Gamelismic family: Difference between revisions

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m Units & misc. cleanup
Switch to Sintel's badness, WE & CWE tunings, per community consensus
Line 20: Line 20:
: Angle (8/7, 5/4) = 90 degrees
: Angle (8/7, 5/4) = 90 degrees


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~8/7 = 233.6875{{c}}, ~5/4 = 385.1853{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.4859{{c}}, ~8/7 = 233.7822{{c}}, ~5/4 = 385.3412{{c}}
: [[error map]]: {{val| +0.486 -0.123 -0.001 -1.151 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 233.7474{{c}}, ~5/4 = 385.5205{{c}}
: error map: {{val| 0.000 -0.713 -0.793 -2.573 }}
<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~8/7 = 233.6875{{c}}, ~5/4 = 385.1853{{c}} -->
<!-- [[TE tuning|TE]] [[tuning map]]: {{val| 1200.486 1901.833 2786.314 3367.676 }} -->


[[Minimax tuning]]: ''c'' = 1029/1024
[[Minimax tuning]]: ''c'' = 1029/1024
Line 30: Line 36:
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5/3.9/7
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5/3.9/7


[[TE tuning|TE]] [[tuning map]]: {{val| 1200.486 1901.833 2786.314 3367.676 }}
{{Optimal ET sequence|legend=1| 5, 10, 15, 26, 31, 41, 72, 118, 190 }}


{{Optimal ET sequence|legend=1| 5, 10, 15, 26, 31, 41, 72, 118, 159, 190 }}
[[Badness]] (Sintel): 0.777
 
[[Badness]] (Smith): 0.176 × 10<sup>-3</sup>


[[Projection pair]]: 3 1024/343 to 2.5.7
[[Projection pair]]: 3 1024/343 to 2.5.7
Line 57: Line 61:
: Angle (8/7, 12/11) = 86.657 degrees
: Angle (8/7, 12/11) = 86.657 degrees


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~8/7 = 233.6884{{c}}, ~5/4 = 385.1618{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.4902{{c}}, ~8/7 = 233.7839{{c}}, ~5/4 = 385.3191{{c}}
: [[error map]]: {{val| +0.490 -0.113 -0.014 -1.139 -0.031 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 233.7616{{c}}, ~5/4 = 385.3149{{c}}
: error map: {{val| 0.000 -0.670 -0.999 -2.587 -1.586 }}
<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~8/7 = 233.6884{{c}}, ~5/4 = 385.1618{{c}} -->


[[Minimax tuning]]: ''c''<sub>1</sub> = 1029/1024, ''c''<sub>2</sub> = 385/384
[[Minimax tuning]]: ''c''<sub>1</sub> = 1029/1024, ''c''<sub>2</sub> = 385/384
Line 64: Line 73:
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/7.11/5
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/7.11/5


{{Optimal ET sequence|legend=1| 10, 15, 26, 31, 41, 72, 118, 159, 190 }}
{{Optimal ET sequence|legend=1| 15, 26, 31, 41, 72, 118, 159, 190 }}


[[Badness]] (Smith): 0.234 × 10<sup>-3</sup>
[[Badness]] (Sintel): 0.281


[[Projection pair]]s: 3 1024/343 11 131072/12005 to 2.5.7
[[Projection pair]]s: 3 1024/343 11 131072/12005 to 2.5.7
Line 79: Line 88:
Mapping: {{mapping| 1 1 0 3 5 6 | 0 3 0 -1 4 12 | 0 0 1 0 -1 -2 }}
Mapping: {{mapping| 1 1 0 3 5 6 | 0 3 0 -1 4 12 | 0 0 1 0 -1 -2 }}


Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~8/7 = 233.9128{{c}}, ~5/4 = 384.7278{{c}}
Optimal tunings:
* WE: ~2 = 1200.4540{{c}}, ~8/7 = 234.0013{{c}}, ~5/4 = 384.8733{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.9748{{c}}, ~5/4 = 384.8812{{c}}
<!-- * POTE: ~2 = 1200.0000{{c}}, ~8/7 = 233.9128{{c}}, ~5/4 = 384.7278{{c}} -->


{{Optimal ET sequence|legend=0| 15, 26, 41, 46, 72, 87, 159, 477cdf }}
{{Optimal ET sequence|legend=0| 15, 26, 31f, 41, 46, 72, 87, 159 }}


