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Diaschismic family: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings, per community consensus (1/)
Switch to Sintel's badness, WE & CWE tunings, per community consensus (2/2)
Line 783: Line 783:
: mapping generators: ~25/21, ~3
: mapping generators: ~25/21, ~3


[[Optimal tuning]] ([[POTE]]): ~25/21 = 300.000{{c}}, ~3/2 = 705.364{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~25/21 = 299.6887{{c}}, ~3/2 = 704.6318{{c}}
: [[error map]]: {{val| -1.245 +1.432 +0.064 +0.854 }}
* [[CWE]]: ~25/21 = 300.0000{{c}}, ~3/2 = 705.5070{{c}}
: error map: {{val| 0.000 +3.552 +2.672 +3.639 }}
<!-- * [[POTE]]: ~25/21 = 300.000{{c}}, ~3/2 = 705.364{{c}} -->


{{Optimal ET sequence|legend=1| 12, 56, 68, 80, 148d }}
{{Optimal ET sequence|legend=1| 12, …, 56, 68, 80, 148d }}


[[Badness]] (Smith): 0.056474
[[Badness]] (Sintel): 1.43


=== 11-limit ===
=== 11-limit ===
Line 796: Line 801:
Mapping: {{mapping| 4 0 22 43 71 | 0 1 -2 -5 -9 }}
Mapping: {{mapping| 4 0 22 43 71 | 0 1 -2 -5 -9 }}


Optimal tuning (POTE): ~25/21 = 300.000{{c}}, ~3/2 = 705.087{{c}}
Optimal tunings:
* WE: ~25/21 = 299.6809{{c}}, ~3/2 = 704.3367{{c}}
* CWE: ~25/21 = 600.0000{{c}}, ~3/2 = 705.2170{{c}}
<!-- * POTE: ~25/21 = 300.000{{c}}, ~3/2 = 705.087{{c}} -->


{{Optimal ET sequence|legend=0| 12, 68, 80 }}
{{Optimal ET sequence|legend=0| 12, 56e, 68, 80 }}


Badness (Smith): 0.040191
Badness (Sintel): 1.33


=== 13-limit ===
=== 13-limit ===
Line 809: Line 817:
Mapping: {{mapping| 4 0 22 43 71 -36 | 0 1 -2 -5 -9 8 }}
Mapping: {{mapping| 4 0 22 43 71 -36 | 0 1 -2 -5 -9 8 }}


Optimal tuning (POTE): ~25/21 = 300.000{{c}}, ~3/2 = 705.301{{c}}
Optimal tunings:
* WE: ~25/21 = 299.7538{{c}}, ~3/2 = 704.7222{{c}}
* CWE: ~25/21 = 600.0000{{c}}, ~3/2 = 705.3241{{c}}
<!-- * POTE: ~25/21 = 300.000{{c}}, ~3/2 = 705.301{{c}} -->


{{Optimal ET sequence|legend=0| 12, 68, 80, 148d, 228bcd, 376bbcddf }}
{{Optimal ET sequence|legend=0| 12, 68, 80, 148d, 228bcd, 376bbcddf }}


Badness (Smith): 0.041137
Badness (Sintel): 1.70


=== 17-limit ===
=== 17-limit ===
Line 822: Line 833:
Mapping: {{mapping| 4 0 22 43 71 -36 10 | 0 1 -2 -5 -9 8 1 }}
Mapping: {{mapping| 4 0 22 43 71 -36 10 | 0 1 -2 -5 -9 8 1 }}


Optimal tuning (POTE): ~25/21 = 300.000{{c}}, ~3/2 = 705.334{{c}}
Optimal tunings:
* WE: ~25/21 = 299.7883{{c}}, ~3/2 = 704.8365{{c}}
* CWE: ~25/21 = 600.0000{{c}}, ~3/2 = 705.3496{{c}}
<!-- * POTE: ~25/21 = 300.000{{c}}, ~3/2 = 705.334{{c}} -->


{{Optimal ET sequence|legend=0| 12, 68, 80, 148d, 228bcd, 376bbcddf }}
{{Optimal ET sequence|legend=0| 12, 68, 80, 148d }}


Badness (Smith): 0.028631
Badness (Sintel): 1.46


=== 19-limit ===
=== 19-limit ===
Line 835: Line 849:
Mapping: {{mapping| 4 0 22 43 71 -36 10 17 | 0 1 -2 -5 -9 8 1 0 }}
Mapping: {{mapping| 4 0 22 43 71 -36 10 17 | 0 1 -2 -5 -9 8 1 0 }}


