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Breed family: Difference between revisions

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Line 9: Line 9:
{{Mapping|legend=1| 1 1 1 2 | 0 2 1 1 | 0 0 2 1 }}
{{Mapping|legend=1| 1 1 1 2 | 0 2 1 1 | 0 0 2 1 }}


: mapping generators: ~2, ~49/40, ~10/7
: Mapping generators: ~2, ~49/40, ~10/7


[[Mapping to lattice]]: [{{val| 0 2 -1 0 }}, {{val| 0 0 -2 -1 }}]
[[Mapping to lattice]]: [{{val| 0 2 -1 0 }}, {{val| 0 0 -2 -1 }}]
Line 20: Line 20:
* [[7-odd-limit|7-]] and [[9-odd-limit]] [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.5
* [[7-odd-limit|7-]] and [[9-odd-limit]] [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.5


[[Optimal tuning]] (POTE): ~2 = 1\1, ~49/40 = 350.9664, ~10/7 = 617.6720
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.021¢, ~49/40 = 350.972¢, ~10/7 = 617.683¢
* [[CWE]]: ~2 = 1200.000¢, ~49/40 = 350.974¢, ~10/7 = 617.681¢


{{Optimal ET sequence|legend=1| 27, 31, 41, 58, 68, 72, 99, 171, 441, 612, 1966, 2308, 2578, 2749, 3361d }}
{{Optimal ET sequence|legend=1| 27, 31, 41, 58, 68, 72, 99, 171, 441, 612, 1966, 2308, 2578, 2749, 3361d }}


[[Badness]]: 0.0153 × 10<sup>-3</sup>
[[Badness]] (Sintel): 0.067


[[Projection pair]]: 3 = ~2401/800 to 2.5.7
[[Projection pair]]: ~3 = ~2401/800 to 2.5.7


Scales: [[breed11]]
Scales: [[breed11]]
Line 47: Line 49:
* [[11-odd-limit]] [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5.11
* [[11-odd-limit]] [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5.11


[[Optimal tuning]] (POTE): ~2 = 1\1, ~11/9 = 350.5034, ~10/7 = 617.8275
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.098¢, ~11/9 = 350.532¢, ~10/7 = 617.878¢
* [[CWE]]: ~2 = 1200.000¢, ~11/9 = 350.537¢, ~10/7 = 617.871¢


{{Optimal ET sequence|legend=1| 27e, 31, 41, 58, 72, 130, 202 }}
{{Optimal ET sequence|legend=1| 27e, 31, 41, 58, 72, 130, 202 }}


[[Badness]]: 0.241 × 10<sup>-3</sup>
[[Badness]] (Sintel): 0.290


Projection pairs: ~3 = ~242/81, ~5 = ~2200/441, ~7 = ~440/63, ~11 = ~644204/59049 to 2.7/5.11/9
Projection pairs: ~3 = ~242/81, ~5 = ~2200/441, ~7 = ~440/63, ~11 = ~644204/59049 to 2.7/5.11/9
Line 66: Line 70:
* 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.7/5.15/13
* 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.7/5.15/13


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.7179, ~10/7 = 617.8286
Optimal tunings:
* WE: ~2 = 1199.977¢, ~11/9 = 350.711¢, ~10/7 = 617.817¢
* CWE: ~2 = 1200.000¢, ~11/9 = 350.713¢, ~10/7 = 617.818¢


Optimal ET sequence: {{Optimal ET sequence| 27eff, 31f, 41, 58, 72, 130, 243, 301e, 373e }}
Optimal ET sequence: {{Optimal ET sequence| 27eff, 31f, 41, 58, 72, 130, 243, 301e, 373e }}


Badness: 0.624 × 10<sup>-3</sup>
Badness (Sintel): 0.583


==== 17-limit ====
==== 17-limit ====
Line 82: Line 88:
* 17-odd-limit unchanged-interval (eigenmonzo) basis: 2.5/3.17/9
* 17-odd-limit unchanged-interval (eigenmonzo) basis: 2.5/3.17/9


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.6947, ~10/7 = 617.5315
Optimal tunings:
* WE: ~2 = 1200.088¢, ~11/9 = 350.720¢, ~10/7 = 617.577¢
* CWE: ~2 = 1200.000¢, ~11/9 = 350.714¢, ~10/7 = 617.561¢


