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Ragismic microtemperaments: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings (3/)
Switch to Sintel's badness, WE & CWE tunings (4/)
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[[Comma list]]: 4375/4374, 589824/588245
[[Comma list]]: 4375/4374, 589824/588245


{{Mapping|legend=1| 1 6 10 3 | 0 -23 -40 -1 }}
{{Mapping|legend=1| 1 -17 -30 2 | 0 23 40 1 }}
: mapping generators: ~2, ~8/7
: mapping generators: ~2, ~7/4


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~8/7 = 230.336{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.8483{{c}}, ~7/4 = 969.5415{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 969.6608{{c}}


{{Optimal ET sequence|legend=1| 26, 73, 99, 224, 323, 422, 745d }}
{{Optimal ET sequence|legend=1| 26, 73, 99, 224, 323, 422, 745d }}
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Comma list: 3025/3024, 4375/4374, 589824/588245
Comma list: 3025/3024, 4375/4374, 589824/588245


Mapping: {{mapping| 2 12 20 6 5 | 0 -23 -40 -1 5 }}
Mapping: {{mapping| 2 -11 -20 5 10 | 0 23 40 1 -5 }}
: mapping generators: ~99/70, ~8/7
: mapping generators: ~99/70, ~99/80


Optimal tuning (POTE): ~99/70 = 600.0000{{c}}, ~8/7 = 230.3370{{c}}
Optimal tunings:
* CWE: ~99/70 = 599.9323{{c}}, ~99/80 = 369.6212{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~99/80 = 369.6610{{c}}


{{Optimal ET sequence|legend=0| 26, 198, 224, 422, 646, 1068d }}
{{Optimal ET sequence|legend=0| 26, 172c, 198, 224, 422, 646, 1068d }}


Badness (Sintel): 1.354
Badness (Sintel): 1.35


==== 13-limit ====
==== 13-limit ====
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Comma list: 1716/1715, 2080/2079, 2200/2197, 3025/3024
Comma list: 1716/1715, 2080/2079, 2200/2197, 3025/3024


Mapping: {{mapping| 2 12 20 6 5 17 | 0 -23 -40 -1 5 -25 }}
Mapping: {{mapping| 2 -11 -20 5 10 -8 | 0 23 40 1 -5 25 }}


Optimal tuning (POTE): ~99/70 = 600.0000{{c}}, ~8/7 = 230.3373{{c}}
Optimal tunings:
* WE: ~99/70 = 599.9207{{c}}, ~26/21 = 369.6139{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~26/21 = 369.6603{{c}}


{{Optimal ET sequence|legend=0| 26, 198, 224, 422, 646f, 1068df }}
{{Optimal ET sequence|legend=0| 26, 172cf, 198, 224, 422, 646f, 1068df }}


Badness (Sintel): 0.844
Badness (Sintel): 0.844
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Comma list: 4375/4374, 14641/14580, 15488/15435
Comma list: 4375/4374, 14641/14580, 15488/15435


Mapping: {{mapping| 1 6 10 3 12 | 0 -46 -80 -2 -89 }}
Mapping: {{mapping| 1 -40 -70 1 -77 | 0 46 80 2 89 }}
: mapping generators: ~2, ~77/72
: mapping generators: ~2, ~144/77


Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~77/72 = 115.1642{{c}}
Optimal tunings:
* WE: ~2 = 1199.8845{{c}}, ~144/77 = 1084.7314{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~144/77 = 1084.8345{{c}}


{{Optimal ET sequence|legend=1| 73, 125, 198, 323, 521 }}
{{Optimal ET sequence|legend=0| 73, 125, 198, 323, 521 }}


Badness (Sintel): 2.589
Badness (Sintel): 2.59


==== 13-limit ====
==== 13-limit ====
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Comma list: 676/675, 1001/1000, 4375/4374, 14641/14580
Comma list: 676/675, 1001/1000, 4375/4374, 14641/14580


Mapping: {{mapping| 1 6 10 3 12 18 | 0 -46 -80 -2 -89 -149 }}
Mapping: {{mapping| 1 -40 -70 1 -77 -131 | 0 46 80 2 89 149 }}


Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~77/72 = 115.1628{{c}}
Optimal tunings:
* WE: ~2 = 1199.8726{{c}}, ~144/77 = 1084.7220{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~144/77 = 1084.8359{{c}}


{{Optimal ET sequence|legend=0| 73f, 125f, 198, 323, 521 }}
{{Optimal ET sequence|legend=0| 73f, 125f, 198, 323, 521 }}