Optimal tuning (POTE): ~19/16 = 300.000{{c}}, ~3/2 = 705.339{{c}}
Optimal tunings:
* WE: ~19/16 = 299.7967{{c}}, ~3/2 = 704.8609{{c}}
* CWE: ~19/16 = 600.0000{{c}}, ~3/2 = 705.3519{{c}}
<!-- * POTE: ~19/16 = 300.000{{c}}, ~3/2 = 705.339{{c}} -->


{{Optimal ET sequence|legend=0| 12, 68, 80, 148d, 376bbcddfh }}
{{Optimal ET sequence|legend=0| 12, 68, 80, 148d }}


Badness (Smith): 0.020590
Badness (Sintel): 1.25


=== 23-limit ===
=== 23-limit ===
Line 849: Line 866:


Optimal tunings:
Optimal tunings:
* [[TE]]: ~19/16 = 299.797{{c}}, ~3/2 = 704.860{{c}}
* WE: ~19/16 = 299.7961{{c}}, ~3/2 = 704.8577{{c}}
* [[CWE]]: ~19/16 = 300.000{{c}}, ~3/2 = 705.341{{c}}
* CWE: ~19/16 = 300.0000{{c}}, ~3/2 = 705.3413{{c}}
* [[POTE]]: ~19/16 = 300.000{{c}}, ~3/2 = 705.337{{c}}
<!-- * POTE: ~19/16 = 300.000{{c}}, ~3/2 = 705.337{{c}} -->


{{Optimal ET sequence|legend=0| 12, 68, 80, 148di }}
{{Optimal ET sequence|legend=0| 12, 68, 80, 148di }}


Badness (Smith): 0.017301
Badness (Sintel): 1.24


== Echidna ==
== Echidna ==
Line 874: Line 891:
: mapping generators: ~45/32, ~9/7
: mapping generators: ~45/32, ~9/7


[[Optimal tuning]] ([[POTE]]): ~45/32 = 600.000{{c}}, ~9/7 = 434.856{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~45/32 = 599.3056{{c}}, ~9/7 = 434.3524{{c}}
: [[error map]]: {{val| -1.389 +0.408 +1.322 +1.547 }}
* [[CWE]]: ~45/32 = 600.0000{{c}}, ~9/7 = 434.8327{{c}}
: error map: {{val| 0.000 +2.543 +4.690 +5.338 }}
<!-- * [[POTE]]: ~45/32 = 600.000{{c}}, ~9/7 = 434.856{{c}} -->


{{Optimal ET sequence|legend=1| 22, 58, 80, 138cd, 218cd }}
{{Optimal ET sequence|legend=1| 22, 58, 80, 138cd, 218cd }}


[[Badness]] (Smith): 0.058033
[[Badness]] (Sintel): 1.47


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


Line 888: Line 909:
Mapping: {{mapping| 2 1 9 2 12 | 0 3 -6 5 -7 }}
Mapping: {{mapping| 2 1 9 2 12 | 0 3 -6 5 -7 }}


Optimal tuning (POTE): ~45/32 = 600.000{{c}}, ~9/7 = 434.852{{c}}
Optimal tunings:
* WE: ~45/32 = 599.3085{{c}}, ~9/7 = 434.3511{{c}}
* CWE: ~45/32 = 600.0000{{c}}, ~9/7 = 434.8647{{c}}
<!-- * POTE: ~45/32 = 600.000{{c}}, ~9/7 = 434.852{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 897: Line 921:
{{Optimal ET sequence|legend=0| 22, 58, 80, 138cde, 218cde }}
{{Optimal ET sequence|legend=0| 22, 58, 80, 138cde, 218cde }}


Badness (Smith): 0.025987
Badness (Sintel): 0.859


=== 13-limit ===
=== 13-limit ===
Line 906: Line 930:
Mapping: {{mapping| 2 1 9 2 12 19 | 0 3 -6 5 -7 -16 }}
Mapping: {{mapping| 2 1 9 2 12 19 | 0 3 -6 5 -7 -16 }}


Optimal tuning (POTE): ~45/32 = 600.000{{c}}, ~9/7 = 434.756{{c}}
Optimal tunings:
* WE: ~45/32 = 599.3397{{c}}, ~9/7 = 434.2772{{c}}
* CWE: ~45/32 = 600.0000{{c}}, ~9/7 = 434.7864{{c}}
<!-- * POTE: ~45/32 = 600.000{{c}}, ~9/7 = 434.756{{c}} -->


{{Optimal ET sequence|legend=0| 22, 58, 80, 138cde }}
{{Optimal ET sequence|legend=0| 22, 36f, 58, 80, 138cde }}


Badness (Smith): 0.023679
Badness (Sintel): 0.978


=== 17-limit ===
=== 17-limit ===
Line 919: Line 946:
Mapping: {{mapping| 2 1 9 2 12 19 6 | 0 3 -6 5 -7 -16 3 }}
Mapping: {{mapping| 2 1 9 2 12 19 6 | 0 3 -6 5 -7 -16 3 }}


Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~9/7 = 434.816{{c}}
Optimal tunings:
* WE: ~45/32 = 599.4645{{c}}, ~9/7 = 434.4282{{c}}
* CWE: ~45/32 = 600.0000{{c}}, ~9/7 = 434.8340{{c}}
<!-- * POTE: ~17/12 = 600.000{{c}}, ~9/7 = 434.816{{c}} -->


{{Optimal ET sequence|legend=0| 22, 58, 80, 138cde }}
{{Optimal ET sequence|legend=0| 22, 36f, 58, 80, 138cde }}


Badness (Smith): 0.020273
Badness (Sintel): 1.03


== Echidnic ==
== Echidnic ==
Line 934: Line 964:
: mapping generators: ~45/32, ~8/7
: mapping generators: ~45/32, ~8/7


[[Optimal tuning]] ([[POTE]]): ~45/32 = 600.000{{c}}, ~8/7 = 234.492{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~45/32 = 599.7208{{c}}, ~8/7 = 234.8330{{c}}
: [[error map]]: {{val| -0.558 +1.986 +2.733 -5.334 }}
* [[CWE]]: ~45/32 = 600.0000{{c}}, ~8/7 = 234.9539{{c}}
: error map: {{val| 0.000 +2.907 +3.963 -3.780 }}
<!-- * [[POTE]]: ~45/32 = 600.000{{c}}, ~8/7 = 234.492{{c}} -->


{{Optimal ET sequence|legend=1| 10, 36, 46, 194bcd, 240bcd, 286bcd, 332bccdd }}
{{Optimal ET sequence|legend=1| 10, 26c, 36, 46 }}


[[Badness]] (Smith): 0.072246
[[Badness]] (Sintel): 1.83


=== 11-limit ===
=== 11-limit ===
Line 947: Line 982:
Mapping: {{mapping| 2 2 7 6 3 | 0 3 -6 -1 10 }}
Mapping: {{mapping| 2 2 7 6 3 | 0 3 -6 -1 10 }}


Optimal tuning (POTE): ~45/32 = 600.000{{c}}, ~8/7 = 235.096{{c}}
Optimal tunings:
* WE: ~45/32 = 599.8022{{c}}, ~8/7 = 235.0185{{c}}
* CWE: ~45/32 = 600.0000{{c}}, ~8/7 = 235.0893{{c}}
<!-- * POTE: ~45/32 = 600.000{{c}}, ~8/7 = 235.096{{c}} -->


{{Optimal ET sequence|legend=0| 10, 36e, 46, 102, 148, 342bcdd }}
{{Optimal ET sequence|legend=0| 10, 36e, 46, 102, 148 }}


Badness (Smith): 0.045127
Badness (Sintel): 1.49


=== 13-limit ===
=== 13-limit ===
Line 960: Line 998:
Mapping: {{mapping| 2 2 7 6 3 7 | 0 3 -6 -1 10 1 }}
Mapping: {{mapping| 2 2 7 6 3 7 | 0 3 -6 -1 10 1 }}


Optimal tuning (POTE): ~45/32 = 600.000{{c}}, ~8/7 = 235.088{{c}}
Optimal tunings:
* WE: ~45/32 = 599.9570{{c}}, ~8/7 = 235.0708{{c}}
* CWE: ~45/32 = 600.0000{{c}}, ~8/7 = 235.0862{{c}}
<!-- * POTE: ~45/32 = 600.000{{c}}, ~8/7 = 235.088{{c}} -->


{{Optimal ET sequence|legend=0| 10, 46, 102, 148f, 194bcdf }}
{{Optimal ET sequence|legend=0| 10, 36e, 46, 102, 148f }}


Badness (Smith): 0.028874
Badness (Sintel): 1.19


=== 17-limit ===
=== 17-limit ===
Line 973: Line 1,014:
Mapping: {{mapping| 2 2 7 6 3 7 7 | 0 3 -6 -1 10 1 3 }}
Mapping: {{mapping| 2 2 7 6 3 7 7 | 0 3 -6 -1 10 1 3 }}


Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~8/7 = 235.088{{c}}
Optimal tunings:
* WE: ~17/12 = 599.9571{{c}}, ~8/7 = 235.0709{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~8/7 = 235.0860{{c}}
<!-- * POTE: ~17/12 = 600.000{{c}}, ~8/7 = 235.088{{c}} -->


{{Optimal ET sequence|legend=0| 10, 46, 102, 148f, 194bcdf }}
{{Optimal ET sequence|legend=0| 10, 36e, 46, 102, 148f }}


Badness (Smith): 0.019304
Badness (Sintel): 0.983


; Music
; Music
Line 996: Line 1,040:
: mapping generators: ~45/32, ~35/24
: mapping generators: ~45/32, ~35/24