Optimal ET sequence: {{Optimal ET sequence| 27effg, 31fg, 41, 58, 72, 130, 171, 243 }}
Optimal ET sequence: {{Optimal ET sequence| 27effg, 31fg, 41, 58, 72, 130, 171, 243 }}


Badness: 0.741 × 10<sup>-3</sup>
Badness (Sintel): 0.704


==== Heartlandia ====
==== Heartlandia ====
Line 95: Line 103:
Mapping: {{mapping| 1 1 1 2 2 1 3 | 0 4 0 1 10 23 12 | 0 0 2 1 0 -1 -1 }}
Mapping: {{mapping| 1 1 1 2 2 1 3 | 0 4 0 1 10 23 12 | 0 0 2 1 0 -1 -1 }}


: mapping generators: ~2, ~119/108, ~27/17
: Mapping generators: ~2, ~119/108, ~27/17


Optimal tuning (POTE): ~2 = 1\1, ~119/108 = 175.4177, ~27/17 = 793.9762
Optimal tunings:
* WE: ~2 = 1199.559¢, ~119/108 = 175.353¢, ~27/17 = 793.685¢
* CWE: ~2 = 1200.000¢, ~119/108 = 175.371¢, ~27/17 = 793.756¢


Optimal ET sequence: {{Optimal ET sequence| 14cf, 27effg, 41, 89, 130g }}
Optimal ET sequence: {{Optimal ET sequence| 14cf, 27effg, 41, 89, 130g }}
Badness (Sintel): 2.843


===== 19-limit =====
===== 19-limit =====
Line 108: Line 120:
Mapping: {{mapping| 1 1 1 2 2 1 3 3 | 0 4 0 1 10 23 12 4 | 0 0 2 1 0 -1 -1 1 }}
Mapping: {{mapping| 1 1 1 2 2 1 3 3 | 0 4 0 1 10 23 12 4 | 0 0 2 1 0 -1 -1 1 }}


Optimal tuning (POTE): ~2 = 1\1, ~21/19 = 175.3862, ~19/12 = 793.9558
Optimal tunings:
* WE: ~2 = 1199.733¢, ~21/19 = 175.347¢, ~19/12 = 793.779¢
* CWE: ~2 = 1200.000¢, ~21/19 = 175.358¢, ~19/12 = 793.819¢


Optimal ET sequence: {{Optimal ET sequence| 14cf, 27effg, 41, 89, 130g }}
Optimal ET sequence: {{Optimal ET sequence| 14cf, 27effg, 41, 89, 130g }}
Badness (Sintel): 2.294


=== Jofur ===
=== Jofur ===
Line 119: Line 135:
Mapping: {{mapping| 1 1 1 2 2 4 | 0 2 1 1 5 -1 | 0 0 2 1 0 0 }}
Mapping: {{mapping| 1 1 1 2 2 4 | 0 2 1 1 5 -1 | 0 0 2 1 0 0 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 351.4477, ~10/7 = 618.8891
Optimal tunings:
* WE: ~2 = 1198.953¢, ~11/9 = 351.141¢, ~10/7 = 618.349¢
* CWE: ~2 = 1200.000¢, ~11/9 = 351.254¢, ~10/7 = 618.593¢


Optimal ET sequence: {{Optimal ET sequence| 27e, 31, 41, 58, 99ef, 157eff }}
Optimal ET sequence: {{Optimal ET sequence| 27e, 31, 41, 58, 99ef, 157eff }}


Badness: 0.749 × 10<sup>-3</sup>
Badness (Sintel): 0.701


=== Jovis ===
=== Jovis ===
Line 132: Line 150:
Mapping: {{mapping| 1 1 1 2 2 2 | 0 2 1 1 5 -3 | 0 0 2 1 0 5 }}
Mapping: {{mapping| 1 1 1 2 2 2 | 0 2 1 1 5 -3 | 0 0 2 1 0 5 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 350.3935, ~10/7 = 618.1036
Optimal tunings:
* WE: ~2 = 1200.144¢, ~11/9 = 350.435¢, ~10/7 = 618.177¢
* CWE: ~2 = 1200.000¢, ~11/9 = 350.440¢, ~10/7 = 618.176¢


