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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:  
* ''[[Sharp]]'', {25/24, 28/27} → [[Dicot family #Sharp|Dicot family]]
* ''[[Pelogic]]'' → [[Mavila family #Pelogic|Mavila family]] (+21/20 or 135/128, generated by the fifth with 5/4 mapped to the m3)
* ''[[Pelogic]]'', {21/20, 135/128} → [[Pelogic family #Pelogic|Pelogic family]]
* [[Meantone]] → [[Meantone family #Septimal meantone|Meantone family]] (+81/80 or 126/125, generated by the fifth with 5/4 mapped to the M3)
* ''[[August]]'', {36/35, 128/125} → [[Augmented family #August|Augmented family]]
* [[Garibaldi]] → [[Schismatic family #Garibaldi|Schismatic family]] (+3125/3087, generated by the fifth with 5/4 mapped to the d4)
* [[Pajara]], {50/49, 64/63} → [[Diaschismic family #Pajara|Diaschismic family]]
* [[Pajara]] → [[Diaschismic family #Pajara|Diaschismic family]] (+50/49 or 64/63, generated by the fifth with a semioctave period)
* [[Meantone]], {81/80, 126/125} → [[Meantone family #Septimal meantone|Meantone family]]
* ''[[Sharpie]]'' → [[Dicot family #Sharpie|Dicot family]] (+25/24 or 28/27, fifth sliced in two)
* [[Magic]], {225/224, 245/243} → [[Magic family #Magic|Magic family]]
* ''[[Immune]]'' → [[Immunity family #Immune|Immunity family]] (+781250/750141, twelfth sliced in two)
* ''[[Passive]]'', {225/224, 256/245} → [[Passion family #Passive|Passion family]]
* ''[[August]]'' → [[Augmented family #August|Augmented family]] (+36/35 or 128/125, generated by the fifth with a 1/3-octave period)
* [[Miracle]], {225/224, 1029/1024} → [[Gamelismic clan #Miracle|Gamelismic clan]]
* ''[[Fog]]'' → [[Misty family #Fog|Misty family]] (+156250/151263, generated by the fifth with a 1/3-octave period)
* [[Orwell]], {225/224, 1728/1715} → [[Semicomma family #Orwell|Semicomma family]]
* [[Negri]] → [[Slendro clan #Negri|Slendro clan]] (+49/48, fourth sliced in four)
* [[Garibaldi temperament|Garibaldi]], {225/224, 3125/3087} → [[Schismatic family #Garibaldi|Schismatic family]]
* [[Magic]] → [[Magic family #Magic|Magic family]] (+245/243, twelfth sliced in five)
* [[Catakleismic]], {225/224, 4375/4374} → [[Kleismic family #Catakleismic|Kleismic family]]
* ''[[Passive]]'' → [[Passion family #Passive|Passion family]] (+256/245, fourth sliced in five)
* ''[[Decic]]'', {225/224, 16807/16384} → [[Cloudy clan #Decic|Cloudy clan]]
* ''[[Quintapole]]'' → [[Quintaleap family #Quintapole|Quintaleap family]] (+7812500/7411887, fourth sliced in five)
* ''[[Amavil]]'', {225/224, 17496/16807} → [[Mabila family #Amavil|Mabila family]]
* ''[[Houborizic]]'' → [[Amity family #Houborizic|Amity family]] (+1250000/1240029, eleventh sliced in five)
* ''[[Escapade]]'', {225/224, 65625/65536} → [[Escapade family #Escapade|Escapade family]]
* ''[[Qintosec]]'' → [[Quintosec family #Qintosec|Quintosec family]] (+2560000/2470629, generated by the classical minor second with a 1/5-octave period)
* ''[[Fog]]'', {225/224, 156250/151263} → [[Misty family #Fog|Misty family]]
* [[Miracle]] → [[Gamelismic clan #Miracle|Gamelismic clan]] (+1029/1024, fifth sliced in six)
* ''[[Compton]]'', {225/224, 250047/250000} → [[Compton family #Compton|Compton family]]
* [[Catakleismic]] → [[Kleismic family #Catakleismic|Kleismic family]] (+4375/4374, twelfth sliced in six)
* ''[[Immune]]'', {225/224, 781250/750141} → [[Immunity family #Immune|Immunity family]]
* ''[[Marvo]]'' → [[Gravity family #Marvo|Gravity family]] (+78125000/78121827, two octaves and a fifth sliced in six)
* ''[[Betic]]'', {225/224, 1071875/1062882} → [[Sycamore family #Betic|Sycamore family]]
* [[Orwell]] → [[Semicomma family #Orwell|Semicomma family]] (+1728/1715, twelfth sliced in seven)
* ''[[Houborizic]]'' {225/224, 1250000/1240029} → [[Amity family #Houborizic|Amity family]]
* ''[[Snipes]]'' → [[Wesley family #Snipes|Wesley family]] (+6125/5832, two octaves and a fourth sliced in seven)
* ''[[Qintosec]]'', {225/224, 2560000/2470629} → [[Qintosec family #Qintosec|Qintosec family]]
* ''[[Submajor]]'' → [[Buzzardsmic clan #Submajor|Buzzardsmic clan]] (+65536/64827, two octaves and a fourth sliced in eight)
* ''[[Quintapole]]'', {225/224, 7812500/7411887} → [[Quintaleap family #Quintapole|Quintaleap family]]
* ''[[Escapist]]'' → [[Escapade family #Escapist|Escapade family]] (+65625/65536, fourth sliced in nine)
* ''[[Maquila]]'', {225/224, 30233088/28824005} → [[Maquila family #Septimal maquila|Maquila family]]
* ''[[Decic]]'' → [[Cloudy clan #Decic|Cloudy clan]] (+16807/16384, generated by the fifth with a 1/10-octave period)
* ''[[Marvo]]'', {225/224, 78125000/78121827} → [[Gravity family #Marvo|Gravity family]]
* ''[[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)
* ''[[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)
* ''[[Raccoon]]'' → [[Vavoom family #Raccoon|Vavoom family]] (+41943040/40353607, twelfth sliced in seventeen)
* ''[[Maquila]]'' → [[Maquila family #Septimal maquila|Maquila family]] (+30233088/28824005, seven octaves and a fifth sliced in seventeen)
* ''[[Gammy]]'' → [[Gammic family #Gammy|Gammic family]] (+94143178827/91913281250, fifth sliced in twenty)


Considered below are negri, 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}}.)


== Negri ==
== Wizard ==
{{main| Negri }}
{{Main| Wizard }}
: ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Wizard]].''


