 -1 10 -3 -10 6 18 }}
Mapping: {{mapping| 2 1 5 2 8 11 6 2 | 0 6 -1 10 -3 -10 6 18 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~5/4 = 383.477 (~17/15 = 216.523)
Optimal tunings:
* CTE: ~17/12 = 600.000, ~17/15 = 216.677
* POTE: ~17/12 = 600.000, ~17/15 = 216.523


{{Optimal ET sequence|legend=1| 22h, 50, 72, 122g, 194dfg }}
{{Optimal ET sequence|legend=0| 22h, 50, 72, 122g, 194dfg }}


Badness: 0.015702
Badness (Smith): 0.015702


==== Gizzard ====
==== Gizzard ====
Line 121: Line 132:
Mapping: {{mapping| 2 1 5 2 8 -2 | 0 6 -1 10 -3 26 }}
Mapping: {{mapping| 2 1 5 2 8 -2 | 0 6 -1 10 -3 26 }}


Optimal tuning (POTE): ~99/70 = 1\2, ~5/4 = 383.170 (~25/22 = 216.830)
Optimal tunings:
* CTE: ~99/70 = 600.000, ~25/22 = 216.928
* POTE: ~99/70 = 600.000, ~25/22 = 216.830


{{Optimal ET sequence|legend=1| 72, 166, 238cf }}
{{Optimal ET sequence|legend=0| 22f, 72, 166, 238cf }}


Badness: 0.020252
Badness (Smith): 0.020252


===== 17-limit =====
===== 17-limit =====
Line 134: Line 147:
Mapping: {{mapping| 2 1 5 2 8 -2 6 | 0 6 -1 10 -3 26 6 }}
Mapping: {{mapping| 2 1 5 2 8 -2 6 | 0 6 -1 10 -3 26 6 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~5/4 = 383.175 (~25/22 = 216.825)
Optimal tunings:
* CTE: ~17/12 = 600.000, ~17/15 = 216.943
* POTE: ~17/12 = 600.000, ~17/15 = 216.825


{{Optimal ET sequence|legend=1| 72, 166g, 238cfg }}
{{Optimal ET sequence|legend=0| 22f, 72, 166g, 238cfg }}


Badness: 0.013624
Badness (Smith): 0.013624


===== 19-limit =====
===== 19-limit =====
Line 147: Line 162:
Mapping: {{mapping| 2 1 5 2 8 -2 6 15 | 0 6 -1 10 -3 26 6 -18 }}
Mapping: {{mapping| 2 1 5 2 8 -2 6 15 | 0 6 -1 10 -3 26 6 -18 }}


Optimal tuning (POTE): ~17/12 = 1\2, ~5/4 = 383.138 (~17/15 = 216.862)
Optimal tunings:
* CTE: ~17/12 = 600.000, ~17/15 = 216.918
* POTE: ~17/12 = 600.000, ~17/15 = 216.862


{{Optimal ET sequence|legend=1| 72, 94, 166g }}
{{Optimal ET sequence|legend=0| 72, 94, 166g }}


Badness: 0.014810
Badness (Smith): 0.014810


=== Mage ===
=== Mage ===
Line 160: Line 177:
Mapping: {{mapping| 2 1 5 2 4 | 0 6 -1 10 8 }}
Mapping: {{mapping| 2 1 5 2 4 | 0 6 -1 10 8 }}


Optimal tuning (POTE): ~77/54 = 1\2, ~5/4 = 383.124 (~55/48 = 216.876)
Optimal tunings:
* CTE: ~77/54 = 600.000, ~55/48 = 217.247
* POTE: ~77/54 = 600.000, ~55/48 = 216.876


{{Optimal ET sequence|legend=1| 22, 50e, 72ee, 94ee }}
{{Optimal ET sequence|legend=0| 22, 50e, 72ee }}


Badness: 0.057799
Badness (Smith): 0.057799


== 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
Line 175: Line 194:
{{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 190: 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 205: 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, 151cde }}
{{Optimal ET sequence|legend=1| 29, 31, 60e }}


Badness: 0.022993
Badness: 0.022993
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
Comma list: 105/104, 121/120, 154/153, 196/195, 273/272
Mapping: {{mapping| 1 4 -3 -3 2 -5 -8 | 0 -5 11 12 3 18 25 }}
Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 580.055
{{Optimal ET sequence|legend=1| 29g, 31, 60e }}
Badness: 0.019093
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 77/76, 105/104, 121/120, 153/152, 196/195, 273/272
Mapping: {{mapping| 1 4 -3 -3 2 -5 -8 -3 | 0 -5 11 12 3 18 25 15 }}
Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 580.026
{{Optimal ET sequence|legend=1| 29g, 31, 60e }}
Badness: 0.017010
==== 23-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 77/76, 105/104, 115/114, 121/120, 153/152, 161/160, 196/195
Mapping: {{mapping| 1 4 -3 -3 2 -5 -8 -3 5 | 0 -5 11 12 3 18 25 15 -1 }}
Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 580.009
{{Optimal ET sequence|legend=1| 29g, 31, 60e }}
Badness: 0.014471


=== Tritoni ===
=== Tritoni ===
Line 218: Line 272:
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 }}
Line 227: Line 279:


== 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
Line 235: Line 287:
{{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 }}
Line 250: Line 300:
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 }}
Line 263: Line 313:
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 }}
Line 270: Line 320:


== 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
Line 278: Line 328:
{{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 }}
Line 293: Line 341:
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 306: 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 }}
Line 313: Line 361:


== Slender ==
== Slender ==
Slender (31 &amp; 32) tempers out the [[Hewuermera temperaments|hewuermera comma]] in addition to the marvel comma. This temperament has a generator of [[49/48]], 3 of which equal marvel's 16/15~15/14, and 10 generators is 5/4.
Slender ({{nowrap|31 &amp; 32}}) tempers out the [[Hewuermera temperaments|hewuermera comma]] in addition to the marvel comma. This temperament has a generator of [[49/48]], 3 of which equal marvel's 16/15~15/14, and 10 generators is 5/4.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 321: Line 369:
{{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 336: 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 349: 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 }}
Line 356: Line 402:


== 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
Line 364: Line 410:
{{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 379: 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 ==
{{ See also | Greater tendoneutralic }}
[[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
=== 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 ====
{{ See also | Greater tendoneutralic }}
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 ==
Line 474: Line 436:
{{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 489: 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 502: 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 515: 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 526: 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 ==
Line 537: Line 501:
{{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 = 1\9, ~12005/6912 = 950.1680 (~1728/1715 = 16.8347)
[[Optimal tuning]] ([[POTE]]): ~2592/2401 = 133.3333, ~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 554: 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 }}
Line 567: Line 529:
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 }}
Line 574: Line 536:


== 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
Line 582: Line 544:
{{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 597: 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 610: 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 623: 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 636: 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 649: 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 662: 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 675: 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 688: 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 701: 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 714: 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 727: 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 740: 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 755: 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 762: 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 770: 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 785: 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 798: 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 811: 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 818: 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 826: 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 841: 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 854: 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 867: 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 882: 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 895: 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 908: 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 923: 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 938: 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 945: 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 953: 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 968: 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 975: 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"