Optimal ET sequence: {{Optimal ET sequence| 27e, 31, 45ef, 58, 72, 103, 130, 233, 363 }}
Optimal ET sequence: {{Optimal ET sequence| 27e, 31, 45ef, 58, 72, 103, 130, 233, 363 }}


Badness: 0.542 × 10<sup>-3</sup>
Badness (Sintel): 0.507


== Agni ==
== Agni ==
Line 156: Line 176:
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.11/5
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.11/5


[[Optimal tuning]] (POTE): ~2 = 1\1, ~49/40 = 350.7145, ~10/7 = 617.0044
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.417¢, ~49/40 = 350.836¢, ~10/7 = 617.219¢
* [[CWE]]: ~2 = 1200.000¢, ~49/40 = 350.837¢, ~10/7 = 616.991¢


{{Optimal ET sequence|legend=1| 27, 31, 41, 68, 72, 140, 171e, 212, 284, 496ce, 527cee, 739cdeee, 811ccdeee, 1023ccdeee }}
{{Optimal ET sequence|legend=1| 27, 31, 41, 68, 72, 140, 171e, 212, 284, 496ce, 527cee, 739cdeee, 811ccdeee, 1023ccdeee }}


[[Badness]]: 0.494 × 10<sup>-3</sup>
[[Badness]] (Sintel): 0.593


=== 13-limit ===
=== 13-limit ===
Line 169: Line 191:
Mapping: {{mapping| 1 1 1 2 5 -1 | 0 2 1 1 0 2 | 0 0 2 1 -3 8 }}
Mapping: {{mapping| 1 1 1 2 5 -1 | 0 2 1 1 0 2 | 0 0 2 1 -3 8 }}


Optimal tuning (POTE): ~2 = 1\1, ~49/40 = 350.6803, ~10/7 = 617.1448
Optimal tunings:
* WE: ~2 = 1200.441¢, ~49/40 = 350.809¢, ~10/7 = 617.372¢
* CWE: ~2 = 1200.000¢, ~49/40 = 350.805¢, ~10/7 = 617.157¢


Optimal ET sequence: {{Optimal ET sequence| 31, 68, 72, 103, 140, 212, 243e, 315ef, 455eef, 770cdeeeff }}
Optimal ET sequence: {{Optimal ET sequence| 31, 68, 72, 103, 140, 212, 243e, 315ef, 455eef, 770cdeeeff }}


Badness: 0.923 × 10<sup>-3</sup>
Badness (Sintel): 0.863


== Zisa ==
== Zisa ==
Line 243: Line 267:
{{Mapping|legend=1| 2 0 1 3 7 | 0 2 1 1 -2 | 0 0 2 1 3 }}
{{Mapping|legend=1| 2 0 1 3 7 | 0 2 1 1 -2 | 0 0 2 1 3 }}


: mapping generators: ~99/70, ~343/198, ~10/7
: Mapping generators: ~99/70, ~343/198, ~10/7


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 249: Line 273:
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 3/4 0 1/2 1/2 -1/2 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 23/16 0 5/8 1/8 -1/8 }}, {{monzo| 23/16 0 5/8 -7/8 7/8 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 3/4 0 1/2 1/2 -1/2 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 23/16 0 5/8 1/8 -1/8 }}, {{monzo| 23/16 0 5/8 -7/8 7/8 }}]
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.11/7
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.11/7
[[Optimal tuning]]s:
* [[WE]]: ~99/70 = 600.015¢, ~343/198 = 950.972¢, ~10/7 = 617.701¢
* [[CWE]]: ~99/70 = 600.000¢, ~343/198 = 950.956¢, ~10/7 = 617.702¢


{{Optimal ET sequence|legend=1| 58, 72, 130, 198, 212, 270, 342, 612, 954, 1084, 1354, 1696, 4004de, 5700de }}
{{Optimal ET sequence|legend=1| 58, 72, 130, 198, 212, 270, 342, 612, 954, 1084, 1354, 1696, 4004de, 5700de }}


[[Badness]]: 0.166 × 10<sup>-3</sup>
[[Badness]] (Sintel): 0.200


[[Projection pair]]s: 2 9801/4900 3 117649/39204 7 9801/1400 11  913517247483640899/83082326424002500 to 5.7/2.99/4
[[Projection pair]]s: ~2 = ~9801/4900, ~3 = ~117649/39204, ~7 = ~9801/1400, ~11 = ~913517247483640899/83082326424002500 to 5.7/2.99/4