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.  
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
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 16875/16384
[[Comma list]]: 225/224, 118098/117649
 
[[Mapping]]: [{{val| 1 2 2 }}, {{val| 0 -4 3 }}]
 
{{Multival|legend=1| 4 -3 -14 }}
 
[[POTE generator]]: ~16/15 = 125.7549
 
{{Val list|legend=1| 9, 10, 19, 67c, 86c, 105c }}
 
[[Badness]]: 0.086856
 
=== 7-limit ===
Subgroup: 2.3.5.7
 
[[Comma list]]: 49/48, 225/224
 
[[Mapping]]: [{{val| 1 2 2 3 }}, {{val| 0 -4 3 -2 }}]


{{Multival|legend=1| 4 -3 2 -14 -8 13 }}
{{Mapping|legend=1| 2 1 5 2 | 0 6 -1 10 }}


[[POTE generator]]: ~15/14 = 125.608
: mapping generators: ~1225/864, ~245/216


{{Val list|legend=1| 9, 10, 19, 48d, 67cdd, 86cdd }}
[[Optimal tuning]]s:
* [[CTE]]: ~1225/864 = 600.000, ~245/216 = 216.919
: [[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 }}


[[Badness]]: 0.026483
{{Optimal ET sequence|legend=1| 22, 50, 72, 166, 238c, 310c, 382c }}


==== Negra ====
[[Badness]] (Smith): 0.040846
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]]: [{{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]]: [2 14/13; 49/48 65/64 91/90]
 
[[POTE generator]]: ~14/13 = 125.567
 
{{Val list|legend=1| 9, 10, 19, 48df, 67cddf, 86cddff }}


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


Comma list: 45/44, 49/48, 56/55
Comma list: 225/224, 385/384, 4000/3993


Mapping: [{{val| 1 2 2 3 4 }}, {{val| 0 -4 3 -2 -5 }}]
Mapping: {{mapping| 2 1 5 2 8 | 0 6 -1 10 -3 }}


POTE generator: ~15/14 = 126.474
Optimal tunings:
* CTE: ~99/70 = 600.000, ~25/22 = 216.900
* POTE: ~99/70 = 600.000, ~25/22 = 216.768


Optimal GPV sequence: {{Val list| 9, 10, 19 }}
{{Optimal ET sequence|legend=0| 22, 50, 72, 166, 238c, 310c }}


Badness: 0.026190
Badness (Smith): 0.018539


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


Comma list: 45/44, 49/48, 56/55, 78/77
Comma list: 225/224, 351/350, 364/363, 385/384


Mapping: [{{val| 1 2 2 3 4 4 }}, {{val| 0 -4 3 -2 -5 -3 }}]
Mapping: {{mapping| 2 1 5 2 8 11 | 0 6 -1 10 -3 -10 }}


POTE generator: ~14/13 = 126.431
Optimal tunings:
* CTE: ~55/39 = 600.000, ~25/22 = 216.703
* POTE: ~55/39 = 600.000, ~25/22 = 216.711


Optimal GPV sequence: {{Val list| 9, 10, 19 }}
{{Optimal ET sequence|legend=0| 22, 50, 72, 122, 194df }}


Badness: 0.017833
Badness (Smith): 0.021781


=== Negril ===
===== 17-limit =====
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11.13.17


Comma list: 49/48, 100/99, 225/224
Comma list: 221/220, 273/272, 289/288, 351/350, 375/374


Mapping: [{{val| 1 2 2 3 2 }}, {{val| 0 -4 3 -2 14 }}]
Mapping: {{mapping| 2 1 5 2 8 11 6 | 0 6 -1 10 -3 -10 6 }}


POTE generator: ~15/14 = 124.767
Optimal tunings:
* CTE: ~17/12 = 600.000, ~17/15 = 216.748
* POTE: ~17/12 = 600.000, ~17/15 = 216.619


Optimal GPV sequence: {{Val list| 19, 29, 48d, 77cdd }}
{{Optimal ET sequence|legend=0| 22, 50, 72, 122g, 194dfg }}


Badness: 0.038679
Badness (Smith): 0.014536


==== 13-limit ====
===== 19-limit =====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13.17.19


Comma list: 49/48, 65/64, 91/90, 875/858
Comma list: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342


Mapping: [{{val| 1 2 2 3 2 4 }}, {{val| 0 -4 3 -2 14 -3 }}]
Mapping: {{mapping| 2 1 5 2 8 11 6 2 | 0 6 -1 10 -3 -10 6 18 }}


POTE generator: ~14/13 = 124.716
Optimal tunings:
* CTE: ~17/12 = 600.000, ~17/15 = 216.677
* POTE: ~17/12 = 600.000, ~17/15 = 216.523


Optimal GPV sequence: {{Val list| 19, 29, 48df, 77cddf }}
{{Optimal ET sequence|legend=0| 22h, 50, 72, 122g, 194dfg }}


Badness: 0.024383
Badness (Smith): 0.015702


=== Negric ===
==== Gizzard ====
Subgroup: 2.3.5.7.11
 
Comma list: 33/32, 49/48, 77/75
 
Mapping: [{{val| 1 2 2 3 3 }}, {{val| 0 -4 3 -2 4 }}]
 
POTE generator: ~15/14 = 127.039
 
Optimal GPV sequence: {{Val list| 9, 19e }}
 
Badness: 0.030617
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 33/32, 49/48, 65/64, 91/90
Comma list: 225/224, 325/324, 385/384, 1573/1568


Mapping: [{{val| 1 2 2 3 3 4 }}, {{val| 0 -4 3 -2 4 -3 }}]
Mapping: {{mapping| 2 1 5 2 8 -2 | 0 6 -1 10 -3 26 }}


POTE generator: ~14/13 = 127.039
Optimal tunings:
* CTE: ~99/70 = 600.000, ~25/22 = 216.928
* POTE: ~99/70 = 600.000, ~25/22 = 216.830


Optimal GPV sequence: {{Val list| 9, 19e }}
{{Optimal ET sequence|legend=0| 22f, 72, 166, 238cf }}


Badness: 0.020205
Badness (Smith): 0.020252


=== Negroni ===
===== 17-limit =====
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11.13.17


Comma list: 49/48, 55/54, 225/224
Comma list: 225/224, 289/288, 325/324, 375/374, 385/384


Mapping: [{{val| 1 2 2 3 5 }}, {{val| 0 -4 3 -2 -15 }}]
Mapping: {{mapping| 2 1 5 2 8 -2 6 | 0 6 -1 10 -3 26 6 }}


POTE generator: ~15/14 = 124.539
Optimal tunings:
* CTE: ~17/12 = 600.000, ~17/15 = 216.943
* POTE: ~17/12 = 600.000, ~17/15 = 216.825


Optimal GPV sequence: {{Val list| 10, 19e, 29, 77cddee }}
{{Optimal ET sequence|legend=0| 22f, 72, 166g, 238cfg }}


Badness: 0.035296
Badness (Smith): 0.013624


==== 13-limit ====
===== 19-limit =====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13.17.19


Comma list: 49/48, 55/54, 65/64, 91/90
Comma list: 225/224, 325/324, 375/374, 385/384, 400/399, 595/594


Mapping: [{{val| 1 2 2 3 5 4 }}, {{val| 0 -4 3 -2 -15 -3 }}]
Mapping: {{mapping| 2 1 5 2 8 -2 6 15 | 0 6 -1 10 -3 26 6 -18 }}


POTE generator: ~14/13 = 124.545
Optimal tunings:
* CTE: ~17/12 = 600.000, ~17/15 = 216.918
* POTE: ~17/12 = 600.000, ~17/15 = 216.862


Optimal GPV sequence: {{Val list| 10, 19e, 29, 77cddeef }}
{{Optimal ET sequence|legend=0| 72, 94, 166g }}


Badness: 0.021559
Badness (Smith): 0.014810


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


Comma list: 49/48, 121/120, 225/224
Comma list: 99/98, 176/175, 1331/1296


Mapping: [{{val| 1 6 -1 5 4 }}, {{val| 0 -8 6 -4 -1 }}]
Mapping: {{mapping| 2 1 5 2 4 | 0 6 -1 10 8 }}


POTE generator: ~11/8 = 537.186
Optimal tunings:
* CTE: ~77/54 = 600.000, ~55/48 = 217.247
* POTE: ~77/54 = 600.000, ~55/48 = 216.876


Optimal GPV sequence: {{Val list| 9, 20, 29, 38d, 67cdde }}
{{Optimal ET sequence|legend=0| 22, 50e, 72ee }}


Badness: 0.041886
Badness (Smith): 0.057799


==== 13-limit ====
== Tritonic ==
Subgroup: 2.3.5.7.11.13
: ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Tritonic]].''