Badness (Sintel): 1.821
Badness (Sintel): 1.82


== Crazy ==
== Crazy ==
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~332150625/234881024 = 600.0000{{c}}, ~1125/1024 = 162.7475{{c}}
* [[WE]]: ~332150625/234881024 = 600.0019{{c}}, ~1125/1024 = 162.7479{{c}}
* [[error map]]: {{val| 0.0000 +0.0253 -0.0514 -0.0133 }}
* [[error map]]: {{val| +0.004 +0.030 -0.042 -0.014 }}
* [[CWE]]: ~332150625/234881024 = 600.0000{{c}}, ~1125/1024 = 162.7474{{c}}
* [[CWE]]: ~332150625/234881024 = 600.0000{{c}}, ~1125/1024 = 162.7474{{c}}
* error map: {{val| 0.0000 +0.0244 -0.0508 -0.0218 }}
* error map: {{val| 0.000 +0.024 -0.051 -0.022 }}


{{Optimal ET sequence|legend=1| 118, 376, 494, 612, 1106, 1718 }}
{{Optimal ET sequence|legend=1| 118, 376, 494, 612, 1106, 1718 }}
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Optimal tunings:
Optimal tunings:
* CTE: ~99/70 = 162.7485{{c}}, ~1125/1024 = 162.7485{{c}}
* WE: ~99/70 = 600.0047{{c}}, ~1125/1024 = 162.7493{{c}}
* CWE: ~99/70 = 162.7485{{c}}, ~1125/1024 = 162.7481{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~1125/1024 = 162.7481{{c}}


{{Optimal ET sequence|legend=0| 118, 376, 494, 612, 1106, 2824, 3930e }}
{{Optimal ET sequence|legend=0| 118, 376, 494, 612, 1106, 2824, 3930e }}
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[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 4375/4374, 54975581388800/54936068900769
[[Comma list]]: 4375/4374, {{monzo| 41 -4 2 -14 }}


{{Mapping|legend=1| 2 21 36 5 | 0 -29 -51 1 }}
{{Mapping|legend=1| 2 -8 -15 6 | 0 29 51 -1 }}
: Mapping generators: ~7411887/5242880, ~1310720/1058841
: mapping generators: ~7411887/5242880, ~8/7


[[Optimal tuning]] ([[POTE]]): ~7411887/5242880 = 600.000{{c}}, ~8/7 = 231.104{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~7411887/5242880 = 599.9927{{c}}, ~8/7 = 231.1012{{c}}
* [[CWE]]: ~7411887/5242880 = 600.0000{{c}}, ~8/7 = 231.1037{{c}}


{{Optimal ET sequence|legend=1| 26, 244, 270, 836, 1106, 1376, 2482 }}
{{Optimal ET sequence|legend=1| 26, …, 244, 270, 836, 1106, 1376, 2482 }}


[[Badness]] (Sintel): 1.018
[[Badness]] (Sintel): 1.02


=== 11-limit ===
=== 11-limit ===
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Comma list: 3025/3024, 4375/4374, 5767168/5764801
Comma list: 3025/3024, 4375/4374, 5767168/5764801


Mapping: {{mapping| 2 21 36 5 2 | 0 -29 -51 1 8 }}
Mapping: {{mapping| 2 -8 -15 6 10 | 0 29 51 -1 -8 }}


Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~8/7 = 231.103{{c}}
Optimal tunings:
* WE: ~99/70 = 600.0025{{c}}, ~8/7 = 231.1039{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~8/7 = 231.1030{{c}}


{{Optimal ET sequence|legend=0| 26, 244, 270, 566, 836, 1106 }}
{{Optimal ET sequence|legend=0| 26, 244, 270, 566, 836, 1106 }}
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Comma list: 1716/1715, 2080/2079, 3025/3024, 15379/15360
Comma list: 1716/1715, 2080/2079, 3025/3024, 15379/15360


Mapping: {{mapping| 2 21 36 5 2 24 | 0 -29 -51 1 8 -27 }}
Mapping: {{mapping| 2 -8 -15 6 10 -3 | 0 29 51 -1 -8 27 }}


Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~8/7 = 231.103{{c}}
Optimal tunings:
* WE: ~99/70 = 600.0192{{c}}, ~8/7 = 231.1102{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~8/7 = 231.1033{{c}}


{{Optimal ET sequence|legend=0| 26, 244, 270, 566, 836f, 1106f }}
{{Optimal ET sequence|legend=0| 26, 244, 270, 566, 836f, 1106f }}
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