=== Greenland ===
=== Greenland ===
Line 262: Line 290:


Mapping: {{mapping| 2 0 1 3 7 -1 | 0 2 1 1 -2 4 | 0 0 2 1 3 2 }}
Mapping: {{mapping| 2 0 1 3 7 -1 | 0 2 1 1 -2 4 | 0 0 2 1 3 2 }}
Optimal tunings:
* WE: ~99/70 = 599.987¢, ~26/15 = 951.054¢, ~10/7 = 617.806¢
* CWE: ~99/70 = 600.000¢, ~26/15 = 951.069¢, ~10/7 = 617.807¢


{{Optimal ET sequence|legend=1| 58, 72, 130, 198, 270, 940, 1210f }}
{{Optimal ET sequence|legend=1| 58, 72, 130, 198, 270, 940, 1210f }}


Badness: 0.433 × 10<sup>-3</sup>
Badness (Sintel): 0.415


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


Projection pairs: 2 19600/9801 3 676/225 5 10400/2079 7 20384000/2910897 11 19208000000000000/1750211597736459 13 5026736/385875 to 10/7.200/99.26/15
Projection pairs: ~2 = ~19600/9801, ~3 = ~676/225, ~5 = ~10400/2079, ~7 = ~20384000/2910897, ~11 = ~19208000000000000/1750211597736459, ~13 = ~5026736/385875 to 10/7.200/99.26/15
 
==== Midnatssol ====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 289/288, 442/441, 561/560, 676/675
 
Mapping: {{mapping| 2 0 1 3 7 -1 5 | 0 2 1 1 -2 4 2 | 0 0 2 1 3 2 0 }}
 
Optimal tunings:
* WE: ~17/12 = 600.112¢, ~26/15 = 951.191¢, ~10/7 = 617.610¢
* CWE: ~17/12 = 600.000¢, ~26/15 = 951.063¢, ~10/7 = 617.584¢
 
{{Optimal ET sequence|legend=1| 58, 72, 130, 140, 198, 270g }}
 
Badness (Sintel): 0.720


== Freya ==
== Freya ==
Line 278: Line 325:
{{Mapping|legend=1| 1 1 3 3 2 | 0 2 3 2 1 | 0 0 -4 -2 3 }}
{{Mapping|legend=1| 1 1 3 3 2 | 0 2 3 2 1 | 0 0 -4 -2 3 }}


: mapping generators: ~2, ~49/40, ~55/42
: Mapping generators: ~2, ~49/40, ~55/42


[[Minimax tuning]]:
[[Minimax tuning]]:
Line 361: Line 408:
Mapping: {{mapping| 1 1 3 3 2 7 7 | 0 2 3 2 1 6 6 | 0 0 -4 -2 3 -13 -12 }}
Mapping: {{mapping| 1 1 3 3 2 7 7 | 0 2 3 2 1 6 6 | 0 0 -4 -2 3 -13 -12 }}


: mapping generators: ~2, ~49/40, ~17/13
: Mapping generators: ~2, ~49/40, ~17/13


{{Optimal ET sequence|legend=1| 8bcefg, 15bbccdeeffggg, 23bcfg, 31, 64be, 72, 103, 167, 198g, 239, 270 }}
{{Optimal ET sequence|legend=1| 8bcefg, 15bbccdeeffggg, 23bcfg, 31, 64be, 72, 103, 167, 198g, 239, 270 }}
Line 421: Line 468:
{{Mapping|legend=1| 9 1 1 12 0 | 0 2 3 2 0 | 0 0 0 0 1 }}
{{Mapping|legend=1| 9 1 1 12 0 | 0 2 3 2 0 | 0 0 0 0 1 }}


: mapping generators: ~27/25, ~5/3, ~11
: Mapping generators: ~27/25, ~5/3, ~11


{{Optimal ET sequence|legend=1| 27, 45, 72, 171, 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 6561dd }}
{{Optimal ET sequence|legend=1| 27, 45, 72, 171, 198, 270, 342, 612, 954, 1323, 1395, 1665, 2007, 2277, 2619, 4284d, 6561dd }}
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