[[Optimal tuning]] ([[POTE]]): ~45/32 = 600.000{{c}}, ~35/24 = 652.811{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~45/32 = 599.5401{{c}}, ~35/24 = 652.3108{{c}}
: [[error map]]: {{val| -0.920 +2.207 +0.304 -1.730 }}
* [[CWE]]: ~45/32 = 600.0000{{c}}, ~35/24 = 652.7736{{c}}
: error map: {{val| 0.000 +3.592 +2.592 +0.589 }}
<!-- * [[POTE]]: ~45/32 = 600.000{{c}}, ~35/24 = 652.811{{c}} -->


{{Optimal ET sequence|legend=1| 22, 46, 68, 182b, 250bc }}
{{Optimal ET sequence|legend=1| 22, 46, 68, 182b, 250bc }}


[[Badness]] (Smith): 0.189510
[[Badness]] (Sintel): 1.20


=== 11-limit ===
=== 11-limit ===
Line 1,009: Line 1,058:
Mapping: {{mapping| 2 1 9 -2 8 | 0 2 -4 7 -1 }}
Mapping: {{mapping| 2 1 9 -2 8 | 0 2 -4 7 -1 }}


Optimal tuning (POTE): ~45/32 = 600.000{{c}}, ~16/11 = 652.680{{c}}
Optimal tunings:
* WE: ~45/32 = 599.7721{{c}}, ~16/11 = 652.4321{{c}}
* CWE: ~45/32 = 600.0000{{c}}, ~16/11 = 652.6672{{c}}
<!-- * POTE: ~45/32 = 600.000{{c}}, ~16/11 = 652.680{{c}} -->


{{Optimal ET sequence|legend=0| 22, 46, 68, 114, 296bce, 410bce }}
{{Optimal ET sequence|legend=0| 22, 46, 68, 114 }}


Badness (Smith): 0.084098
Badness (Sintel): 0.876


=== 13-limit ===
=== 13-limit ===
Line 1,022: Line 1,074:
Mapping: {{mapping| 2 1 9 -2 8 -10 | 0 2 -4 7 -1 16 }}
Mapping: {{mapping| 2 1 9 -2 8 -10 | 0 2 -4 7 -1 16 }}


Optimal tuning (POTE): ~45/32 = 600.000{{c}}, ~16/11 = 652.654{{c}}
Optimal tunings:
* WE: ~45/32 = 599.7699{{c}}, ~16/11 = 652.4035{{c}}
* CWE: ~45/32 = 600.0000{{c}}, ~16/11 = 652.6374{{c}}
<!-- * POTE: ~45/32 = 600.000{{c}}, ~16/11 = 652.654{{c}} -->


{{Optimal ET sequence|legend=0| 22f, 24f, 46, 68, 114 }}
{{Optimal ET sequence|legend=0| 22f, 46, 68, 114 }}


Badness (Smith): 0.079358
Badness (Sintel): 1.16


=== 17-limit ===
=== 17-limit ===
Line 1,035: Line 1,090:
Mapping: {{mapping| 2 1 9 -2 8 -10 6 | 0 2 -4 7 -1 16 2 }}
Mapping: {{mapping| 2 1 9 -2 8 -10 6 | 0 2 -4 7 -1 16 2 }}


Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~16/11 = 652.647{{c}}
Optimal tunings:
* WE: ~17/12 = 599.7995{{c}}, ~16/11 = 652.4287{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~16/11 = 652.6334{{c}}
<!-- * POTE: ~17/12 = 600.000{{c}}, ~16/11 = 652.647{{c}} -->


{{Optimal ET sequence|legend=0| 22f, 24f, 46, 68, 114 }}
{{Optimal ET sequence|legend=0| 22f, 46, 68, 114 }}


Badness (Smith): 0.049392
Badness (Sintel): 0.953


=== 19-limit ===
=== 19-limit ===
Line 1,048: Line 1,106:
Mapping: {{mapping| 2 1 9 -2 8 -10 6 -10 | 0 2 -4 7 -1 16 2 17 }}
Mapping: {{mapping| 2 1 9 -2 8 -10 6 -10 | 0 2 -4 7 -1 16 2 17 }}


Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~16/11 = 652.730{{c}}
Optimal tunings:
* WE: ~17/12 = 599.8060{{c}}, ~16/11 = 652.5190{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~16/11 = 652.7164{{c}}
<!-- * POTE: ~17/12 = 600.000{{c}}, ~16/11 = 652.730{{c}} -->


{{Optimal ET sequence|legend=0| 22fh, 24fh, 46, 68, 114, 182bef }}
{{Optimal ET sequence|legend=0| 22fh, 46, 68, 114, 182bef }}


