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Review, +CTE tunings and error maps
Line 16: Line 16:
: sval mapping generators: ~2, ~3, ~7
: sval mapping generators: ~2, ~3, ~7


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 703.8345, ~7/4 = 969.8722
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~3/2 = 703.576, ~7/4 = 967.554
: [[error map]]: {{val| 0.000 +1.621 -1.272 +1.937 }}
* [[POTE]]: ~2 = 1200.000, ~3/2 = 703.834, ~7/4 = 969.872
: error map: {{val| 0.000 +1.879 +1.046 +3.216 }}


{{Optimal ET sequence|legend=1| 12, 17, 36, 41, 58, 63, 104, 225e, 266e, 370bee, 699bbdeee }}
{{Optimal ET sequence|legend=1| 12, 17, 36, 41, 58, 63, 104, 225e, 266e, 370bee, 699bbdeee }}
Line 54: Line 58:
Sval mapping: {{mapping| 1 0 0 7 12 | 0 1 0 -4 -7 | 0 0 1 1 1 }}
Sval mapping: {{mapping| 1 0 0 7 12 | 0 1 0 -4 -7 | 0 0 1 1 1 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 703.8563, ~7/4 = 969.9074
Optimal tunings:
* CTE: ~2 = 1200.000, ~3/2 = 703.786, ~7/4 = 967.665
* POTE: ~2 = 1200.000, ~3/2 = 703.856, ~7/4 = 969.907


{{Optimal ET sequence|legend=1| 12f, 17, 41, 46, 58, 87, 104, 266ef, 329bef, 370beef, 474beef, 595bdeeeff, 699bbdeeeff }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 17, 41, 46, 58, 87, 104, 266ef, 329bef, 370beef, 474beef, 595bdeeeff, 699bbdeeeff }}


Badness: 0.101 × 10<sup>-3</sup>
Badness: 0.101 × 10<sup>-3</sup>
Line 67: Line 73:
Sval mapping: {{mapping| 1 0 0 7 12 -13 | 0 1 0 -4 -7 9 | 0 0 1 1 1 1 }}
Sval mapping: {{mapping| 1 0 0 7 12 -13 | 0 1 0 -4 -7 9 | 0 0 1 1 1 1 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.0315, ~7/4 = 970.6051
Optimal tunings:
* CTE: ~2 = 1200.000, ~3/2 = 703.978, ~7/4 = 968.399
* POTE: ~2 = 1200.000, ~3/2 = 704.032, ~7/4 = 970.605


{{Optimal ET sequence|legend=1| 12f, 17g, 29g, 41g, 46, 58, 75e, 104, 121, 225e }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 17g, 29g, 41g, 46, 58, 75e, 104, 121, 225e }}


Badness: 0.325 × 10<sup>-3</sup>
Badness: 0.325 × 10<sup>-3</sup>
Line 84: Line 92:
: mapping generators: ~2, ~3, ~7
: mapping generators: ~2, ~3, ~7


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 704.1814, ~7/4 = 970.6217
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~3/2 = 704.102, ~7/4 = 968.390
: [[error map]]: {{val| 0.000 +2.147 -0.163 -0.436 +0.662 }}
* [[POTE]]: ~2 = 1200.000, ~3/2 = 704.181, ~7/4 = 970.622
: error map: {{val| 0.000 +2.226 +1.496 +1.796 +2.578 }}


{{Optimal ET sequence|legend=1| 17c, 29, 46, 92de, 121, 167, 288be }}
{{Optimal ET sequence|legend=1| 17c, 29, 46, 92de, 121, 167, 288be }}
Line 97: Line 109:
Mapping: {{mapping| 1 0 -31 0 7 12 | 0 1 0 21 0 4 -7 | 0 0 0 1 1 1 }}
Mapping: {{mapping| 1 0 -31 0 7 12 | 0 1 0 21 0 4 -7 | 0 0 0 1 1 1 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.1691, ~7/4 = 970.8432
Optimal tunings:
* CTE: ~2 = 1200.000, ~3/2 = 704.099, ~7/4 = 968.601
* POTE: ~2 = 1200.000, ~3/2 = 704.169, ~7/4 = 970.843