Comma list: 49/48, 65/64, 91/90, 121/120
[[Subgroup]]: 2.3.5.7


Mapping: [{{val| 1 6 -1 5 4 7 }}, {{val| 0 -8 6 -4 -1 -6 }}]
[[Comma list]]: 225/224, 50421/50000


POTE generator: ~11/8 = 537.208
{{Mapping|legend=1| 1 4 -3 -3 | 0 -5 11 12 }}


Optimal GPV sequence: {{Val list| 9, 20, 29, 38df, 67cddef }}
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~7/5 = 580.286


Badness: 0.025192
{{Optimal ET sequence|legend=1| 29, 31, 60, 91, 122, 213bcd }}


==== 17-limit ====
[[Badness]]: 0.047578
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 49/48, 65/64, 91/90, 121/120, 154/153
 
Mapping: [{{val| 1 6 -1 5 4 7 -2 }}, {{val| 0 -8 6 -4 -1 -6 11 }}]
 
POTE generator: ~11/8 = 537.230
 
Optimal GPV sequence: {{Val list| 9, 20g, 29g, 38df, 67cddefg }}
 
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: [{{val| 1 6 -1 5 4 7 -2 7 }}, {{val| 0 -8 6 -4 -1 -6 11 -5 }}]
 
POTE generator: ~11/8 = 537.214
 
Optimal GPV sequence: {{Val list| 9, 20g, 29g, 38df, 67cddefgh }}
 
Badness: 0.016828
 
== Wizard ==
{{Main|Wizard}}
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Wizard]].''
 
Subgroup: 2.3.5.7
 
[[Comma list]]: 225/224, 118098/117649
 
[[Mapping]]: [{{val| 2 1 5 2 }}, {{val| 0 6 -1 10 }}]
 
Mapping generators: ~1225/864, ~245/216
 
[[POTE generator]]: ~5/4 = 383.256
 
{{Multival|legend=1| 12 -2 20 -31 -2 52 }}
 
{{Val list|legend=1| 22, 50, 72, 166, 238c, 310c, 382c }}
 
[[Badness]]: 0.040846
 
Scales: [[wizard22]]


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


Comma list: 225/224, 385/384, 4000/3993
Comma list: 121/120, 225/224, 441/440


Mapping: [{{val| 2 1 5 2 8 }}, {{val| 0 6 -1 10 -3 }}]
Mapping: {{mapping| 1 4 -3 -3 2 | 0 -5 11 12 3 }}


Mapping generators: ~99/70, ~25/22
Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 580.267


POTE generator: ~5/4 = 383.232
{{Optimal ET sequence|legend=1| 29, 31, 60e }}


Optimal GPV sequence: {{Val list| 22, 50, 72, 166, 238c, 310c }}
Badness: 0.023659


Badness: 0.018539
==== 13-limit ====
 
Scales: [[wizard22]]
 
==== Lizard ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 225/224, 351/350, 364/363, 385/384
Comma list: 105/104, 121/120, 196/195, 275/273


Mapping: [{{val| 2 1 5 2 8 11 }}, {{val| 0 6 -1 10 -3 -10 }}]
Mapping: {{mapping| 1 4 -3 -3 2 -5 | 0 -5 11 12 3 18 }}


Mapping generators: ~99/70, ~25/22
Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 580.108


POTE generator: ~5/4 = 383.389
{{Optimal ET sequence|legend=1| 29, 31, 60e }}


Optimal GPV sequence: {{Val list| 22, 50, 72, 122, 194df }}
Badness: 0.022993


Badness: 0.021781
==== 17-limit ====
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Comma list: 221/220, 273/272, 289/288, 351/350, 375/374
Comma list: 105/104, 121/120, 154/153, 196/195, 273/272
 
Mapping: [{{val| 2 1 5 2 8 11 6 }}, {{val| 0 6 -1 10 -3 -10 6 }}]


Mapping generators: ~17/12, ~17/15
Mapping: {{mapping| 1 4 -3 -3 2 -5 -8 | 0 -5 11 12 3 18 25 }}


POTE generator: ~5/4 = 383.381
Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 580.055


Optimal GPV sequence: {{Val list| 22, 50, 72, 122g, 194dfg }}
{{Optimal ET sequence|legend=1| 29g, 31, 60e }}


Badness: 0.014536
Badness: 0.019093


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


Comma list: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342
Comma list: 77/76, 105/104, 121/120, 153/152, 196/195, 273/272


Mapping: [{{val| 2 1 5 2 8 11 6 2 }}, {{val| 0 6 -1 10 -3 -10 6 18 }}]
Mapping: {{mapping| 1 4 -3 -3 2 -5 -8 -3 | 0 -5 11 12 3 18 25 15 }}


Mapping generators: ~17/12, ~17/15
Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 580.026


POTE generator: ~5/4 = 383.477
{{Optimal ET sequence|legend=1| 29g, 31, 60e }}


Optimal GPV sequence: {{Val list| 22h, 50, 72, 122g, 194dfg }}
Badness: 0.017010


Badness: 0.015702
==== 23-limit ====
 
Subgroup: 2.3.5.7.11.13.17.19.23
==== Gizzard ====
Subgroup: 2.3.5.7.11.13


Comma list: 225/224, 325/324, 385/384, 1573/1568
Comma list: 77/76, 105/104, 115/114, 121/120, 153/152, 161/160, 196/195


Mapping: [{{val| 2 1 5 2 8 -2 }}, {{val| 0 6 -1 10 -3 26 }}]
Mapping: {{mapping| 1 4 -3 -3 2 -5 -8 -3 5 | 0 -5 11 12 3 18 25 15 -1 }}


Mapping generators: ~99/70, ~25/22
Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 580.009


POTE generator: ~5/4 = 383.170
{{Optimal ET sequence|legend=1| 29g, 31, 60e }}


Optimal GPV sequence: {{Val list| 72, 166, 238cf }}
Badness: 0.014471


Badness: 0.020252
=== Tritoni ===
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 225/224, 289/288, 325/324, 375/374, 385/384
 
Mapping: [{{val| 2 1 5 2 8 -2 6 }}, {{val| 0 6 -1 10 -3 26 6 }}]
 
Mapping generators: ~17/12, ~17/15
 
POTE generator: ~5/4 = 383.175
 
Optimal GPV sequence: {{Val list| 72, 166g, 238cfg }}
 
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: [{{val| 2 1 5 2 8 -2 6 15 }}, {{val| 0 6 -1 10 -3 26 6 -18 }}]
 
Mapping generators: ~17/12, ~17/15
 
POTE generator: ~5/4 = 383.138
 
Optimal GPV sequence: {{Val list| 72, 94, 166g }}
 
Badness: 0.014810
 
=== Mage ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 99/98, 176/175, 1331/1296
Comma list: 225/224, 385/384, 27783/27500


Mapping: [{{val| 2 1 5 2 4 }}, {{val| 0 6 -1 10 8 }}]
Mapping: {{mapping| 1 4 -3 -3 17 | 0 -5 11 12 -28 }}


Mapping generators: ~77/54, ~55/48
Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 580.389


POTE generator: ~5/4 = 383.124
{{Optimal ET sequence|legend=1| 31, 91, 122, 153d }}


Optimal GPV sequence: {{Val list| 22, 50e, 72ee, 94ee }}
Badness: 0.045456


Badness: 0.057799
== Septimin ==
 
: ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Septimin]].''
== Triton ==
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Stump]].''