Badness (Smith): 0.627 × 10<sup>-3</sup>
Badness (Sintel): 0.587


Complexity spectrum: 8/7, 4/3, 11/8, 6/5, 14/11, 7/6, 10/9, 12/11, 5/4, 13/11, 9/8, 7/5, 11/9, 9/7, 18/13, 13/12, 16/15, 11/10, 15/14, 16/13, 14/13, 15/11, 13/10, 15/13
Complexity spectrum: 8/7, 4/3, 11/8, 6/5, 14/11, 7/6, 10/9, 12/11, 5/4, 13/11, 9/8, 7/5, 11/9, 9/7, 18/13, 13/12, 16/15, 11/10, 15/14, 16/13, 14/13, 15/11, 13/10, 15/13
Line 94: Line 106:
Mapping: {{mapping| 1 1 0 3 5 -5 | 0 3 0 -1 4 -3 | 0 0 1 0 -1 4 }}
Mapping: {{mapping| 1 1 0 3 5 -5 | 0 3 0 -1 4 -3 | 0 0 1 0 -1 4 }}


Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~8/7 = 233.6843{{c}}, ~5/4 = 384.9830{{c}}
Optimal tunings:
* WE: ~2 = 1200.4888{{c}}, ~8/7 = 233.7795{{c}}, ~5/4 = 385.1398{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.7575{{c}}, ~5/4 = 385.1447{{c}}
<!-- * POTE: ~2 = 1200.0000{{c}}, ~8/7 = 233.6843{{c}}, ~5/4 = 384.9830{{c}} -->


{{Optimal ET sequence|legend=0| 15, 31, 56, 72, 87, 103, 159, 190, 262df, 349f, 452cdef, 611cdef }}
{{Optimal ET sequence|legend=0| 15, 31, 56, 72, 87, 103, 159, 190, 262df, 452cdef, 611cddef }}


Badness (Smith): 0.662 × 10<sup>-3</sup>
Badness (Sintel): 0.618


=== Ominous ===
=== Ominous ===
Line 107: Line 122:
Mapping: {{mapping| 1 1 0 3 5 1 | 0 3 0 -1 4 -10 | 0 0 1 0 -1 2 }}
Mapping: {{mapping| 1 1 0 3 5 1 | 0 3 0 -1 4 -10 | 0 0 1 0 -1 2 }}


Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~8/7 = 233.4088{{c}}, ~5/4 = 385.3825{{c}}
Optimal tunings:
* WE: ~2 = 1200.7019{{c}}, ~8/7 = 233.5453{{c}}, ~5/4 = 385.6079{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.4510{{c}}, ~5/4 = 385.6739{{c}}
<!-- * POTE: ~2 = 1200.0000{{c}}, ~8/7 = 233.4088{{c}}, ~5/4 = 385.3825{{c}} -->


{{Optimal ET sequence|legend=0| 26, 31, 46, 72, 103, 149, 221ef, 324bdef, 473bdef }}
{{Optimal ET sequence|legend=0| 15f, 26, 31, 46, 72, 103, 149, 221ef, 324bdef, 473bdeeff, 545bddeefff }}


Badness (Smith): 0.751 × 10<sup>-3</sup>
Badness (Sintel): 0.702


==== 17-limit ====
==== 17-limit ====
Line 126: Line 144:
: Angle (8/7, 6/5) = 98.6015
: Angle (8/7, 6/5) = 98.6015


Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~8/7 = 233.4313{{c}}, ~5/4 = 385.2890{{c}}
Optimal tunings:
* WE: ~2 = 1200.6745{{c}}, ~8/7 = 233.5625{{c}}, ~5/4 = 385.5056{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.4679{{c}}, ~5/4 = 385.5892{{c}}
<!-- * POTE: ~2 = 1200.0000{{c}}, ~8/7 = 233.4313{{c}}, ~5/4 = 385.2890{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 133: Line 154:
: unchanged-interval (eigenmonzo) basis: 2.11/9.13/9
: unchanged-interval (eigenmonzo) basis: 2.11/9.13/9


{{Optimal ET sequence|legend=0| 26, 31, 46, 72, 103, 149, 175f, 221ef }}
{{Optimal ET sequence|legend=0| 15f, 20c, 26, 31, 46, 72, 103, 149, 221ef }}


