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- CTE tunings
Sorting (putting prodigy next to undecimal marvel cuz it deserves that spot)
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Badness (Sintel): 0.935
Badness (Sintel): 0.935
== Prodigy ==
Prodigy shrinks 1024/1029, 243/242, 384/385 and 2400/2401 down to the same tiny interval. Hence in practice it probably makes the most sense to temper this out as well, leading to [[miracle]]. This, however, does not render it pointless to consider prodigy; for one thing, scales in prodigy such as hobbit scales translate into interesting scales for miracle.
[[Subgroup]]: 2.3.5.7.11
[[Comma list]]: 225/224, 441/440
{{Mapping|legend=1| 1 0 0 -5 -13 | 0 1 0 2 6 | 0 0 1 2 3 }}
Map to lattice: [{{val| 0 0 -1 -2 -3 }}, {{val| 0 1 -1 0 3 }}]
Lattice basis:
: ~15/14 length = 0.9111, ~3/2 length = 0.9477
: angle (~15/14, ~3/2) = 65.933°
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.7854{{c}}, ~3/2 = 700.2562{{c}}, ~5/4 = 383.7624{{c}}
: [[error map]]: {{val| +0.785 -0.913 -0.980 -0.003 +0.721 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 699.8610{{c}}, ~5/4 = 383.7724{{c}}
: error map: {{val| 0.000 -2.094 -2.541 -1.559 -0.835 }}
[[Minimax tuning]]:
* [[11-odd-limit]]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 13/12 1/2 -1/4 0 1/12 }}, {{monzo| 13/6 -1 1/2 0 1/6 }}, {{monzo| 3/2 -1 1/2 0 1/2 }}, {{monzo| 0 0 0 0 1 }}]
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/5.11
{{Optimal ET sequence|legend=1| 10, 12, 19e, 29, 31, 41, 60e, 72, 247c, 319bcde, 391bcde, 463bccde }}
[[Badness]] (Sintel): 0.402
[[Projection pair]]s: <code>7 225/32 11 91125/8192</code>
Scales: [[prodigy11]], [[prodigy12]], [[prodigy29]]
[[Associated temperament]]: [[miracle]]
{{Databox|Hobbit bases|
2.3.5 subgroup
* 31: 81/80, 34171875/33554432
* 41: 34171875/33554432, 32805/32768
}}
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 196/195, 352/351
Mapping: {{mapping| 1 0 0 -5 -13 -8 | 0 1 0 2 6 3 | 0 0 1 2 3 3 }}
Optimal tunings:
* WE: ~2 = 1200.8252{{c}}, ~3/2 = 700.8823{{c}}, ~5/4 = 381.6647{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.4689{{c}}, ~5/4 = 381.6687{{c}}
{{Optimal ET sequence|legend=0| 10, 12f, 19e, 29, 31, 41, 60e, 72f, 101cd }}
Badness (Sintel): 0.689
=== Prodigious ===
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 364/363, 441/440
Mapping: {{mapping| 1 0 0 -5 -13 -23 | 0 1 0 2 6 11 | 0 0 1 2 3 4 }}
Optimal tunings:
* WE: ~2 = 1200.6284{{c}}, ~3/2 = 700.7075{{c}}, ~5/4 = 383.4599{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.3302{{c}}, ~5/4 = 383.5030{{c}}
{{Optimal ET sequence|legend=0| 12f, 29, 31f, 41, 72, 185cf, 257cff }}
Badness (Sintel): 0.841
=== Prodigal ===
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 351/350, 441/440
Mapping: {{mapping| 1 0 0 -5 -13 -4 | 0 1 0 2 6 -1 | 0 0 1 2 3 4 }}
Optimal tunings:
* WE: ~2 = 1200.7798{{c}}, ~3/2 = 699.9410{{c}}, ~5/4 = 384.3494{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 699.5538{{c}}, ~5/4 = 384.3496{{c}}
{{Optimal ET sequence|legend=0| 12f, 19e, 31, 53e, 60eff, 72, 103, 175f }}
Badness (Sintel): 0.831
=== Protannic ===
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 441/440, 1001/1000
Mapping: {{mapping| 1 0 0 -5 -13 21 | 0 1 0 2 6 -8 | 0 0 1 2 3 -2 }}
Optimal tunings:
* WE: ~2 = 1200.9450{{c}}, ~3/2 = 700.1045{{c}}, ~5/4 = 383.8716{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 699.4224{{c}}, ~5/4 = 383.9828{{c}}
{{Optimal ET sequence|legend=0| 29, 31, 43, 60e, 72, 103, 175f, 482bccddeefff, 554bbccddeeeffff }}
Badness (Sintel): 0.891
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
Comma list: 225/224, 273/272, 375/374, 441/440
Mapping: {{mapping| 1 0 0 -5 -13 21 12 | 0 1 0 2 6 -8 -5 | 0 0 1 2 3 -2 0 }}
Optimal tunings:
* WE: ~2 = 1200.9342{{c}}, ~3/2 = 700.1708{{c}}, ~5/4 = 383.7444{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 699.4849{{c}}, ~5/4 = 383.8744{{c}}
{{Optimal ET sequence|legend=0| 29g, 31, 43, 60e, 72, 103, 175f, 307bcdeeffg, 379bccdeeffgg, 482bccddeefffgg, 554bbccddeeeffffgg }}
Badness (Sintel): 0.734