{{Optimal ET sequence|legend=1| 17c, 29, 46, 75e, 92def, 121, 167, 288be }}
Optimal ET sequence: {{Optimal ET sequence| 17c, 29, 46, 75e, 92def, 121, 167, 288be }}


Badness: 2.48 × 10<sup>-3</sup>
Badness: 2.48 × 10<sup>-3</sup>
Line 110: Line 124:
Mapping: {{mapping| 1 0 -31 0 7 12 -13 | 0 1 0 21 0 4 -7 9 | 0 0 0 1 1 1 1 1 }}
Mapping: {{mapping| 1 0 -31 0 7 12 -13 | 0 1 0 21 0 4 -7 9 | 0 0 0 1 1 1 1 1 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.1628, ~7/4 = 970.6620
Optimal tunings:
* CTE: ~2 = 1200.000, ~3/2 = 704.096, ~7/4 = 968.504
* POTE: ~2 = 1200.000, ~3/2 = 704.163, ~7/4 = 970.662


{{Optimal ET sequence|legend=1| 17cg, 29g, 46, 75e, 92defg, 121, 167, 288beg }}
Optimal ET sequence: {{Optimal ET sequence| 17cg, 29g, 46, 75e, 92defg, 121, 167, 288beg }}


Badness: 1.52 × 10<sup>-3</sup>
Badness: 1.52 × 10<sup>-3</sup>
Line 128: Line 144:


[[Optimal tuning]]s:
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~3/2 = 701.883, ~7/4 = 964.864
* [[CTE]]: ~2 = 1200.000, ~3/2 = 701.883, ~7/4 = 964.864
* [[CWE]]: ~2 = 1\1, ~3/2 = 701.903, ~7/4 = 964.614
: [[error map]]: {{val| 0.000 -0.072 -1.375 -3.962 +6.016 }}
* [[CE]]: ~2 = 1\1, ~3/2 = 702.006, ~7/4 = 964.085
* [[CWE]]: ~2 = 1200.000, ~3/2 = 701.903, ~7/4 = 964.614
: error map: {{val| 0.000 -0.052 -1.541 -4.212 +5.683 }}
* [[CE]]: ~2 = 1200.000, ~3/2 = 702.006, ~7/4 = 964.085
: error map: {{val| 0.000 +0.051 -2.364 -4.741 +4.741 }}


{{Optimal ET sequence|legend=1| 12, 24, 29, 36, 41, 106d }}
{{Optimal ET sequence|legend=1| 12, 24, 29, 36, 41, 106d }}
Line 146: Line 165:


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1\1, ~3/2 = 702.106, ~7/4 = 962.655
* CTE: ~2 = 1200.000, ~3/2 = 702.106, ~7/4 = 962.655
* CWE: ~2 = 1\1, ~3/2 = 702.145, ~7/4 = 962.175
* CWE: ~2 = 1200.000, ~3/2 = 702.145, ~7/4 = 962.175
* CE: ~2 = 1\1, ~3/2 = 702.360, ~7/4 = 962.210
* CE: ~2 = 1200.000, ~3/2 = 702.360, ~7/4 = 962.210


Optimal ET sequence: {{Optimal ET sequence| 12f, 24, 29, 41 }}
Optimal ET sequence: {{Optimal ET sequence| 12f, 24, 29, 41 }}
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Optimal tunings:
Optimal tunings:
* CTE: 2 = 1\1, ~3/2 = 701.783, ~7/4 = 966.113
* CTE: 2 = 1200.000, ~3/2 = 701.783, ~7/4 = 966.113
* CWE: 2 = 1\1, ~3/2 = 701.753, ~7/4 = 966.445
* CWE: 2 = 1200.000, ~3/2 = 701.753, ~7/4 = 966.445
* CE: 2 = 1\1, ~3/2 = 701.770, ~7/4 = 965.771
* CE: 2 = 1200.000, ~3/2 = 701.770, ~7/4 = 965.771