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224, 1029/1000
[[Comma list]]: 225/224, 84035/82944


[[Mapping]]: [{{val| 1 0 6 7 }}, {{val| 0 3 -7 -8 }}]
{{Mapping|legend=1| 1 4 1 5 | 0 -11 6 -10 }}


{{Multival|legend=1| 3 -7 -8 -18 -21 1 }}
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~7/6 = 263.632


[[POTE generator]]: ~7/5 = 568.865
{{Optimal ET sequence|legend=1| 41, 91, 132d }}


{{Val list|legend=1| 2, 17d, 19, 78bd, 97bd }}
[[Badness]]: 0.054502
 
[[Badness]]: 0.059245


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


Comma list: 45/44, 56/55, 1029/1000
Comma list: 225/224, 385/384, 2401/2376


Mapping: [{{val| 1 0 6 7 4 }}, {{val| 0 3 -7 -8 -1 }}]
Mapping: {{mapping| 1 4 1 5 5 | 0 -11 6 -10 -7 }}


POTE generator: ~7/5 = 569.144
Optimal tuning (POTE): ~2 = 1200.000, ~7/6 = 263.634


Optimal GPV sequence: {{Val list| 2, 17d, 19, 59bde, 78bde, 97bde }}
{{Optimal ET sequence|legend=1| 41, 91, 223cdef }}


Badness: 0.045675
Badness: 0.031309


== Tritonic ==
=== 13-limit ===
: ''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]]: [{{val| 1 4 -3 -3 }}, {{val| 0 -5 11 12 }}]
 
{{Multival|legend=1| 5 -11 -12 -29 -33 3 }}
 
[[POTE generator]]: ~7/5 = 580.286
 
{{Val list|legend=1| 29, 31, 60, 91, 122, 213bcd }}
 
[[Badness]]: 0.047578
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 121/120, 225/224, 441/440
 
Mapping: [{{val| 1 4 -3 -3 2 }}, {{val| 0 -5 11 12 3 }}]
 
POTE generator: ~7/5 = 580.267
 
Optimal GPV sequence: {{Val list| 29, 31, 60e }}
 
Badness: 0.023659
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 105/104, 121/120, 196/195, 275/273
Comma list: 105/104, 144/143, 196/195, 245/242


Mapping: [{{val| 1 4 -3 -3 2 -5 }}, {{val| 0 -5 11 12 3 18 }}]
Mapping: {{mapping| 1 4 1 5 5 7 | 0 -11 6 -10 -7 -15 }}


POTE generator: ~7/5 = 580.108
Optimal tuning (POTE): ~2 = 1200.000, ~7/6 = 263.700


Optimal GPV sequence: {{Val list| 29, 31, 60e, 151cde }}
{{Optimal ET sequence|legend=1| 41, 91 }}


Badness: 0.022993
Badness: 0.023117
 
=== Tritoni ===
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 385/384, 27783/27500
 
Mapping: [{{val| 1 4 -3 -3 17 }}, {{val| 0 -5 11 12 -28 }}]
 
POTE generator: ~7/5 = 580.389
 
Optimal GPV sequence: {{Val list| 31, 91, 122, 153d }}
 
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 [[Miscellaneous 5-limit temperaments #Merman]].''


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224, 2500000/2470629
[[Comma list]]: 225/224, 2500000/2470629


[[Mapping]]: [{{val| 1 5 -5 -5 }}, {{val| 0 -7 15 16 }}]
{{Mapping|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


[[POTE generator]]: ~7/5 = 585.585
{{Optimal ET sequence|legend=1| 41, 84, 125 }}
 
{{Val list|legend=1| 41, 84, 125 }}


[[Badness]]: 0.055078
[[Badness]]: 0.055078
Line 493: Line 339:
Comma list: 225/224, 441/440, 1344/1331
Comma list: 225/224, 441/440, 1344/1331


Mapping: [{{val| 1 5 -5 -5 2 }}, {{val| 0 -7 15 16 3 }}]
Mapping: {{mapping| 1 5 -5 -5 2 | 0 -7 15 16 3 }}


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


Optimal GPV sequence: {{Val list| 41, 84, 125e }}
{{Optimal ET sequence|legend=1| 41, 84, 125e }}


Badness: 0.036383
Badness: 0.036383
Line 506: Line 352:
Comma list: 144/143, 225/224, 364/363, 441/440
Comma list: 144/143, 225/224, 364/363, 441/440


Mapping: [{{val| 1 5 -5 -5 2 12 }}, {{val| 0 -7 15 16 3 -17 }}]
Mapping: {{mapping| 1 5 -5 -5 2 12 | 0 -7 15 16 3 -17 }}


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


Optimal GPV sequence: {{Val list| 41, 84, 125e, 209ef, 293ef }}
{{Optimal ET sequence|legend=1| 41, 84, 125e, 209ef, 293ef }}


Badness: 0.027544
Badness: 0.027544


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


[[Comma list]]: 225/224, 125000000/121060821
[[Comma list]]: 225/224, 589824/588245


[[Mapping]]: [{{Val|1 6 -7 -7}}, {{Val|0 -9 19 20}}]
{{Mapping|legend=1| 1 2 2 3 | 0 -13 10 -6 }}


{{Multival|legend=1|9 -19 -20 -51 -57 7}}
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~49/48 = 38.413


[[POTE generator]]: ~7/5 = 588.641
{{Optimal ET sequence|legend=1| 31, 94, 125 }}


{{Val list|legend=1| 51, 53, 316cd, 369cdd, 422cdd }}
[[Badness]]: 0.056934
 
[[Badness]]: 0.143976


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


Comma list: 121/120, 225/224, 22000/21609
Comma list: 225/224, 385/384, 1331/1323


Mapping: [{{Val|1 6 -7 -7 1}}, {{Val|0 -9 19 20 5}}]
Mapping: {{mapping| 1 2 2 3 4 | 0 -13 10 -6 -17 }}


POTE generator: ~7/5 = 588.626
Optimal tuning (POTE): ~2 = 1200.000, ~49/48 = 38.387


Optimal GPV sequence: {{Val list| 51, 53 }}
{{Optimal ET sequence|legend=1| 31, 63, 94, 125 }}


Badness: 0.074295
Badness: 0.025342


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


Comma list: 121/120, 225/224, 275/273, 1040/1029
Comma list: 225/224, 275/273, 385/384, 1331/1323


Mapping: [{{Val|1 6 -7 -7 1 -12}}, {{Val|0 -9 19 20 5 32}}]
Mapping: {{mapping| 1 2 2 3 4 3 | 0 -13 10 -6 -17 22 }}


POTE generator: ~7/5 = 588.654
Optimal tuning (POTE): ~2 = 1200.000, ~49/48 = 38.314


Optimal GPV sequence: {{Val list| 51f, 53 }}
{{Optimal ET sequence|legend=1| 31, 63, 94 }}


Badness: 0.047441
Badness: 0.025913


== Septimin ==
== Triton ==
: ''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 #Stump]].''