Badness (Smith): 0.044197
Badness (Sintel): 1.07


=== 23-limit ===
=== 23-limit ===
Line 1,061: Line 1,122:
Mapping: {{mapping| 2 1 9 -2 8 -10 6 -10 -4 | 0 2 -4 7 -1 16 2 17 12 }}
Mapping: {{mapping| 2 1 9 -2 8 -10 6 -10 -4 | 0 2 -4 7 -1 16 2 17 12 }}


Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~16/11 = 652.708{{c}}
Optimal tunings:
* WE: ~17/12 = 599.7879{{c}}, ~16/11 = 652.4776{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~16/11 = 652.6926{{c}}
<!-- * POTE: ~17/12 = 600.000{{c}}, ~16/11 = 652.708{{c}} -->


{{Optimal ET sequence|legend=0| 22fh, 46, 68, 114 }}
{{Optimal ET sequence|legend=0| 22fh, 46, 68, 114 }}


Badness (Smith): 0.035137
Badness (Sintel): 1.03


== Sruti ==
== Sruti ==
Line 1,076: Line 1,140:
: mapping generators: ~45/32, ~140/81
: mapping generators: ~45/32, ~140/81


[[Optimal tuning]] ([[POTE]]): ~45/32 = 600.000{{c}}, ~140/81 = 951.876{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~45/32 = 599.2764{{c}}, ~140/81 = 950.7284{{c}}
: [[error map]]: {{val| -1.447 -0.498 +2.813 +1.497 }}
* [[CWE]]: ~45/32 = 600.0000{{c}}, ~140/81 = 951.8227{{c}}
: error map: {{val| 0.000 +1.690 +6.395 +4.869 }}
<!-- * [[POTE]]: ~45/32 = 600.000{{c}}, ~140/81 = 951.876{{c}} -->


{{Optimal ET sequence|legend=1| 24, 34d, 58, 150cd, 208ccdd, 266ccdd }}
{{Optimal ET sequence|legend=1| 24, 34d, 58, 150cd, 208ccdd, 266ccdd }}


[[Badness]] (Smith): 0.117358
[[Badness]] (Sintel): 2.97


=== 11-limit ===
=== 11-limit ===
Line 1,089: Line 1,158:
Mapping: {{mapping| 2 0 11 -15 -1 | 0 2 -4 13 5 }}
Mapping: {{mapping| 2 0 11 -15 -1 | 0 2 -4 13 5 }}


Optimal tuning (POTE): ~45/32 = 600.000{{c}}, ~121/70 = 951.863{{c}}
Optimal tunings:
* WE: ~45/32 = 599.1951{{c}}, ~121/70 = 950.5864{{c}}
* CWE: ~45/32 = 600.0000{{c}}, ~121/70 = 951.7972{{c}}
<!-- * POTE: ~45/32 = 600.000{{c}}, ~121/70 = 951.863{{c}} -->


{{Optimal ET sequence|legend=0| 24, 34d, 58 }}
{{Optimal ET sequence|legend=0| 24, 34d, 58, 150cdee, 208ccddee, 266ccddeee }}


Badness (Smith): 0.041459
Badness (Sintel): 1.37


=== 13-limit ===
=== 13-limit ===
Line 1,102: Line 1,174:
Mapping: {{mapping| 2 0 11 -15 -1 9 | 0 2 -4 13 5 -1 }}
Mapping: {{mapping| 2 0 11 -15 -1 9 | 0 2 -4 13 5 -1 }}


Optimal tuning (POTE): ~45/32 = 600.000{{c}}, ~26/15 = 951.886{{c}}
Optimal tunings:
* WE: ~45/32 = 599.1479{{c}}, ~26/15 = 950.5337{{c}}
* CWE: ~45/32 = 600.0000{{c}}, ~26/15 = 951.8314{{c}}
<!-- * POTE: ~45/32 = 600.000{{c}}, ~26/15 = 951.886{{c}} -->


{{Optimal ET sequence|legend=0| 24, 34d, 58, 150cdeef, 208ccddeeff }}
{{Optimal ET sequence|legend=0| 24, 34d, 58, 150cdeef, 208ccddeeff, 266ccddeeefff }}


Badness (Smith): 0.023791
Badness (Sintel): 0.983


=== 17-limit ===
=== 17-limit ===
Line 1,115: Line 1,190:
Mapping: {{mapping| 2 0 11 -15 -1 9 5 | 0 2 -4 13 5 -1 2 }}
Mapping: {{mapping| 2 0 11 -15 -1 9 5 | 0 2 -4 13 5 -1 2 }}


Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~26/15 = 951.857{{c}}
Optimal tunings:
* WE: ~17/12 = 599.3003{{c}}, ~26/15 = 950.7465{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~26/15 = 951.8142{{c}}
<!-- * POTE: ~17/12 = 600.000{{c}}, ~26/15 = 951.857{{c}} -->