Optimal ET sequence: {{Optimal ET sequence| 12, 17, 24, 36, 41, 77e }}
Optimal ET sequence: {{Optimal ET sequence| 12, 17, 24, 36, 41, 77e }}
Line 182: Line 201:
: mapping generators: ~2, ~3, ~5
: mapping generators: ~2, ~3, ~5


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 703.9571, ~5/4 = 386.8863
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~3/2 = 703.608, ~5/4 = 385.669
: [[error map]]: {{val| 0.000 +1.653 -0.645 -0.472 }}
* [[POTE]]: ~2 = 1200.000, ~3/2 = 703.957, ~5/4 = 386.886
: error map: {{val| 0.000 +2.002 +0.573 +0.930 }}


{{Optimal ET sequence|legend=1| 41, 80, 87, 121, 167, 208, 329b, 375b, 537b, 583b, 704bd }}
{{Optimal ET sequence|legend=1| 34d, 39d, 41, 80, 87, 121, 167, 208, 329b, 375b, 496bd }}


[[Badness]]: 0.165 × 10<sup>-3</sup>
[[Badness]]: 0.165 × 10<sup>-3</sup>
Line 195: Line 218:
{{Mapping|legend=1| 1 0 0 -10 -3 | 0 1 0 11 7 | 0 0 1 -2 -2 }}
{{Mapping|legend=1| 1 0 0 -10 -3 | 0 1 0 11 7 | 0 0 1 -2 -2 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 704.0412, ~5/4 = 387.2927
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~3/2 = 703.642, ~5/4 = 386.223
: [[error map]]: {{val| 0.000 +1.687 -0.091 -1.207 +1.732 }}
* [[POTE]]: ~2 = 1200.000, ~3/2 = 704.041, ~5/4 = 387.293
: error map: {{val| 0.000 +2.086 +0.979 +1.042 +2.385 }}


{{Optimal ET sequence|legend=1| 41, 80, 87, 121, 167, 208, 334be, 375be, 542bce }}
{{Optimal ET sequence|legend=1| 34d, 39d, 41, 80, 87, 121, 167, 208, 288be, 375be }}


[[Badness]]: 1.039 × 10<sup>-3</sup>
[[Badness]]: 1.039 × 10<sup>-3</sup>
Line 208: Line 235:
Mapping: {{mapping| 1 0 0 -10 -3 2 | 0 1 0 11 7 4 | 0 0 1 -2 -2 -2 }}
Mapping: {{mapping| 1 0 0 -10 -3 2 | 0 1 0 11 7 4 | 0 0 1 -2 -2 -2 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 703.9605, ~5/4 = 386.9831
Optimal tunings:
* CTE: ~2 = 1200.000, ~3/2 = 703.705, ~5/4 = 386.616
* POTE: ~2 = 1200.000, ~3/2 = 703.961, ~5/4 = 386.983


{{Optimal ET sequence|legend=1| 41, 46, 80, 87, 121, 167, 208, 375be, 583bef }}
Optimal ET sequence: {{Optimal ET sequence| 34d, 41, 46, 75e, 80, 87, 121, 167, 208, 375be }}


Badness: 1.021 × 10<sup>-3</sup>
Badness: 1.02 × 10<sup>-3</sup>


=== 17-limit ===
=== 17-limit ===
Line 221: Line 250:
Mapping: {{mapping| 1 0 0 -10 -3 2 8 | 0 1 0 11 7 4 -1 | 0 0 1 -2 -2 -2 -1 }}
Mapping: {{mapping| 1 0 0 -10 -3 2 8 | 0 1 0 11 7 4 -1 | 0 0 1 -2 -2 -2 -1 }}


Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 704.0831, ~5/4 = 387.3269
Optimal tunings:
* CTE: ~2 = 1200.000, ~3/2 = 703.891, ~5/4 = 387.424
* POTE: ~2 = 1200.000, ~3/2 = 704.083, ~5/4 = 387.327


