Augmented family: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings, per community consensus
- CTE & POTE tunings
Line 20: Line 20:
* [[CWE]]: ~5/4 = 400.0000{{c}}, ~3/2 = 705.0691{{c}} (~16/15 = 94.9309{{c}})
* [[CWE]]: ~5/4 = 400.0000{{c}}, ~3/2 = 705.0691{{c}} (~16/15 = 94.9309{{c}})
: error map: {{val| 0.000 +3.114 +13.686 }}
: error map: {{val| 0.000 +3.114 +13.686 }}
<!-- * [[CTE]]: ~5/4 = 400.000{{c}}, ~3/2 = 701.955{{c}} (~16/15 = 98.045{{c}})
: [[error map]]: {{val| 0.000 0.000 +13.686 }}
* [[POTE]]: ~5/4 = 400.000{{c}}, ~3/2 = 706.638{{c}} (~16/15 = 93.362{{c}})
: error map: {{val| 0.000 +4.683 +13.686 }} -->


{{Optimal ET sequence|legend=1| 3, 9, 12, 27, 39, 51c, 90cc }}
{{Optimal ET sequence|legend=1| 3, 9, 12, 27, 39, 51c, 90cc }}
Line 44: Line 40:
* [[CWE]]: ~5/4 = 400.0000{{c}}, ~3/2 = 694.6812{{c}} (~16/15 = 105.3188{{c}})
* [[CWE]]: ~5/4 = 400.0000{{c}}, ~3/2 = 694.6812{{c}} (~16/15 = 105.3188{{c}})
: error map: {{val| 0.000 -7.274 +13.686 +20.537 }}
: error map: {{val| 0.000 -7.274 +13.686 +20.537 }}
<!-- * [[CTE]]: ~5/4 = 400.000{{c}}, ~3/2 = 692.124{{c}} (~16/15 = 107.876{{c}})
: [[error map]]: {{val| 0.000 -9.831 +13.686 +15.422 }}
* [[POTE]]: ~5/4 = 400.000{{c}}, ~3/2 = 696.011{{c}} (~16/15 = 103.989{{c}})
: error map: {{val| 0.000 -5.944 +13.686 +23.195 }} -->


{{Optimal ET sequence|legend=1| 9, 12, 45cd }}
{{Optimal ET sequence|legend=1| 9, 12, 45cd }}
Line 63: Line 55:
* WE: ~5/4 = 398.9225{{c}}, ~3/2 = 690.6486{{c}} (~16/15 = 107.1966{{c}})
* WE: ~5/4 = 398.9225{{c}}, ~3/2 = 690.6486{{c}} (~16/15 = 107.1966{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~3/2 = 690.8519{{c}} (~16/15 = 109.1481{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~3/2 = 690.8519{{c}} (~16/15 = 109.1481{{c}})
<!-- * CTE: ~5/4 = 400.000{{c}}, ~3/2 = 687.685{{c}} (~16/15 = 112.315{{c}})
* POTE: ~5/4 = 400.000{{c}}, ~3/2 = 692.514{{c}} (~16/15 = 107.486{{c}}) -->


{{Optimal ET sequence|legend=0| 9, 12, 21, 33e }}
{{Optimal ET sequence|legend=0| 9, 12, 21, 33e }}
Line 80: Line 70:
* WE: ~5/4 = 399.0956{{c}}, ~3/2 = 687.2261{{c}} (~16/15 = 110.9651{{c}})
* WE: ~5/4 = 399.0956{{c}}, ~3/2 = 687.2261{{c}} (~16/15 = 110.9651{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~3/2 = 687.5057{{c}} (~16/15 = 112.4943{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~3/2 = 687.5057{{c}} (~16/15 = 112.4943{{c}})
<!-- * CTE: ~5/4 = 400.000{{c}}, ~3/2 = 685.084{{c}} (~16/15 = 114.916{{c}})
* POTE: ~5/4 = 400.000{{c}}, ~3/2 = 688.783{{c}} (~16/15 = 111.217{{c}}) -->


{{Optimal ET sequence|legend=0| 9, 12f, 21, 33ef }}
{{Optimal ET sequence|legend=0| 9, 12f, 21, 33ef }}
Line 97: Line 85:
* WE: ~5/4 = 400.4230{{c}}, ~3/2 = 686.0809{{c}} (~16/15 = 114.7650{{c}})
* WE: ~5/4 = 400.4230{{c}}, ~3/2 = 686.0809{{c}} (~16/15 = 114.7650{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~3/2 = 685.8446{{c}} (~16/15 = 114.1554{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~3/2 = 685.8446{{c}} (~16/15 = 114.1554{{c}})
<!-- * CTE: ~5/4 = 400.000{{c}}, ~3/2 = 687.685{{c}} (~16/15 = 112.315{{c}})
* POTE: ~5/4 = 400.000{{c}}, ~3/2 = 685.356{{c}} (~16/15 = 114.644{{c}}) -->