{{Optimal ET sequence|legend=0| 24, 34d, 58 }}
{{Optimal ET sequence|legend=0| 24, 34d, 58 }}


Badness (Smith): 0.020536
Badness (Sintel): 1.05


== Anguirus ==
== Anguirus ==
Line 1,130: Line 1,208:
: mapping generators: ~45/32, ~7/4
: mapping generators: ~45/32, ~7/4


[[Optimal tuning]] ([[POTE]]): ~45/32 = 600.000{{c}}, ~7/4 = 953.021{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~45/32 = 600.2758{{c}}, ~7/4 = 953.4593{{c}}
: [[error map]]: {{val| +0.552 +4.964 +2.883 -14.264 }}
* [[CWE]]: ~45/32 = 600.0000{{c}}, ~7/4 = 953.0188{{c}}
: error map: {{val| 0.000 +4.083 +1.611 -15.807 }}
<!-- * [[POTE]]: ~45/32 = 600.000{{c}}, ~7/4 = 953.021{{c}} -->


{{Optimal ET sequence|legend=1| 10, 24, 34 }}
{{Optimal ET sequence|legend=1| 10, 24, 34 }}


[[Badness]] (Smith): 0.077955
[[Badness]] (Sintel): 1.97


=== 11-limit ===
=== 11-limit ===
Line 1,143: Line 1,226:
Mapping: {{mapping| 2 0 11 4 -1 | 0 2 -4 1 5 }}
Mapping: {{mapping| 2 0 11 4 -1 | 0 2 -4 1 5 }}


Optimal tuning (POTE): ~45/32 = 600.000{{c}}, ~7/4 = 952.184{{c}}
Optimal tunings:
* WE: ~45/32 = 599.9250{{c}}, ~7/4 = 952.0646{{c}}
* CWE: ~45/32 = 600.0000{{c}}, ~7/4 = 952.1784{{c}}
<!-- * POTE: ~45/32 = 600.000{{c}}, ~7/4 = 952.184{{c}} -->


{{Optimal ET sequence|legend=0| 10, 24, 34, 58d, 92de }}
{{Optimal ET sequence|legend=0| 10, 24, 34 }}


Badness (Smith): 0.049253
Badness (Sintel): 1.63


=== 13-limit ===
=== 13-limit ===
Line 1,156: Line 1,242:
Mapping: {{mapping| 2 0 11 4 -1 9 | 0 2 -4 1 5 -1 }}
Mapping: {{mapping| 2 0 11 4 -1 9 | 0 2 -4 1 5 -1 }}


Optimal tuning (POTE): ~45/32 = 600.000{{c}}, ~7/4 = 952.309{{c}}
Optimal tunings:
* WE: ~45/32 = 599.7575{{c}}, ~7/4 = 951.9241{{c}}
* CWE: ~45/32 = 600.0000{{c}}, ~7/4 = 952.2980{{c}}
<!-- * POTE: ~45/32 = 600.000{{c}}, ~7/4 = 952.309{{c}} -->


{{Optimal ET sequence|legend=0| 10, 24, 34, 58d, 92ddef }}
{{Optimal ET sequence|legend=0| 10, 24, 34, 58d, 92ddef }}


Badness (Smith): 0.030829
Badness (Sintel): 1.27


=== 17-limit ===
=== 17-limit ===
Line 1,169: Line 1,258:
Mapping: {{mapping| 2 0 11 4 -1 9 5 | 0 2 -4 1 5 -1 2 }}
Mapping: {{mapping| 2 0 11 4 -1 9 5 | 0 2 -4 1 5 -1 2 }}


Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~7/4 = 952.330{{c}}
Optimal tunings:
* WE: ~17/12 = 599.7925{{c}}, ~7/4 = 952.0004{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~7/4 = 952.3178{{c}}
<!-- * POTE: ~17/12 = 600.000{{c}}, ~7/4 = 952.330{{c}} -->


{{Optimal ET sequence|legend=0| 10, 24, 34, 58d, 92ddef }}
{{Optimal ET sequence|legend=0| 10, 24, 34 }}


Badness (Smith): 0.021796
Badness (Sintel): 1.10


== Shru ==
== Shru ==
Line 1,184: Line 1,276:
: mapping generators: ~45/32, ~10/7
: mapping generators: ~45/32, ~10/7


[[Optimal tuning]] ([[POTE]]): ~45/32 = 600.000{{c}}, ~10/7 = 650.135{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~45/32 = 600.2519{{c}}, ~10/7 = 650.4083{{c}}
: [[error map]]: {{val| +0.504 -0.887 +14.321 -18.096 }}
* [[CWE]]: ~45/32 = 600.0000{{c}}, ~10/7 = 650.1017{{c}}
: error map: {{val| 0.000 -1.752 +13.279 -19.334 }}
<!-- * [[POTE]]: ~45/32 = 600.000{{c}}, ~10/7 = 650.135{{c}} -->