{{Optimal ET sequence|legend=1| 41, 46, 75e, 80, 87, 121, 167, 288beg }}
Optimal ET sequence: {{Optimal ET sequence| 34d, 41, 46, 75e, 80, 87, 121, 167, 288beg, 496bdeefggg }}


Badness: 0.982 × 10<sup>-3</sup>
Badness: 0.982 × 10<sup>-3</sup>
Line 238: Line 269:
: mapping generators: ~2, ~121/70, ~5
: mapping generators: ~2, ~121/70, ~5


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~121/70 = 951.4956, ~5/4 = 386.7868
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~121/70 = 951.837, ~5/4 = 386.405
: [[error map]]: {{val| 0.000 +1.718 +0.091 -1.198 +1.617 }}
* [[CWE]]: ~2 = 1200.000, ~121/70 = 951.871, ~5/4 = 387.243
: error map: {{val| 0.000 +1.787 +0.930 +0.220 +2.762 }}


{{Optimal ET sequence|legend=1| 24, 29, 34d, 53d, 58, 87, 121, 145, 179e, 208, 266e }}
{{Optimal ET sequence|legend=1| 24, 29, 34d, 53d, 58, 87, 121, 145, 179e, 208, 266e }}
Line 251: Line 286:
Mapping: {{mapping| 1 0 0 -13 -6 -1 | 0 2 0 17 9 3 | 0 0 1 1 1 1 }}
Mapping: {{mapping| 1 0 0 -13 -6 -1 | 0 2 0 17 9 3 | 0 0 1 1 1 1 }}


Optimal tuning (CTE): ~2 = 1\1, ~26/15 = 951.8367, ~5/4 = 386.4048
Optimal tunings:
* CTE: ~2 = 1200.000, ~26/15 = 951.852, ~5/4 = 386.089
* CWE: ~2 = 1200.000, ~26/15 = 951.881, ~5/4 = 387.104


{{Optimal ET sequence|legend=1| 24, 29, 34d, 53d, 58, 87, 121, 179ef, 208, 266ef, 474beef }}
Optimal ET sequence: {{Optimal ET sequence| 24, 29, 34d, 53d, 58, 87, 121, 179ef, 208, 266ef, 474beef }}


Badness: 1.06 × 10<sup>-3</sup>
Badness: 1.06 × 10<sup>-3</sup>
Line 266: Line 303:
Mapping: {{mapping| 1 0 0 -13 -6 -1 8 | 0 2 0 17 9 3 -2 | 0 0 1 1 1 1 -1 }}
Mapping: {{mapping| 1 0 0 -13 -6 -1 8 | 0 2 0 17 9 3 -2 | 0 0 1 1 1 1 -1 }}


Optimal tuning (CTE): ~2 = 1\1, ~26/15 = 951.8015, ~5/4 = 386.9912
Optimal tunings:
* CTE: ~2 = 1200.000, ~26/15 = 951.802, ~5/4 = 386.991
* CWE: ~2 = 1200.000, ~26/15 = 951.879, ~5/4 = 387.723


{{Optimal ET sequence|legend=1| 24, 34d, 58, 87, 121, 179ef, 208g, 266efg }}
Optimal ET sequence: {{Optimal ET sequence| 24, 34d, 58, 87, 121, 179ef, 208g, 266efg }}


Badness: 1.24 × 10<sup>-3</sup>
Badness: 1.24 × 10<sup>-3</sup>
[[Category:Temperament clans]]
[[Category:Pentacircle clan| ]] <!-- main article -->
[[Category:Rank 3]]
[[Category:Tolerant]]