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224, 84035/82944
[[Comma list]]: 225/224, 1029/1000


[[Mapping]]: [{{val| 1 4 1 5 }}, {{val| 0 -11 6 -10 }}]
{{Mapping|legend=1| 1 0 6 7 | 0 3 -7 -8 }}


{{Multival|legend=1| 11 -6 10 -35 -15 40 }}
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~7/5 = 568.865


[[POTE generator]]: ~7/6 = 263.632
{{Optimal ET sequence|legend=1| 2, 17d, 19, 78bd, 97bd }}


{{Val list|legend=1| 41, 91, 132d }}
[[Badness]]: 0.059245
 
[[Badness]]: 0.054502


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


Comma list: 225/224, 385/384, 2401/2376
Comma list: 45/44, 56/55, 1029/1000


Mapping: [{{val| 1 4 1 5 5 }}, {{val| 0 -11 6 -10 -7 }}]
Mapping: {{mapping| 1 0 6 7 4 | 0 3 -7 -8 -1 }}


POTE generator: ~7/6 = 263.634
Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 569.144


Optimal GPV sequence: {{Val list| 41, 91, 223cdef }}
{{Optimal ET sequence|legend=1| 2, 17d, 19, 59bde, 78bde, 97bde }}


Badness: 0.031309
Badness: 0.045675


=== 13-limit ===
== Marvolo ==
Subgroup: 2.3.5.7.11.13
[[Subgroup]]: 2.3.5.7


Comma list: 105/104, 144/143, 196/195, 245/242
[[Comma list]]: 225/224, 156250000/155649627


Mapping: [{{val| 1 4 1 5 5 7 }}, {{val| 0 -11 6 -10 -7 -15 }}]
{{Mapping|legend=1| 1 2 1 1 | 0 -6 19 26 }}


POTE generator: ~7/6 = 263.700
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~21/20 = 83.348


Optimal GPV sequence: {{Val list| 41, 91 }}
{{Optimal ET sequence|legend=1| 29, 43, 72, 619bcd, 691bcd }}


Badness: 0.023117
[[Badness]]: 0.083338


== Misneb ==
=== 11-limit ===
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Misneb]].''
Subgroup: 2.3.5.7.11


Subgroup: 2.3.5.7
Comma list: 225/224, 441/440, 4000/3993


[[Comma list]]: 225/224, 4194304/4117715
Mapping: {{mapping| 1 2 1 1 2 | 0 -6 19 26 21 }}


[[Mapping]]: [{{Val|1 3 1 3}}, {{Val|0 -15 14 -2}}]
Optimal tuning (POTE): ~2 = 1200.000, ~21/20 = 83.340


{{Multival|legend=1|15 -14 2 -57 -39 44}}
{{Optimal ET sequence|legend=1| 29, 43, 72 }}


[[POTE generator]]: ~16/15 = 113.235
Badness: 0.028965


{{Val list|legend=1| 21, 32, 53 }}
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


[[Badness]]: 0.140970
Comma list: 169/168, 225/224, 364/363, 441/440


=== 11-limit ===
Mapping: {{mapping| 1 2 1 1 2 3 | 0 -6 19 26 21 10 }}
Subgroup: 2.3.5.7.11


Comma list: 99/98, 176/175, 1310720/1294139
Optimal tuning (POTE): ~2 = 1200.000, ~21/20 = 83.330


Mapping: [{{Val|1 3 1 3 1}}, {{Val|0 -15 14 -2 26}}]
{{Optimal ET sequence|legend=1| 29, 43, 72, 115f }}


POTE generator: ~16/15 = 113.323
Badness: 0.021470


Optimal GPV sequence: {{Val list| 21, 32e, 53, 127, 180de }}
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17


Badness: 0.085390
Comma list: 169/168, 221/220, 225/224, 364/363, 441/440


==== 13-limit ====
Mapping: {{mapping| 1 2 1 1 2 3 2 | 0 -6 19 26 21 10 30 }}
Subgroup: 2.3.5.7.11.13


Comma list: 99/98, 176/175, 640/637, 847/845
Optimal tuning (POTE): ~2 = 1200.000, ~21/20 = 83.330


Mapping: [{{Val|1 3 1 3 1 2}}, {{Val|0 -15 14 -2 26 18}}]
{{Optimal ET sequence|legend=1| 29g, 43, 72 }}


POTE generator: ~16/15 = 113.323
Badness: 0.014924


Optimal GPV sequence: {{Val list| 21, 32e, 53, 127, 180de }}
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19


Badness: 0.045569
Comma list: 169/168, 210/209, 221/220, 225/224, 364/363, 441/440


=== Musneb ===
Mapping: {{mapping| 1 2 1 1 2 3 2 3 | 0 -6 19 26 21 10 30 18 }}
Subgroup: 2.3.5.7.11


Comma list: 225/224, 385/384, 66550/64827
Optimal tuning (POTE): ~2 = 1200.000, ~21/20 = 83.330


Mapping: [{{Val|1 3 1 3 6}}, {{Val|0 -15 14 -2 -27}}]
{{Optimal ET sequence|legend=1| 29g, 43, 72 }}


POTE generator: ~16/15 = 113.142
Badness: 0.014722


Optimal GPV sequence: {{Val list| 32, 53, 191de, 244cddee, 297cddee }}
== Enneaportent ==
[[Subgroup]]: 2.3.5.7


Badness: 0.087333
[[Comma list]]: 225/224, 40353607/40310784


== Slender ==
{{Mapping|legend=1| 9 0 28 11 | 0 2 -1 2 }}
Slender (31&amp;32) tempers out the [[Hewuermera temperaments|hewuermera comma]] in addition to the marvel comma, this has a generator [[49/48]], 3 of which equal marvel's 16/15 - 15/14, and 10 generators is 5/4.


Subgroup: 2.3.5.7
: Mapping generators: ~2592/2401, ~12005/6912


[[Comma list]]: 225/224, 589824/588245
[[Optimal tuning]] ([[POTE]]): ~2592/2401 = 133.3333, ~12005/6912 = 950.1680 (~1728/1715 = 16.8347)


[[Mapping]]: [{{val| 1 2 2 3 }}, {{val| 0 -13 10 -6 }}]
{{Optimal ET sequence|legend=1| 9, 63, 72, 495bcd }}


{{Multival|legend=1| 13 -10 6 -46 -27 42 }}
[[Badness]]: 0.093679
 
[[POTE generator]]: ~49/48 = 38.413
 
{{Val list|legend=1| 31, 94, 125 }}
 
[[Badness]]: 0.056934


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


Comma list: 225/224, 385/384, 1331/1323
Comma list: 225/224, 385/384, 12005/11979


Mapping: [{{val| 1 2 2 3 4 }}, {{val| 0 -13 10 -6 -17 }}]
Mapping: {{mapping| 9 0 28 11 24 | 0 2 -1 2 1 }}


POTE generator: ~49/48 = 38.387
Optimal tuning (POTE): ~121/112 = 133.3333, ~210/121 = 950.1873 (~99/98 = 16.8540)


Optimal GPV sequence: {{Val list| 31, 63, 94, 125 }}
{{Optimal ET sequence|legend=1| 9, 63, 72, 423cd, 495bcd }}


Badness: 0.025342
Badness: 0.030426


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


Comma list: 225/224, 275/273, 385/384, 1331/1323
Comma list: 169/168, 225/224, 364/363, 1716/1715


Mapping: [{{val| 1 2 2 3 4 3 }}, {{val| 0 -13 10 -6 -17 22 }}]
Mapping: {{mapping| 9 0 28 11 24 19 | 0 2 -1 2 1 2 }}


POTE generator: ~49/48 = 38.314
Optimal tuning (POTE): ~14/13 = 133.3333, ~26/15 = 950.2867 (~105/104 = 16.9534)


Optimal GPV sequence: {{Val list| 31, 63, 94 }}
{{Optimal ET sequence|legend=1| 9, 63, 72, 279cf }}


Badness: 0.025913
Badness: 0.022322


== Marvolo ==
== Gracecordial ==
Subgroup: 2.3.5.7
: ''For the 5-limit version of this temperament, see [[Schismic–Pythagorean equivalence continuum #Gracecordial]].''