{{Optimal ET sequence|legend=1| 2, 22d, 24 }}
{{Optimal ET sequence|legend=1| 2, 22d, 24 }}


[[Badness]] (Smith): 0.157619
[[Badness]] (Sintel): 3.99


=== 11-limit ===
=== 11-limit ===
Line 1,197: Line 1,294:
Mapping: {{mapping| 2 1 9 11 8 | 0 2 -4 -5 -1 }}
Mapping: {{mapping| 2 1 9 11 8 | 0 2 -4 -5 -1 }}


Optimal tuning (POTE): ~45/32 = 600.000{{c}}, ~10/7 = 650.130{{c}}
Optimal tunings:
* WE: ~17/12 = 600.2356{{c}}, ~10/7 = 650.3856{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~10/7 = 650.1008{{c}}
<!-- * POTE: ~45/32 = 600.000{{c}}, ~10/7 = 650.130{{c}} -->


{{Optimal ET sequence|legend=0| 2, 22d, 24 }}
{{Optimal ET sequence|legend=0| 2, 22d, 24 }}


Badness (Smith): 0.063483
Badness (Sintel): 2.10


=== 13-limit ===
=== 13-limit ===
Line 1,210: Line 1,310:
Mapping: {{mapping| 2 1 9 11 8 15 | 0 2 -4 -5 -1 -7 }}
Mapping: {{mapping| 2 1 9 11 8 15 | 0 2 -4 -5 -1 -7 }}


Optimal tuning (POTE): ~45/32 = 600.000{{c}}, ~10/7 = 650.535{{c}}
Optimal tunings:
* WE: ~45/32 = 599.9067{{c}}, ~10/7 = 649.4907{{c}}
* CWE: ~45/32 = 600.0000{{c}}, ~10/7 = 649.5950{{c}}
<!-- * POTE: ~45/32 = 600.000{{c}}, ~10/7 = 650.535{{c}} -->


{{Optimal ET sequence|legend=0| 22df, 24 }}
{{Optimal ET sequence|legend=0| 2, 24 }}


Badness (Smith): 0.045731
Badness (Sintel): 2.12


== Quadrasruta ==
== Quadrasruta ==
Line 1,225: Line 1,328:
: mapping generators: ~45/32, ~21/16
: mapping generators: ~45/32, ~21/16


[[Optimal tuning]] ([[POTE]]): ~45/32 = 600.000{{c}}, ~21/16 = 476.216{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~45/32 = 599.4443{{c}}, ~21/16 = 475.7746{{c}}
: [[error map]]: {{val| -1.111 +1.143 +1.377 -0.595 }}
* [[CWE]]: ~45/32 = 600.0000{{c}}, ~21/16 = 476.2394{{c}}
: error map: {{val| 0.000 +3.003 +3.771 +2.456 }}
<!-- * [[POTE]]: ~45/32 = 600.000{{c}}, ~21/16 = 476.216{{c}} -->


{{Optimal ET sequence|legend=1| 10, 38c, 48c, 58, 68, 126 }}
{{Optimal ET sequence|legend=1| 10, …, 58, 68, 126, 446bbccd }}


[[Badness]] (Smith): 0.073569
[[Badness]] (Sintel): 1.86


=== 11-limit ===
=== 11-limit ===
Line 1,238: Line 1,346:
Mapping: {{mapping| 2 0 11 8 22 | 0 4 -8 -3 -19 }}
Mapping: {{mapping| 2 0 11 8 22 | 0 4 -8 -3 -19 }}


Optimal tuning (POTE): ~45/32 = 600.000{{c}}, ~21/16 = 476.118{{c}}
Optimal tunings:
* WE: ~45/32 = 599.4648{{c}}, ~21/16 = 475.6929{{c}}
* CWE: ~45/32 = 600.0000{{c}}, ~21/16 = 476.1507{{c}}
<!-- * POTE: ~45/32 = 600.000{{c}}, ~21/16 = 476.118{{c}} -->


{{Optimal ET sequence|legend=0| 58, 126, 184c, 310bccde }}
{{Optimal ET sequence|legend=0| 10e, …, 58, 126, 184c, 310bccde }}


Badness (Smith): 0.049018
Badness (Sintel): 1.62


==== 13-limit ====
==== 13-limit ====
Line 1,251: Line 1,362:
Mapping: {{mapping| 2 0 11 8 22 9 | 0 4 -8 -3 -19 -2 }}
Mapping: {{mapping| 2 0 11 8 22 9 | 0 4 -8 -3 -19 -2 }}