Badness (Smith): 0.612 × 10<sup>-3</sup>
Badness (Sintel): 0.582


=== Momentous ===
=== Momentous ===
Line 144: Line 165:
Mapping: {{mapping| 1 1 0 3 5 7 | 0 3 0 -4 1 -5 | 0 0 1 0 -1 -1 }}
Mapping: {{mapping| 1 1 0 3 5 7 | 0 3 0 -4 1 -5 | 0 0 1 0 -1 -1 }}


Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~8/7 = 233.4088{{c}}, ~5/4 = 385.3825{{c}}
Optimal tunings:
* WE: ~2 = 1200.0652{{c}}, ~8/7 = 234.1856{{c}}, ~5/4 = 386.6199{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 234.1748{{c}}, ~5/4 = 386.5951{{c}}
<!-- * POTE: ~2 = 1200.0000{{c}}, ~8/7 = 233.4088{{c}}, ~5/4 = 385.3825{{c}} -->


{{Optimal ET sequence|legend=0| 10, 31, 41, 46, 77, 87, 118, 164, 205d, 574def }}
{{Optimal ET sequence|legend=0| 15f, 21e, 31, 41, 46, 72f, 77, 87, 118, 164, 205d }}


Badness (Smith): 0.832 × 10<sup>-3</sup>
Badness (Sintel): 0.778


=== Foreboding ===
=== Foreboding ===
Line 157: Line 181:
Mapping: {{mapping| 1 1 0 3 5 1 | 0 3 0 -1 4 2 | 0 0 1 0 -1 1 }}
Mapping: {{mapping| 1 1 0 3 5 1 | 0 3 0 -1 4 2 | 0 0 1 0 -1 1 }}


Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~8/7 = 233.3664{{c}}, ~5/4 = 382.3425{{c}}
Optimal tunings:
* WE: ~2 = 1200.2251{{c}}, ~8/7 = 233.4102{{c}}, ~5/4 = 382.4142{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.4017{{c}}, ~5/4 = 382.4261{{c}}
<!-- * POTE: ~2 = 1200.0000{{c}}, ~8/7 = 233.3664{{c}}, ~5/4 = 382.3425{{c}} -->


{{Optimal ET sequence|legend=0| 5, 10, 15, 26, 31, 41, 72f, 185cf }}
{{Optimal ET sequence|legend=0| 5, 10, 15, 25e, 26, 31, 41, 72f }}


Badness (Smith): 0.873 × 10<sup>-3</sup>
Badness (Sintel): 0.816


=== Portannic ===
=== Portannic ===
Line 169: Line 196:


Mapping: {{mapping| 1 1 2 3 3 4 | 0 3 0 -1 4 -1 | 0 0 3 0 -3 -1 }}
Mapping: {{mapping| 1 1 2 3 3 4 | 0 3 0 -1 4 -1 | 0 0 3 0 -3 -1 }}
: mapping generators: ~2, ~8/7, ~14/13


Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~8/7 = 233.6434{{c}}, ~14/13 = 128.3440{{c}}
Optimal tunings:
* WE: ~2 = 1200.5451{{c}}, ~8/7 = 233.7495{{c}}, ~14/13 = 128.4023{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.6930{{c}}, ~14/13 = 128.3684{{c}}
<!-- * POTE: ~2 = 1200.0000{{c}}, ~8/7 = 233.6434{{c}}, ~14/13 = 128.3440{{c}} -->


{{Optimal ET sequence|legend=0| 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 570ddeff, 832bcdddeefff }}
{{Optimal ET sequence|legend=0| 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 570ddeff, 832bcdddeefff }}


Badness (Smith): 1.783 × 10<sup>-3</sup>
Badness (Sintel): 1.67


==== 17-limit ====
==== 17-limit ====
Line 183: Line 214:
Mapping: {{mapping| 1 1 2 3 3 4 4 | 0 3 0 -1 4 -1 1 | 0 0 3 0 -3 -1 -1 }}
Mapping: {{mapping| 1 1 2 3 3 4 4 | 0 3 0 -1 4 -1 1 | 0 0 3 0 -3 -1 -1 }}


Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~8/7 = 233.6803{{c}}, ~14/13 = 128.4149{{c}}
Optimal tunings:
* WE: ~2 = 1200.4416{{c}}, ~8/7 = 233.7663{{c}}, ~14/13 = 128.4622{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.7173{{c}}, ~14/13 = 128.4269{{c}}
<!-- * POTE: ~2 = 1200.0000{{c}}, ~8/7 = 233.6803{{c}}, ~14/13 = 128.4149{{c}} -->


{{Optimal ET sequence|legend=0| 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 308def }}
{{Optimal ET sequence|legend=0| 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 308def }}


Badness (Smith): 1.303 × 10<sup>-3</sup>
Badness (Sintel): 1.24


== Gamel ==
== Gamel ==
Line 196: Line 230:
{{Mapping|legend=1| 1 1 0 3 -1 | 0 3 0 -1 11 | 0 0 1 0 1 }}
{{Mapping|legend=1| 1 1 0 3 -1 | 0 3 0 -1 11 | 0 0 1 0 1 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~8/7 = 233.2909{{c}}, ~5/4 = 384.2120{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.6462{{c}}, ~8/7 = 233.4166{{c}}, ~5/4 = 384.4189{{c}}
: [[error map]]: {{val| +0.646 -1.059 -0.602 -0.304 +1.329 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 233.3289{{c}}, ~5/4 = 384.5627{{c}}
: error map: {{val| 0.000 -1.968 -1.751 -2.155 -0.137 }}
<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~8/7 = 233.2909{{c}}, ~5/4 = 384.2120{{c}} -->


{{Optimal ET sequence|legend=1| 10, 31, 41, 72 }}
{{Optimal ET sequence|legend=1| 5e, 10, 21e, 26e, 31, 41, 72, 247c, 319bcde, 391bcde, 463bccde }}


[[Badness]] (Smith): 0.853 × 10<sup>-3</sup>
[[Badness]] (Sintel): 1.02


[[Category:Temperament families]]
[[Category:Temperament families]]

Revision as of 13:00, 11 November 2025

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The gamelismic family of rank-3 temperaments tempers out the gamelisma, 1029/1024. The head of this family, gamelismic, tempers out 1029/1024 alone in the full 7-limit, so it has the same 2.3.7-subgroup structure as slendric but giving prime 5 an independent generator.

See Gamelismic clan for the rank-2 temperament without the last generator of gamelismic, and its various extensions.

Gamelismic

Main article: Gamelismic and portent

Subgroup: 2.3.5.7

Comma list: 1029/1024

Mapping: [⟨1 1 0 3], ⟨0 3 0 -1], ⟨0 0 1 0]]

mapping generators: ~2, ~8/7, ~5

Mapping to lattice: [⟨0 3 0 -1], ⟨0 0 1 0]]

Minkowski lattice basis:

8/7 length = 0.5192, 5/4 length = log25
Angle (8/7, 5/4) = 90 degrees

Optimal tunings:

  • WE: ~2 = 1200.4859 ¢, ~8/7 = 233.7822 ¢, ~5/4 = 385.3412 ¢
error map: ⟨+0.486 -0.123 -0.001 -1.151]
  • CWE: ~2 = 1200.0000 ¢, ~8/7 = 233.7474 ¢, ~5/4 = 385.5205 ¢
error map: ⟨0.000 -0.713 -0.793 -2.573]

Minimax tuning: c = 1029/1024

[[1 0 0 0⟩, [5/2 3/4 0 -3/4⟩, [5/2 -1/4 1 -3/4⟩, [5/2 -1/4 0 1/4⟩]
unchanged-interval (eigenmonzo) basis: 2.7/3.5/3
[[1 0 0 0⟩, [10/7 6/7 0 -3/7⟩, [10/7 -1/7 1 -3/7⟩, [20/7 -2/7 0 1/7⟩]
unchanged-interval (eigenmonzo) basis: 2.5/3.9/7

Optimal ET sequence: 5, 10, 15, 26, 31, 41, 72, 118, 190

Badness (Sintel): 0.777

Projection pair: 3 1024/343 to 2.5.7

Scales: portent26

Portent

Main article: Gamelismic and portent

Portent has a normal comma list [1029/1024, 385/384] and also tempers out 441/440.

Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440

Mapping: [⟨1 1 0 3 5], ⟨0 3 0 -1 4], ⟨0 0 1 0 -1]]

Mapping to lattice: [⟨0 3 1 -1 3], ⟨0 0 1 0 -1]]

Minkowski lattice basis:

8/7 length = 0.46467, 12/11 length = 1.931
Angle (8/7, 12/11) = 86.657 degrees

Optimal tunings:

  • WE: ~2 = 1200.4902 ¢, ~8/7 = 233.7839 ¢, ~5/4 = 385.3191 ¢
error map: ⟨+0.490 -0.113 -0.014 -1.139 -0.031]
  • CWE: ~2 = 1200.0000 ¢, ~8/7 = 233.7616 ¢, ~5/4 = 385.3149 ¢
error map: ⟨0.000 -0.670 -0.999 -2.587 -1.586]

Minimax tuning: c1 = 1029/1024, c2 = 385/384

  • 11-odd-limit: 3 (1/7)c1 flat, 5 and 7 (2/7)c1 flat, 11 (c2 - (3/7)c1) flat
[[1 0 0 0 0⟩, [10/7 6/7 0 -3/7 0⟩, [39/14 4/7 1/2 -2/7 -1/2⟩, [20/7 -2/7 0 1/7 0⟩, [39/14 4/7 -1/2 -2/7 1/2⟩]
unchanged-interval (eigenmonzo) basis: 2.9/7.11/5

Optimal ET sequence: 15, 26, 31, 41, 72, 118, 159, 190

Badness (Sintel): 0.281

Projection pairs: 3 1024/343 11 131072/12005 to 2.5.7

Scales: portent26

Portending

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 364/363, 385/384

Mapping: [⟨1 1 0 3 5 6], ⟨0 3 0 -1 4 12], ⟨0 0 1 0 -1 -2]]

Optimal tunings:

  • WE: ~2 = 1200.4540 ¢, ~8/7 = 234.0013 ¢, ~5/4 = 384.8733 ¢
  • CWE: ~2 = 1200.0000 ¢, ~8/7 = 233.9748 ¢, ~5/4 = 384.8812 ¢

Optimal ET sequence: 15, 26, 31f, 41, 46, 72, 87, 159

Badness (Sintel): 0.587

Complexity spectrum: 8/7, 4/3, 11/8, 6/5, 14/11, 7/6, 10/9, 12/11, 5/4, 13/11, 9/8, 7/5, 11/9, 9/7, 18/13, 13/12, 16/15, 11/10, 15/14, 16/13, 14/13, 15/11, 13/10, 15/13

Portentous

Subgroup: 2.3.5.7.11.13

Comma list: 385/384, 441/440, 625/624

Mapping: [⟨1 1 0 3 5 -5], ⟨0 3 0 -1 4 -3], ⟨0 0 1 0 -1 4]]

Optimal tunings:

  • WE: ~2 = 1200.4888 ¢, ~8/7 = 233.7795 ¢, ~5/4 = 385.1398 ¢
  • CWE: ~2 = 1200.0000 ¢, ~8/7 = 233.7575 ¢, ~5/4 = 385.1447 ¢

Optimal ET sequence: 15, 31, 56, 72, 87, 103, 159, 190, 262df, 452cdef, 611cddef

Badness (Sintel): 0.618

Ominous

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 385/384, 441/440

Mapping: [⟨1 1 0 3 5 1], ⟨0 3 0 -1 4 -10], ⟨0 0 1 0 -1 2]]

Optimal tunings:

  • WE: ~2 = 1200.7019 ¢, ~8/7 = 233.5453 ¢, ~5/4 = 385.6079 ¢
  • CWE: ~2 = 1200.0000 ¢, ~8/7 = 233.4510 ¢, ~5/4 = 385.6739 ¢

Optimal ET sequence: 15f, 26, 31, 46, 72, 103, 149, 221ef, 324bdef, 473bdeeff, 545bddeefff

Badness (Sintel): 0.702

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 273/272, 351/350, 385/384, 441/440

Mapping: [⟨1 1 0 3 5 1 1], ⟨0 3 0 -1 4 -10 -8], ⟨0 0 1 0 -1 2 2]]

Mapping to lattice: [⟨0 1 1 0 0 -1 0], ⟨0 -1 -1 0 -1 2 1]]

Lattice basis:

8/7 length = 0.3859, 6/5 length = 1.1303
Angle (8/7, 6/5) = 98.6015

Optimal tunings:

  • WE: ~2 = 1200.6745 ¢, ~8/7 = 233.5625 ¢, ~5/4 = 385.5056 ¢
  • CWE: ~2 = 1200.0000 ¢, ~8/7 = 233.4679 ¢, ~5/4 = 385.5892 ¢

Minimax tuning:

  • 17-odd-limit
[[1 0 0 0 0 0 0⟩, [7/4 9/10 0 0 -3/10 -3/20 0⟩, [5/2 7/5 0 0 -4/5 1/10 0⟩, [11/4 -3/10 0 0 1/10 1/20 0⟩, [7/2 -1/5 0 0 2/5 -3/10 0⟩, [7/2 -1/5 0 0 -3/5 7/10 0⟩, [4 2/5 0 0 -4/5 3/5 0⟩]
unchanged-interval (eigenmonzo) basis: 2.11/9.13/9

Optimal ET sequence: 15f, 20c, 26, 31, 46, 72, 103, 149, 221ef

Badness (Sintel): 0.582

Momentous

Subgroup: 2.3.5.7.11.13

Comma list: 196/195, 352/351, 385/384

Mapping: [⟨1 1 0 3 5 7], ⟨0 3 0 -4 1 -5], ⟨0 0 1 0 -1 -1]]

Optimal tunings:

  • WE: ~2 = 1200.0652 ¢, ~8/7 = 234.1856 ¢, ~5/4 = 386.6199 ¢
  • CWE: ~2 = 1200.0000 ¢, ~8/7 = 234.1748 ¢, ~5/4 = 386.5951 ¢

Optimal ET sequence: 15f, 21e, 31, 41, 46, 72f, 77, 87, 118, 164, 205d

Badness (Sintel): 0.778

Foreboding

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 144/143, 275/273

Mapping: [⟨1 1 0 3 5 1], ⟨0 3 0 -1 4 2], ⟨0 0 1 0 -1 1]]

Optimal tunings:

  • WE: ~2 = 1200.2251 ¢, ~8/7 = 233.4102 ¢, ~5/4 = 382.4142 ¢
  • CWE: ~2 = 1200.0000 ¢, ~8/7 = 233.4017 ¢, ~5/4 = 382.4261 ¢

Optimal ET sequence: 5, 10, 15, 25e, 26, 31, 41, 72f

Badness (Sintel): 0.816

Portannic

Subgroup: 2.3.5.7.11.13

Comma list: 385/384, 441/440, 10985/10976

Mapping: [⟨1 1 2 3 3 4], ⟨0 3 0 -1 4 -1], ⟨0 0 3 0 -3 -1]]

mapping generators: ~2, ~8/7, ~14/13

Optimal tunings:

  • WE: ~2 = 1200.5451 ¢, ~8/7 = 233.7495 ¢, ~14/13 = 128.4023 ¢
  • CWE: ~2 = 1200.0000 ¢, ~8/7 = 233.6930 ¢, ~14/13 = 128.3684 ¢

Optimal ET sequence: 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 570ddeff, 832bcdddeefff

Badness (Sintel): 1.67

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 273/272, 385/384, 441/440, 8624/8619

Mapping: [⟨1 1 2 3 3 4 4], ⟨0 3 0 -1 4 -1 1], ⟨0 0 3 0 -3 -1 -1]]

Optimal tunings:

  • WE: ~2 = 1200.4416 ¢, ~8/7 = 233.7663 ¢, ~14/13 = 128.4622 ¢
  • CWE: ~2 = 1200.0000 ¢, ~8/7 = 233.7173 ¢, ~14/13 = 128.4269 ¢

Optimal ET sequence: 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 308def

Badness (Sintel): 1.24

Gamel

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1029/1024

Mapping: [⟨1 1 0 3 -1], ⟨0 3 0 -1 11], ⟨0 0 1 0 1]]

Optimal tunings:

  • WE: ~2 = 1200.6462 ¢, ~8/7 = 233.4166 ¢, ~5/4 = 384.4189 ¢
error map: ⟨+0.646 -1.059 -0.602 -0.304 +1.329]
  • CWE: ~2 = 1200.0000 ¢, ~8/7 = 233.3289 ¢, ~5/4 = 384.5627 ¢
error map: ⟨0.000 -1.968 -1.751 -2.155 -0.137]

Optimal ET sequence: 5e, 10, 21e, 26e, 31, 41, 72, 247c, 319bcde, 391bcde, 463bccde

Badness (Sintel): 1.02

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