[[Comma list]]: 225/224, 156250000/155649627
[[Subgroup]]: 2.3.5.7


[[Mapping]]: [{{val| 1 2 1 1 }}, {{val| 0 -6 19 26 }}]
[[Comma list]]: 225/224, 781250000/771895089


{{Multival|legend=1| 6 -19 -26 -44 -58 -7 }}
{{Mapping|legend=1| 1 0 34 63 | 0 1 -20 -38 }}


[[POTE generator]]: ~21/20 = 83.348
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~3/2 = 700.824


{{Val list|legend=1| 29, 43, 72, 619bcd, 691bcd }}
{{Optimal ET sequence|legend=1| 12, 113, 125, 238c, 363c }}


[[Badness]]: 0.083338
[[Badness]]: 0.096279


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


Comma list: 225/224, 441/440, 4000/3993
Comma list: 225/224, 385/384, 236328125/234365481


Mapping: [{{val| 1 2 1 1 2 }}, {{val| 0 -6 19 26 21 }}]
Mapping: {{mapping| 1 0 34 63 -90 | 0 1 -20 -38 59 }}


POTE generator: ~21/20 = 83.340
Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.834


Optimal GPV sequence: {{Val list| 29, 43, 72 }}
{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125, 238c }}


Badness: 0.028965
Badness: 0.089588


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


Comma list: 169/168, 225/224, 364/363, 441/440
Comma list: 225/224, 325/324, 385/384, 831875/830466


Mapping: [{{val| 1 2 1 1 2 3 }}, {{val| 0 -6 19 26 21 10 }}]
Mapping: {{mapping| 1 0 34 63 -90 -66 | 0 1 -20 -38 59 44 }}


POTE generator: ~21/20 = 83.330
Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.841


Optimal GPV sequence: {{Val list| 29, 43, 72, 115f }}
{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125f, 238cf }}


Badness: 0.021470
Badness: 0.052235


== Enneaportent ==
==== 17-limit ====
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7.11.13.17


[[Comma list]]: 225/224, 40353607/40310784
Comma list: 225/224, 273/272, 325/324, 385/384, 4928/4913


[[Mapping]]: [{{val| 9 0 28 11 }}, {{val| 0 2 -1 2 }}]
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 | 0 1 -20 -38 59 44 7 }}


{{Multival|legend=1| 18 -9 18 -56 -22 67 }}
Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.841


[[POTE generator]]: ~5/4 = 383.165
{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125f, 238cf }}


{{Val list|legend=1| 9, 63, 72, 495bcd }}
Badness: 0.038565


[[Badness]]: 0.093679
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19


=== 11-limit ===
Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 1445/1444
Subgroup: 2.3.5.7.11


Comma list: 225/224, 385/384, 12005/11979
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 | 0 1 -20 -38 59 44 7 -3 }}


Mapping: [{{val| 9 0 28 11 24 }}, {{val| 0 2 -1 2 1 }}]
Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.842


POTE generator: ~5/4 = 383.146
{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125f, 238cf }}


Optimal GPV sequence: {{Val list| 9, 63, 72, 423cd, 495bcd }}
Badness: 0.028165


Badness: 0.030426
==== 23-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23


=== 13-limit ===
Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 460/459, 529/528
Subgroup: 2.3.5.7.11.13


Comma list: 169/168, 225/224, 364/363, 1716/1715
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 | 0 1 -20 -38 59 44 7 -3 30 }}


Mapping: [{{val| 9 0 28 11 24 19 }}, {{val| 0 2 -1 2 1 2 }}]
Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.843


POTE generator: ~5/4 = 383.047
{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 238cfi }}


Optimal GPV sequence: {{Val list| 9, 63, 72, 279cf }}
Badness: 0.021879


Badness: 0.022322
==== 29-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23.29


== Submajor ==
Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 494/493
Subgroup: 2.3.5


[[Comma list]]: 69198046875/68719476736
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 | 0 1 -20 -38 59 44 7 -3 30 34 }}


[[Mapping]]: [{{val| 1 4 -1 }}, {{val| 0 -8 11 }}]
Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.842


[[POTE generator]]: ~10125/8192 = 362.321
{{Optimal ET sequence|legend=1| 12e, 101cde, 113, 125f, 238cfi }}


{{Val list|legend=1| 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc }}
Badness: 0.018011


[[Badness]]: 0.130236
==== 31-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23.29.31


=== 7-limit ===
Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 465/464, 494/493
Subgroup: 2.3.5.7


[[Comma list]]: 225/224, 51200/50421
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]]: [{{val| 1 4 -1 1 }}, {{val| 0 -8 11 6 }}]
Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.838


{{Multival|legend=1| 8 -11 -6 -36 -32 17 }}
{{Optimal ET sequence|legend=1| 12e, 101cdek, 113, 125f, 238cfi }}


[[POTE generator]]: ~49/40 = 362.255
Badness: 0.016007


{{Val list|legend=1| 10, 33, 43, 53 }}
=== Gracecord ===
 
[[Badness]]: 0.060533
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 225/224, 385/384, 6655/6561
Comma list: 225/224, 441/440, 109375/107811


Mapping: [{{val| 1 4 -1 1 11 }}, {{val| 0 -8 11 6 -25 }}]
Mapping: {{mapping| 1 0 34 63 89 | 0 1 -20 -38 -54 }}


POTE generator: ~27/22 = 362.101
Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.885


Optimal GPV sequence: {{Val list| 10, 43e, 53, 116, 169de, 285cde }}
{{Optimal ET sequence|legend=1| 12, 101cd, 113 }}


Badness: 0.050582
Badness: 0.066964


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


Comma list: 169/168, 225/224, 275/273, 385/384
Comma list: 225/224, 364/363, 441/440, 6125/6084


Mapping: [{{val| 1 4 -1 1 11 4 }}, {{val| 0 -8 11 6 -25 -1 }}]
Mapping: {{mapping| 1 0 34 63 89 113 | 0 1 -20 -38 -54 -69 }}


POTE generator: ~16/13 = 362.105
Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.890


Optimal GPV sequence: {{Val list| 10, 43e, 53, 116, 169de, 285cdef }}
{{Optimal ET sequence|legend=1| 12f, 101cdf, 113 }}


Badness: 0.027689
Badness: 0.044196


=== Interpental ===
==== 17-limit ====
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11.13.17


Comma list: 99/98, 176/175, 51200/50421
Comma list: 225/224, 364/363, 441/440, 595/594, 2000/1989


POTE generator: ~49/40 = 362.418
Mapping: {{mapping| 1 0 34 63 89 113 -7 | 0 1 -20 -38 -54 -69 7 }}