Optimal tuning (POTE): ~45/32 = 600.000{{c}}, ~21/16 = 476.099{{c}}
Optimal tunings:
* WE: ~45/32 = 599.3787{{c}}, ~21/16 = 475.6065{{c}}
* CWE: ~45/32 = 600.0000{{c}}, ~21/16 = 476.1345{{c}}
<!-- * POTE: ~45/32 = 600.000{{c}}, ~21/16 = 476.099{{c}} -->


{{Optimal ET sequence|legend=0| 58, 126f, 184cff }}
{{Optimal ET sequence|legend=0| 10e, …, 58, 126f, 184cff }}


Badness (Smith): 0.028463
Badness (Sintel): 1.18


==== 17-limit ====
==== 17-limit ====
Line 1,264: Line 1,378:
Mapping: {{mapping| 2 0 11 8 22 9 5 | 0 4 -8 -3 -19 -2 4 }}
Mapping: {{mapping| 2 0 11 8 22 9 5 | 0 4 -8 -3 -19 -2 4 }}


Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~21/16 = 476.162{{c}}
Optimal tunings:
* WE: ~17/12 = 599.5077{{c}}, ~21/16 = 475.7713{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~21/16 = 476.1814{{c}}
<!-- * POTE: ~17/12 = 600.000{{c}}, ~21/16 = 476.162{{c}} -->


{{Optimal ET sequence|legend=0| 58, 126f }}
{{Optimal ET sequence|legend=0| 10e, 58, 126f }}


Badness (Smith): 0.023820
Badness (Sintel): 1.21


=== Quadrafourths ===
=== Quadrafourths ===
Line 1,277: Line 1,394:
Mapping: {{mapping| 2 0 11 8 -1 | 0 4 -8 -3 10 }}
Mapping: {{mapping| 2 0 11 8 -1 | 0 4 -8 -3 10 }}


Optimal tuning (POTE): ~45/32 = 600.000{{c}}, ~21/16 = 476.017{{c}}
Optimal tunings:
* WE: ~45/32 = 599.2593{{c}}, ~21/16 = 475.4292{{c}}
* CWE: ~45/32 = 600.0000{{c}}, ~21/16 = 476.0088{{c}}
<!-- * POTE: ~45/32 = 600.000{{c}}, ~21/16 = 476.017{{c}} -->


{{Optimal ET sequence|legend=0| 10, 38c, 48c, 58 }}
{{Optimal ET sequence|legend=0| 10, 48c, 58, 184cee, 242ccdeee }}


Badness (Smith): 0.049114
Badness (Sintel): 1.62


==== 13-limit ====
==== 13-limit ====
Line 1,290: Line 1,410:
Mapping: {{mapping| 2 0 11 8 -1 9 | 0 4 -8 -3 10 -2 }}
Mapping: {{mapping| 2 0 11 8 -1 9 | 0 4 -8 -3 10 -2 }}


Optimal tuning (POTE): ~45/32 = 600.000{{c}}, ~21/16 = 476.028{{c}}
Optimal tunings:
* WE: ~45/32 = 599.2147{{c}}, ~21/16 = 475.4052{{c}}
* CWE: ~45/32 = 600.0000{{c}}, ~21/16 = 476.0253{{c}}
<!-- * POTE: ~45/32 = 600.000{{c}}, ~21/16 = 476.028{{c}} -->


{{Optimal ET sequence|legend=0| 10, 38c, 48c, 58 }}
{{Optimal ET sequence|legend=0| 10, 48c, 58, 126eef, 184ceeff, 242ccdeeeff }}


Badness (Smith): 0.026743
Badness (Sintel): 1.11


==== 17-limit ====
==== 17-limit ====
Line 1,303: Line 1,426:
Mapping: {{mapping| 2 0 11 8 -1 9 5 | 0 4 -8 -3 10 -2 4 }}
Mapping: {{mapping| 2 0 11 8 -1 9 5 | 0 4 -8 -3 10 -2 4 }}


Optimal tuning (POTE): ~17/12 = 600.000{{c}}, ~21/16 = 476.077{{c}}
Optimal tunings:
* WE: ~17/12 = 599.3353{{c}}, ~21/16 = 475.5495{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~21/16 = 476.0691{{c}}
<!-- * POTE: ~17/12 = 600.000{{c}}, ~21/16 = 476.077{{c}} -->


{{Optimal ET sequence|legend=0| 10, 38c, 48c, 58, 126eef, 184ceeff }}
{{Optimal ET sequence|legend=0| 10, 48c, 58 }}


Badness (Smith): 0.022239
Badness (Sintel): 1.13


[[Category:Temperament families]]
[[Category:Temperament families]]
Retrieved from "https://en.xen.wiki/w/Diaschismic_family"