== Minerva ==
== Minerva ==
Line 517: Line 634:


Scales: [[malco]]
Scales: [[malco]]
== Prodigy ==
Prodigy shrinks 1024/1029, 243/242, 384/385 and 2400/2401 down to the same tiny interval. Hence in practice it probably makes the most sense to temper this out as well, leading to [[miracle]]. This, however, does not render it pointless to consider prodigy; for one thing, scales in prodigy such as hobbit scales translate into interesting scales for miracle.
[[Subgroup]]: 2.3.5.7.11
[[Comma list]]: 225/224, 441/440
{{Mapping|legend=1| 1 0 0 -5 -13 | 0 1 0 2 6 | 0 0 1 2 3 }}
Map to lattice: [{{val| 0 0 -1 -2 -3 }}, {{val| 0 1 -1 0 3 }}]
Lattice basis:
: ~15/14 length = 0.9111, ~3/2 length = 0.9477
: angle (~15/14, ~3/2) = 65.933°
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.7854{{c}}, ~3/2 = 700.2562{{c}}, ~5/4 = 383.7624{{c}}
: [[error map]]: {{val| +0.785 -0.913 -0.980 -0.003 +0.721 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 699.8610{{c}}, ~5/4 = 383.7724{{c}}
: error map: {{val| 0.000 -2.094 -2.541 -1.559 -0.835 }}
[[Minimax tuning]]:
* [[11-odd-limit]]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 13/12 1/2 -1/4 0 1/12 }}, {{monzo| 13/6 -1 1/2 0 1/6 }}, {{monzo| 3/2 -1 1/2 0 1/2 }}, {{monzo| 0 0 0 0 1 }}]
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.9/5.11
{{Optimal ET sequence|legend=1| 10, 12, 19e, 29, 31, 41, 60e, 72, 247c, 319bcde, 391bcde, 463bccde }}
[[Badness]] (Sintel): 0.402
[[Projection pair]]s: <code>7 225/32 11 91125/8192</code>
Scales: [[prodigy11]], [[prodigy12]], [[prodigy29]]
[[Associated temperament]]: [[miracle]]
{{Databox|Hobbit bases|
2.3.5 subgroup
* 31: 81/80, 34171875/33554432
* 41: 34171875/33554432, 32805/32768
}}
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 196/195, 352/351
Mapping: {{mapping| 1 0 0 -5 -13 -8 | 0 1 0 2 6 3 | 0 0 1 2 3 3 }}
Optimal tunings:
* WE: ~2 = 1200.8252{{c}}, ~3/2 = 700.8823{{c}}, ~5/4 = 381.6647{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.4689{{c}}, ~5/4 = 381.6687{{c}}
{{Optimal ET sequence|legend=0| 10, 12f, 19e, 29, 31, 41, 60e, 72f, 101cd }}
Badness (Sintel): 0.689
=== Prodigious ===
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 364/363, 441/440
Mapping: {{mapping| 1 0 0 -5 -13 -23 | 0 1 0 2 6 11 | 0 0 1 2 3 4 }}
Optimal tunings:
* WE: ~2 = 1200.6284{{c}}, ~3/2 = 700.7075{{c}}, ~5/4 = 383.4599{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.3302{{c}}, ~5/4 = 383.5030{{c}}
{{Optimal ET sequence|legend=0| 12f, 29, 31f, 41, 72, 185cf, 257cff }}
Badness (Sintel): 0.841
=== Prodigal ===
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 351/350, 441/440
Mapping: {{mapping| 1 0 0 -5 -13 -4 | 0 1 0 2 6 -1 | 0 0 1 2 3 4 }}
Optimal tunings:
* WE: ~2 = 1200.7798{{c}}, ~3/2 = 699.9410{{c}}, ~5/4 = 384.3494{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 699.5538{{c}}, ~5/4 = 384.3496{{c}}
{{Optimal ET sequence|legend=0| 12f, 19e, 31, 53e, 60eff, 72, 103, 175f }}
Badness (Sintel): 0.831
=== Protannic ===
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 441/440, 1001/1000
Mapping: {{mapping| 1 0 0 -5 -13 21 | 0 1 0 2 6 -8 | 0 0 1 2 3 -2 }}
Optimal tunings:
* WE: ~2 = 1200.9450{{c}}, ~3/2 = 700.1045{{c}}, ~5/4 = 383.8716{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 699.4224{{c}}, ~5/4 = 383.9828{{c}}
{{Optimal ET sequence|legend=0| 29, 31, 43, 60e, 72, 103, 175f, 482bccddeefff, 554bbccddeeeffff }}
Badness (Sintel): 0.891
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
Comma list: 225/224, 273/272, 375/374, 441/440
Mapping: {{mapping| 1 0 0 -5 -13 21 12 | 0 1 0 2 6 -8 -5 | 0 0 1 2 3 -2 0 }}
Optimal tunings:
* WE: ~2 = 1200.9342{{c}}, ~3/2 = 700.1708{{c}}, ~5/4 = 383.7444{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 699.4849{{c}}, ~5/4 = 383.8744{{c}}
{{Optimal ET sequence|legend=0| 29g, 31, 43, 60e, 72, 103, 175f, 307bcdeeffg, 379bccdeeffgg, 482bccddeefffgg, 554bbccddeeeffffgg }}
Badness (Sintel): 0.734


== Fantastic ==
== Fantastic ==
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