{{Optimal ET sequence|legend=0| 9, 12 }}
{{Optimal ET sequence|legend=0| 9, 12 }}
Line 118: Line 104:
* [[CWE]]: ~5/4 = 400.0000{{c}}, ~3/2 = 709.3249{{c}} (~21/20 = 90.6751{{c}})
* [[CWE]]: ~5/4 = 400.0000{{c}}, ~3/2 = 709.3249{{c}} (~21/20 = 90.6751{{c}})
: error map: {{val| 0.000 +7.370 +13.686 +12.524 }}
: error map: {{val| 0.000 +7.370 +13.686 +12.524 }}
<!-- * [[CTE]]: ~5/4 = 400.000{{c}}, ~3/2 = 709.595{{c}} (~21/20 = 90.405{{c}})
: [[error map]]: {{val| 0.000 +7.640 +13.686 +11.984 }}
* [[POTE]]: ~5/4 = 400.000{{c}}, ~3/2 = 709.257{{c}} (~21/20 = 90.743{{c}})
: error map: {{val| 0.000 +7.302 +13.686 +12.660 }} -->


{{Optimal ET sequence|legend=1| 12, 27, 39d, 66cd }}
{{Optimal ET sequence|legend=1| 12, 27, 39d, 66cd }}
Line 137: Line 119:
* WE: ~5/4 = 398.4962{{c}}, ~3/2 = 708.5030{{c}} (~21/20 = 88.4895{{c}})
* WE: ~5/4 = 398.4962{{c}}, ~3/2 = 708.5030{{c}} (~21/20 = 88.4895{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~3/2 = 711.6031{{c}} (~21/20 = 88.3969{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~3/2 = 711.6031{{c}} (~21/20 = 88.3969{{c}})
<!-- * CTE: ~5/4 = 400.000{{c}}, ~3/2 = 713.570{{c}} (~21/20 = 86.430{{c}})
* POTE: ~5/4 = 400.000{{c}}, ~3/2 = 711.177{{c}} (~21/20 = 88.823{{c}}) -->


{{Optimal ET sequence|legend=0| 12, 15, 27e }}
{{Optimal ET sequence|legend=0| 12, 15, 27e }}
Line 154: Line 134:
* WE: ~5/4 = 398.0488{{c}}, ~3/2 = 708.5402{{c}} (~21/20 = 87.5574{{c}})
* WE: ~5/4 = 398.0488{{c}}, ~3/2 = 708.5402{{c}} (~21/20 = 87.5574{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~3/2 = 712.6704{{c}} (~21/20 = 87.3296{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~3/2 = 712.6704{{c}} (~21/20 = 87.3296{{c}})
<!-- * CTE: ~5/4 = 400.000{{c}}, ~3/2 = 716.123{{c}} (~21/20 = 83.877{{c}})
* POTE: ~5/4 = 400.000{{c}}, ~3/2 = 712.013{{c}} (~21/20 = 87.987{{c}}) -->


{{Optimal ET sequence|legend=0| 12f, 15, 27eff }}
{{Optimal ET sequence|legend=0| 12f, 15, 27eff }}
Line 171: Line 149:
* WE: ~5/4 = 398.6473{{c}}, ~3/2 = 710.1987{{c}} (~21/20 = 87.0959{{c}})
* WE: ~5/4 = 398.6473{{c}}, ~3/2 = 710.1987{{c}} (~21/20 = 87.0959{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~3/2 = 712.5057{{c}} (~21/20 = 87.4943{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~3/2 = 712.5057{{c}} (~21/20 = 87.4943{{c}})
<!-- * CTE: ~5/4 = 400.000{{c}}, ~3/2 = 711.902{{c}} (~21/20 = 88.098{{c}})
* POTE: ~5/4 = 400.000{{c}}, ~3/2 = 712.609{{c}} (~21/20 = 87.391{{c}}) -->