Mapping: [{{val| 1 4 -1 1 -5 }}, {{val| 0 -8 11 6 28 }}]
Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.870


POTE generator: ~49/40 = 362.418
{{Optimal ET sequence|legend=1| 12f, 101cdf, 113 }}


Optimal GPV sequence: {{Val list| 43, 53, 96, 149d }}
Badness: 0.036637


Badness: 0.051806
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19


==== 13-limit ====
Comma list: 210/209, 225/224, 324/323, 364/363, 400/399, 665/663
Subgroup: 2.3.5.7.11.13


Comma list: 99/98, 169/168, 176/175, 640/637
Mapping: {{mapping| 1 0 34 63 89 113 -7 9 | 0 1 -20 -38 -54 -69 7 -3 }}


POTE generator: ~16/13 = 362.402
Optimal tuning (POTE): ~2 = 1200.000, ~3/2 = 700.866


Mapping: [{{val| 1 4 -1 1 -5 4 }}, {{val| 0 -8 11 6 28 -1 }}]
{{Optimal ET sequence|legend=1| 12f, 101cdf, 113 }}


POTE generator: ~16/13 = 362.402
Badness: 0.027559
 
Optimal GPV sequence: {{Val list| 43, 53, 96, 149d }}
 
Badness: 0.029680


== Alphorn ==
== Alphorn ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224, 5764801/5668704
[[Comma list]]: 225/224, 5764801/5668704


[[Mapping]]: [{{val| 1 9 0 13 }}, {{val| 0 -16 5 -22 }}]
{{Mapping|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


[[POTE generator]]: ~48/35 = 556.221
{{Optimal ET sequence|legend=1| 28d, 41, 151cd, 192cd, 233cd }}
 
{{Val list|legend=1| 28d, 41, 151cd, 192cd, 233cd }}


[[Badness]]: 0.129258
[[Badness]]: 0.129258
Line 885: Line 711:
Comma list: 225/224, 385/384, 12250/11979
Comma list: 225/224, 385/384, 12250/11979


Mapping: [{{val| 1 9 0 13 3 }}, {{val| 0 -16 5 -22 1 }}]
Mapping: {{mapping| 1 9 0 13 3 | 0 -16 5 -22 1 }}


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


Optimal GPV sequence: {{Val list| 28d, 41, 315cde }}
{{Optimal ET sequence|legend=1| 28d, 41, 315cde }}


Badness: 0.073459
Badness: 0.073459


== Tertiosec ==
== Misneb ==
: ''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 #Misneb]].''


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224, 14495514624/13841287201
[[Comma list]]: 225/224, 4194304/4117715


[[Mapping]]: [{{val| 3 7 5 9 }}, {{val| 0 -8 7 -2 }}]
{{Mapping|legend=1| 1 3 1 3 | 0 -15 14 -2 }}


{{Multival|legend=1| 24 -21 6 -89 -58 73 }}
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~16/15 = 113.235


[[POTE generator]]: ~15/14 = 112.283
{{Optimal ET sequence|legend=1| 21, 32, 53 }}


{{Val list|legend=1| 21, 54, 75, 96, 171d }}
[[Badness]]: 0.140970
 
[[Badness]]: 0.431636


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


Comma list: 225/224, 3840/3773, 12005/11979
Comma list: 99/98, 176/175, 1310720/1294139


Mapping: [{{val| 3 7 5 9 9 }}, {{val| 0 -8 7 -2 5 }}]
Mapping: {{mapping| 1 3 1 3 1 | 0 -15 14 -2 26 }}


POTE generator: ~15/14 = 112.171
Optimal tuning (POTE): ~2 = 1200.000, ~16/15 = 113.323


Optimal GPV sequence: {{Val list| 21, 54, 75e }}
{{Optimal ET sequence|legend=1| 21, 32e, 53, 127, 180de }}


Badness: 0.173485
Badness: 0.085390


== Gwazy ==
==== 13-limit ====
{{see also|Very high accuracy temperaments #Kwazy}}
Subgroup: 2.3.5.7.11.13


Subgroup: 2.3.5.7
Comma list: 99/98, 176/175, 640/637, 847/845


[[Comma list]]: 225/224, 5971968/5764801
Mapping: {{mapping| 1 3 1 3 1 2 | 0 -15 14 -2 26 18 }}


[[Mapping]]: [{{val| 2 1 6 4 }}, {{val| 0 8 -5 6 }}]
Optimal tuning (POTE): ~2 = 1200.000, ~16/15 = 113.323


{{Multival|legend=1| 16 -10 12 -53 -26 56 }}
{{Optimal ET sequence|legend=1| 21, 32e, 53, 127, 180de }}


[[POTE generator]]: ~35/32 = 162.658
Badness: 0.045569


{{Val list|legend=1| 22, 74, 96, 118d }}
=== Musneb ===
 
[[Badness]]: 0.178826
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 99/98, 176/175, 65536/65219
Comma list: 225/224, 385/384, 66550/64827


Mapping: [{{val| 2 1 6 4 8 }}, {{val| 0 8 -5 6 -4 }}]
Mapping: {{mapping| 1 3 1 3 6 | 0 -15 14 -2 -27 }}


POTE generator: ~11/10 = 162.592
Optimal tuning (POTE): ~2 = 1200.000, ~16/15 = 113.142


Optimal GPV sequence: {{Val list| 22, 74, 96, 118d }}
{{Optimal ET sequence|legend=1| 32, 53, 191de, 244cddee, 297cddee }}


Badness: 0.068410
Badness: 0.087333


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


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224, 781250000/771895089
[[Comma list]]: 225/224, 125000000/121060821


[[Mapping]]: [{{val| 1 0 34 63 }}, {{val| 0 1 -20 -38 }}]
{{Mapping|legend=1| 1 6 -7 -7 | 0 -9 19 20 }}


{{Multival|legend=1| 1 -20 -38 -34 -63 -32 }}
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~7/5 = 588.641


[[POTE generator]]: ~3/2 = 700.824
{{Optimal ET sequence|legend=1| 51, 53, 316cd, 369cdd, 422cdd }}


{{Val list|legend=1| 12, 113, 125, 238c, 363c }}
[[Badness]]: 0.143976
 
[[Badness]]: 0.096279


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


Comma list: 225/224, 385/384, 236328125/234365481
Comma list: 121/120, 225/224, 22000/21609


Mapping: [{{val| 1 0 34 63 -90 }}, {{val| 0 1 -20 -38 59 }}]
Mapping: {{mapping| 1 6 -7 -7 1 | 0 -9 19 20 5 }}


POTE generator: ~3/2 = 700.834
Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 588.626


Optimal GPV sequence: {{Val list| 12e, 101cde, 113, 125, 238c }}
{{Optimal ET sequence|legend=1| 51, 53 }}


Badness: 0.089588
Badness: 0.074295


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


Comma list: 225/224, 325/324, 385/384, 831875/830466
Comma list: 121/120, 225/224, 275/273, 1040/1029


Mapping: [{{val| 1 0 34 63 -90 -66 }}, {{val| 0 1 -20 -38 59 44 }}]
Mapping: {{mapping| 1 6 -7 -7 1 -12 | 0 -9 19 20 5 32 }}


POTE generator: ~3/2 = 700.841
Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 588.654


Optimal GPV sequence: {{Val list| 12e, 101cde, 113, 125f, 238cf }}
{{Optimal ET sequence|legend=1| 51f, 53 }}