== Trienparapyth ==
== Trienparapyth ==
Line 291: Line 325:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~11/10 = 165.4134, ~5/4 = 386.8872
* [[CTE]]: ~2 = 1200.000, ~11/10 = 165.413, ~5/4 = 386.887
* [[CWE]]: ~2 = 1\1, ~11/10 = 165.3593, ~5/4 = 387.8093
: [[error map]]: {{val| 0.000 +1.805 +0.574 -1.486 +0.983 }}
* [[CWE]]: ~2 = 1200.000, ~11/10 = 165.359, ~5/4 = 387.809
: error map: {{val| 0.000 +1.967 +1.496 +0.031 +1.851 }}


{{Optimal ET sequence|legend=1| 7d, 14e, 15d, 22, 51, 58, 80, 87, 145, 167, 312ce, 479bce }}
{{Optimal ET sequence|legend=1| 7d, 14e, 15d, 22, 51, 58, 80, 87, 145, 167, 312ce, 479bce }}
Line 308: Line 344:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~11/10 = 165.3975, ~5/4 = 386.7908
* CTE: ~2 = 1200.000, ~11/10 = 165.398, ~5/4 = 386.791
* CWE: ~2 = 1\1, ~11/10 = 165.3802, ~5/4 = 387.8759
* CWE: ~2 = 1200.000, ~11/10 = 165.380, ~5/4 = 387.876


Optimal ET sequence: {{Optimal ET sequence| 7d, 22, 29, 51f, 51cde, 58, 80, 87, 145, 167, 225ce, 254, 312ce }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 22, 29, 51f, 51cde, 58, 80, 87, 145, 167, 225ce, 254, 312ce }}
Line 315: Line 351:
Badness: 1.23 × 10<sup>-3</sup>
Badness: 1.23 × 10<sup>-3</sup>


=== no-17's 19-limit ===
=== 2.3.5.7.11.13.19 subgroup ===
Note [[109edo]] is a good patent val tuning not listed in the optimal ET sequence here.
Note [[109edo]] is a good patent val tuning not listed in the optimal ET sequence here.


Line 327: Line 363:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~11/10 = 165.2990, ~5/4 = 386.3154
* CTE: ~2 = 1200.000, ~11/10 = 165.299, ~5/4 = 386.315
* CWE: ~2 = 1\1, ~11/10 = 165.2976, ~5/4 = 387.7451
* CWE: ~2 = 1200.000, ~11/10 = 165.298, ~5/4 = 387.745


Optimal ET sequence: {{Optimal ET sequence| 7d, 22, 29, 51fh, 51cde, 58h, 80, 87, 138cdeh, 167h }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 22, 29, 51fh, 51cde, 58h, 80, 87, 138cdeh, 167h }}
Line 334: Line 370:
Badness: 1.22 × 10<sup>-3</sup>
Badness: 1.22 × 10<sup>-3</sup>


=== no-17's 23-limit ===
=== 2.3.5.7.11.13.19.23 subgroup ===
Note [[109edo]] is a good patent val tuning not listed in the optimal ET sequence here.
 
Subgroup: 2.3.5.7.11.13.19.23
Subgroup: 2.3.5.7.11.13.19.23


Line 346: Line 380:


Optimal tunings  
Optimal tunings  
* CTE: ~2 = 1\1, ~11/10 = 165.2579, ~5/4 = 386.1446
* CTE: ~2 = 1200.000, ~11/10 = 165.258, ~5/4 = 386.145
* CWE: ~2 = 1\1, ~11/10 = 165.2679, ~5/4 = 387.7240
* CWE: ~2 = 1200.000, ~11/10 = 165.268, ~5/4 = 387.724


Optimal ET sequence: {{Optimal ET sequence| 22i, 29, 51fhi, 51cde, 58hi, 80, 87, 109, 138cdehi, 167hi }}
Optimal ET sequence: {{Optimal ET sequence| 22i, 29, 51fhi, 51cde, 58hi, 80, 87, 109, 138cdehi, 167hi }}


Badness: 1.04 × 10<sup>-3</sup>
Badness: 1.04 × 10<sup>-3</sup>
[[Category:Temperament clans]]
[[Category:Pentacircle clan| ]] <!-- main article -->
[[Category:Rank 3]]
[[Category:Tolerant]]
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