{{Optimal ET sequence|legend=0| 12, 15, 27e, 69bceef }}
{{Optimal ET sequence|legend=0| 12, 15, 27e, 69bceef }}
Line 188: Line 164:
* WE: ~5/4 = 398.5229{{c}}, ~3/2 = 707.0562{{c}} (~21/20 = 89.9897{{c}})
* WE: ~5/4 = 398.5229{{c}}, ~3/2 = 707.0562{{c}} (~21/20 = 89.9897{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~3/2 = 710.1903{{c}} (~21/20 = 89.8097{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~3/2 = 710.1903{{c}} (~21/20 = 89.8097{{c}})
<!-- * CTE: ~5/4 = 400.000{{c}}, ~3/2 = 712.572{{c}} (~21/20 = 87.428{{c}})
* POTE: ~5/4 = 400.000{{c}}, ~3/2 = 709.677{{c}} (~21/20 = 90.323{{c}}) -->


{{Optimal ET sequence|legend=0| 12f, 27e, 66cdeeef }}
{{Optimal ET sequence|legend=0| 12f, 27e, 66cdeeef }}
Line 205: Line 179:
* WE: ~5/4 = 399.1743{{c}}, ~3/2 = 712.6763{{c}} (~21/20 = 85.6723{{c}})
* WE: ~5/4 = 399.1743{{c}}, ~3/2 = 712.6763{{c}} (~21/20 = 85.6723{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~3/2 = 713.9414{{c}} (~21/20 = 86.0586{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~3/2 = 713.9414{{c}} (~21/20 = 86.0586{{c}})
<!-- * CTE: ~5/4 = 400.000{{c}}, ~3/2 = 713.002{{c}} (~21/20 = 86.998{{c}})
* POTE: ~5/4 = 400.000{{c}}, ~3/2 = 714.150{{c}} (~21/20 = 85.850{{c}}) -->


{{Optimal ET sequence|legend=0| 12e, 15, 27, 42 }}
{{Optimal ET sequence|legend=0| 12e, 15, 27, 42 }}
Line 224: Line 196:
* [[CWE]]: ~5/4 = 400.0000{{c}}, ~3/2 = 721.0196{{c}} (~25/24 = 78.9804{{c}})
* [[CWE]]: ~5/4 = 400.0000{{c}}, ~3/2 = 721.0196{{c}} (~25/24 = 78.9804{{c}})
: error map: {{val| 0.000 +19.065 +13.686 -5.767 }}
: error map: {{val| 0.000 +19.065 +13.686 -5.767 }}
<!-- * [[CTE]]: ~5/4 = 400.000{{c}}, ~3/2 = 717.517{{c}} (~25/24 = 82.483{{c}})
: [[error map]]: {{val| 0.000 +15.562 +13.686 -16.274 }}
* [[POTE]]: ~5/4 = 400.000{{c}}, ~3/2 = 722.719{{c}} (~25/24 = 77.281{{c}})
: error map: {{val| 0.000 +20.764 +13.686 -0.668 }} -->


{{Optimal ET sequence|legend=1| 3d, 12d, 15 }}
{{Optimal ET sequence|legend=1| 3d, 12d, 15 }}
Line 243: Line 211:
* WE: ~5/4 = 398.4016{{c}}, ~3/2 = 719.7758{{c}} (~25/24 = 77.0275{{c}})
* WE: ~5/4 = 398.4016{{c}}, ~3/2 = 719.7758{{c}} (~25/24 = 77.0275{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~3/2 = 720.9386{{c}} (~25/24 = 79.0614{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~3/2 = 720.9386{{c}} (~25/24 = 79.0614{{c}})
<!-- * CTE: ~5/4 = 400.000{{c}}, ~3/2 = 717.382{{c}} (~25/24 = 82.618{{c}})
* POTE: ~5/4 = 400.000{{c}}, ~3/2 = 722.663{{c}} (~25/24 = 77.337{{c}}) -->


{{Optimal ET sequence|legend=0| 3de, 12de, 15 }}
{{Optimal ET sequence|legend=0| 3de, 12de, 15 }}
Line 262: Line 228:
* [[CWE]]: ~5/4 = 400.0000{{c}}, ~3/2 = 682.2587{{c}} (~16/15 = 117.7413{{c}})
* [[CWE]]: ~5/4 = 400.0000{{c}}, ~3/2 = 682.2587{{c}} (~16/15 = 117.7413{{c}})
: error map: {{val| 0.000 -19.696 +13.686 -51.085 }}
: error map: {{val| 0.000 -19.696 +13.686 -51.085 }}
<!-- * [[CTE]]: ~5/4 = 400.000{{c}}, ~3/2 = 684.847{{c}} (~16/15 = 115.153{{c}})
: [[error map]]: {{val| 0.000 -17.108 +13.686 -53.673 }}
* [[POTE]]: ~5/4 = 400.000{{c}}, ~3/2 = 681.629{{c}} (~16/15 = 118.371{{c}})
: error map: {{val| 0.000 -20.326 +13.686 -50.455 }} -->