Badness: 0.052235
Badness: 0.047441
 
== Quintannic ==
[[Subgroup]]: 2.3.5.7


==== 17-limit ====
[[Comma list]]: 225/224, 9805926501/9765625000
Subgroup: 2.3.5.7.11.13.17


Comma list: 225/224, 273/272, 325/324, 385/384, 4928/4913
{{Mapping|legend=1| 1 1 5 7 | 0 5 -23 -36 }}


Mapping: [{{val| 1 0 34 63 -90 -66 -7 }}, {{val| 0 1 -20 -38 59 44 7 }}]
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~10000/9261 = 139.838


POTE generator: ~3/2 = 700.841
{{Optimal ET sequence|legend=1| 43, 60, 103, 266bcd, 369bcd }}


Optimal GPV sequence: {{Val list| 12e, 101cde, 113, 125f, 238cf }}
[[Badness]]: 0.150565


Badness: 0.038565
=== 11-limit ===
Subgroup: 2.3.5.7.11


==== 19-limit ====
Comma list: 225/224, 441/440, 43923/43750
Subgroup: 2.3.5.7.11.13.17.19


Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 1445/1444
Mapping: {{mapping| 1 1 5 7 8 | 0 5 -23 -36 -39 }}


Mapping: [{{val| 1 0 34 63 -90 -66 -7 9 }}, {{val| 0 1 -20 -38 59 44 7 -3 }}]
Optimal tuning (POTE): ~2 = 1200.000, ~320/297 = 139.827


POTE generator: ~3/2 = 700.842
{{Optimal ET sequence|legend=1| 43, 60e, 103 }}


Optimal GPV sequence: {{Val list| 12e, 101cde, 113, 125f, 238cf }}
Badness: 0.052590


Badness: 0.028165
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


==== 23-limit ====
Comma list: 225/224, 441/440, 1001/1000, 1188/1183
Subgroup: 2.3.5.7.11.13.17.19.23


Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 460/459, 529/528
Mapping: {{mapping| 1 1 5 7 8 3 | 0 5 -23 -36 -39 6 }}


Mapping: [{{val| 1 0 34 63 -90 -66 -7 9 -43 }}, {{val| 0 1 -20 -38 59 44 7 -3 30 }}]
Optimal tuning (POTE): ~2 = 1200.000, ~13/12 = 139.812


POTE generator: ~3/2 = 700.843
{{Optimal ET sequence|legend=1| 43, 60e, 103 }}


Optimal GPV sequence: {{Val list| 12e, 101cde, 113, 238cfi }}
Badness: 0.032730


Badness: 0.021879
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17


==== 29-limit ====
Comma list: 225/224, 273/272, 375/374, 441/440, 891/884
Subgroup: 2.3.5.7.11.13.17.19.23.29


Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 494/493
Mapping: {{mapping| 1 1 5 7 8 3 7 | 0 5 -23 -36 -39 6 -25 }}


Mapping: [{{val| 1 0 34 63 -90 -66 -7 9 -43 -49 }}, {{val| 0 1 -20 -38 59 44 7 -3 30 34 }}]
Optimal tuning (POTE): ~2 = 1200.000, ~13/12 = 139.815


POTE generator: ~3/2 = 700.842
{{Optimal ET sequence|legend=1| 43, 60e, 103 }}


Optimal GPV sequence: {{Val list| 12e, 101cde, 113, 125f, 238cfi }}
Badness: 0.023038


Badness: 0.018011
== Gwazy ==
{{See also| Very high accuracy temperaments #Kwazy }}


==== 31-limit ====
[[Subgroup]]: 2.3.5.7
Subgroup: 2.3.5.7.11.13.17.19.23.29.31


Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 465/464, 494/493
[[Comma list]]: 225/224, 5971968/5764801


Mapping: [{{val| 1 0 34 63 -90 -66 -7 9 -43 -49 -79 }}, {{val| 0 1 -20 -38 59 44 7 -3 30 34 53 }}]
{{Mapping|legend=1| 2 1 6 4 | 0 8 -5 6 }}


POTE generator: ~3/2 = 700.838
[[Optimal tuning]] ([[POTE]]): ~2401/1728 = 600.000, ~35/32 = 162.658


Optimal GPV sequence: {{Val list| 12e, 101cdek, 113, 125f, 238cfi }}
{{Optimal ET sequence|legend=1| 22, 74, 96, 118d }}


Badness: 0.016007
[[Badness]]: 0.178826


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


Comma list: 225/224, 441/440, 109375/107811
Comma list: 99/98, 176/175, 65536/65219


Mapping: [{{val| 1 0 34 63 89 }}, {{val| 0 1 -20 -38 -54 }}]
Mapping: {{mapping| 2 1 6 4 8 | 0 8 -5 6 -4 }}


POTE generator: ~3/2 = 700.885
Optimal tuning (POTE): ~363/256 = 600.000, ~11/10 = 162.592


Optimal GPV sequence: {{Val list| 12, 101cd, 113 }}
{{Optimal ET sequence|legend=1| 22, 74, 96, 118d }}


Badness: 0.066964
Badness: 0.068410


==== 13-limit ====
== Tertiosec ==
Subgroup: 2.3.5.7.11.13
: ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Tertiosec]].''


Comma list: 225/224, 364/363, 441/440, 6125/6084
[[Subgroup]]: 2.3.5.7


Mapping: [{{val| 1 0 34 63 89 113 }}, {{val| 0 1 -20 -38 -54 -69 }}]
[[Comma list]]: 225/224, 14495514624/13841287201


POTE generator: ~3/2 = 700.890
{{Mapping|legend=1| 3 7 5 9 | 0 -8 7 -2 }}


Optimal GPV sequence: {{Val list| 12f, 101cdf, 113 }}
[[Optimal tuning]] ([[POTE]]): ~3072/2401 = 400.000, ~15/14 = 112.283


Badness: 0.044196
{{Optimal ET sequence|legend=1| 21, 54, 75, 96, 171d }}


==== 17-limit ====
[[Badness]]: 0.431636
Subgroup: 2.3.5.7.11.13.17


Comma list: 225/224, 364/363, 441/440, 595/594, 2000/1989
=== 11-limit ===
Subgroup: 2.3.5.7.11


Mapping: [{{val| 1 0 34 63 89 113 -7 }}, {{val| 0 1 -20 -38 -54 -69 7 }}]
Comma list: 225/224, 3840/3773, 12005/11979


POTE generator: ~3/2 = 700.870
Mapping: {{mapping| 3 7 5 9 9 | 0 -8 7 -2 5 }}


Optimal GPV sequence: {{Val list| 12f, 101cdf, 113 }}
Optimal tuning (POTE): ~44/35 = 400.000, ~15/14 = 112.171


Badness: 0.036637
{{Optimal ET sequence|legend=1| 21, 54, 75e }}


==== 19-limit ====
Badness: 0.173485
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 210/209, 225/224, 324/323, 364/363, 400/399, 665/663
 
Mapping: [{{val| 1 0 34 63 89 113 -7 9 }}, {{val| 0 1 -20 -38 -54 -69 7 -3 }}]
 
POTE generator: ~3/2 = 700.866
 
Optimal GPV sequence: {{Val list| 12f, 101cdf, 113 }}
 
Badness: 0.027559


[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Marvel]]
[[Category:Pages with mostly numerical content]]
[[Category:Marvel temperaments| ]] <!-- main article -->
[[Category:Marvel temperaments| ]] <!-- main article -->
[[Category:Marvel| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
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