{{Optimal ET sequence|legend=1| 3, 6b, 9 }}
{{Optimal ET sequence|legend=1| 3, 6b, 9 }}
Line 281: Line 243:
* WE: ~5/4 = 402.1799{{c}}, ~3/2 = 683.7477{{c}} (~16/15 = 120.6120{{c}})
* WE: ~5/4 = 402.1799{{c}}, ~3/2 = 683.7477{{c}} (~16/15 = 120.6120{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~3/2 = 680.0162{{c}} (~16/15 = 119.9838{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~3/2 = 680.0162{{c}} (~16/15 = 119.9838{{c}})
<!-- * CTE: ~5/4 = 400.000{{c}}, ~3/2 = 679.881{{c}} (~16/15 = 120.119{{c}})
* POTE: ~5/4 = 400.000{{c}}, ~3/2 = 680.042{{c}} (~16/15 = 119.958{{c}}) -->


{{Optimal ET sequence|legend=0| 3, 6b, 9 }}
{{Optimal ET sequence|legend=0| 3, 6b, 9 }}
Line 302: Line 262:
* [[CWE]]: ~28/25 = 200.0000{{c}}, ~3/2 = 708.6907{{c}} (~25/24 = 91.3093{{c}})
* [[CWE]]: ~28/25 = 200.0000{{c}}, ~3/2 = 708.6907{{c}} (~25/24 = 91.3093{{c}})
: error map: {{val| 0.000 +6.735 +13.686 +31.174 }}
: error map: {{val| 0.000 +6.735 +13.686 +31.174 }}
<!-- * [[CTE]]: ~28/25 = 200.000{{c}}, ~3/2 = 701.955{{c}} (~16/15 = 98.045{{c}})
: [[error map]]: {{val| 0.000 0.000 +13.686 +31.174 }}
* [[POTE]]: ~28/25 = 200.000{{c}}, ~3/2 = 710.963{{c}} (~25/24 = 89.037{{c}})
: error map: {{val| 0.000 +9.008 +13.686 +31.174 }} -->


{{Optimal ET sequence|legend=1| 6, 12, 30d, 42dd, 54cdd }}
{{Optimal ET sequence|legend=1| 6, 12, 30d, 42dd, 54cdd }}
Line 321: Line 277:
* WE: ~28/25 = 198.6942{{c}}, ~3/2 = 709.6404{{c}} (~25/24 = 85.1362{{c}})
* WE: ~28/25 = 198.6942{{c}}, ~3/2 = 709.6404{{c}} (~25/24 = 85.1362{{c}})
* CWE: ~28/25 = 200.0000{{c}}, ~3/2 = 711.8043{{c}} (~25/24 = 88.1957{{c}})
* CWE: ~28/25 = 200.0000{{c}}, ~3/2 = 711.8043{{c}} (~25/24 = 88.1957{{c}})
<!-- * CTE: ~28/25 = 200.000{{c}}, ~3/2 = 701.955{{c}} (~16/15 = 98.045{{c}})
* POTE: ~28/25 = 200.000{{c}}, ~3/2 = 714.304{{c}} (~25/24 = 85.696{{c}}) -->


{{Optimal ET sequence|legend=0| 6, 12, 30dee, 42ddeee }}
{{Optimal ET sequence|legend=0| 6, 12, 30dee, 42ddeee }}
Line 338: Line 292:
* WE: ~28/25 = 198.4492{{c}}, ~3/2 = 704.4994{{c}} (~25/24 = 89.2973{{c}})
* WE: ~28/25 = 198.4492{{c}}, ~3/2 = 704.4994{{c}} (~25/24 = 89.2973{{c}})
* CWE: ~28/25 = 200.0000{{c}}, ~3/2 = 706.6050{{c}} (~16/15 = 93.3950{{c}})
* CWE: ~28/25 = 200.0000{{c}}, ~3/2 = 706.6050{{c}} (~16/15 = 93.3950{{c}})
<!-- * CTE: ~28/25 = 200.000{{c}}, ~3/2 = 692.433{{c}} (~16/15 = 92.433{{c}})
* POTE: ~28/25 = 200.000{{c}}, ~3/2 = 710.005{{c}} (~16/15 = 89.995{{c}}) -->


{{Optimal ET sequence|legend=0| 6f, 12f }}
{{Optimal ET sequence|legend=0| 6f, 12f }}
Line 361: Line 313:
* [[CWE]]: ~5/4 = 400.0000{{c}}, ~7/4 = 952.7463{{c}} (~35/32 = 152.7463{{c}})
* [[CWE]]: ~5/4 = 400.0000{{c}}, ~7/4 = 952.7463{{c}} (~35/32 = 152.7463{{c}})
: error map: {{val| 0.000 +3.538 +13.686 -16.080 }}
: error map: {{val| 0.000 +3.538 +13.686 -16.080 }}
<!-- * [[CTE]]: ~5/4 = 400.000{{c}}, ~7/4 = 952.295{{c}} (~35/32 = 152.295{{c}})
: [[error map]]: {{val| 0.000 +2.635 +13.686 -16.531 }}
* [[POTE]]: ~5/4 = 400.000{{c}}, ~7/4 = 952.951{{c}} (~35/32 = 152.951{{c}})
: error map: {{val| 0.000 +3.947 +13.686 -15.875 }} -->


{{Optimal ET sequence|legend=1| 6, 9, 15, 24, 39 }}
{{Optimal ET sequence|legend=1| 6, 9, 15, 24, 39 }}
Line 380: Line 328:
* WE: ~5/4 = 399.7654{{c}}, ~7/4 = 952.3730{{c}} (~12/11 = 152.8421{{c}})
* WE: ~5/4 = 399.7654{{c}}, ~7/4 = 952.3730{{c}} (~12/11 = 152.8421{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~7/4 = 952.7447{{c}} (~12/11 = 152.7447{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~7/4 = 952.7447{{c}} (~12/11 = 152.7447{{c}})
<!-- * CTE: ~5/4 = 400.000{{c}}, ~7/4 = 952.250{{c}} (~12/11 = 152.250{{c}})
* POTE: ~5/4 = 400.000{{c}}, ~7/4 = 952.932{{c}} (~12/11 = 152.932{{c}}) -->


{{Optimal ET sequence|legend=0| 6, 9, 15, 24, 39 }}
{{Optimal ET sequence|legend=0| 6, 9, 15, 24, 39 }}
Line 401: Line 347:
* WE: ~5/4 = 399.7107{{c}}, ~7/4 = 950.9983{{c}} (~12/11 = 151.5768{{c}})
* WE: ~5/4 = 399.7107{{c}}, ~7/4 = 950.9983{{c}} (~12/11 = 151.5768{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~7/4 = 951.4465{{c}} (~12/11 = 151.4465{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~7/4 = 951.4465{{c}} (~12/11 = 151.4465{{c}})
<!-- * CTE: ~5/4 = 400.000{{c}}, ~7/4 = 950.805{{c}} (~12/11 = 150.805{{c}})
* POTE: ~5/4 = 400.000{{c}}, ~7/4 = 951.687{{c}} (~12/11 = 151.687{{c}}) -->


{{Optimal ET sequence|legend=0| 6f, 9, 15, 24 }}
{{Optimal ET sequence|legend=0| 6f, 9, 15, 24 }}
Line 423: Line 367:
* WE: ~44/39 = 199.8321{{c}}, ~7/4 = 952.5580{{c}} (~40/39 = 46.6024{{c}})
* WE: ~44/39 = 199.8321{{c}}, ~7/4 = 952.5580{{c}} (~40/39 = 46.6024{{c}})
* CWE: ~44/39 = 200.0000{{c}}, ~7/4 = 953.2005{{c}} (~40/39 = 46.7995{{c}})
* CWE: ~44/39 = 200.0000{{c}}, ~7/4 = 953.2005{{c}} (~40/39 = 46.7995{{c}})
<!-- * CTE: ~44/39 = 200.000{{c}}, ~7/4 = 952.531{{c}} (~40/39 = 47.469{{c}})
* POTE: ~44/39 = 200.000{{c}}, ~7/4 = 953.358{{c}} (~40/39 = 46.642{{c}}) -->


{{Optimal ET sequence|legend=0| 6, 18bd, 24 }}
{{Optimal ET sequence|legend=0| 6, 18bd, 24 }}
Line 444: Line 386:
* [[CWE]]: ~5/4 = 400.0000{{c}}, ~14/9 = 754.2078{{c}} (~36/35 = 45.7922{{c}})
* [[CWE]]: ~5/4 = 400.0000{{c}}, ~14/9 = 754.2078{{c}} (~36/35 = 45.7922{{c}})
: error map: {{val| 0.000 +6.461 +13.686 +2.213 }}
: error map: {{val| 0.000 +6.461 +13.686 +2.213 }}
<!-- * [[CTE]]: ~5/4 = 400.000{{c}}, ~14/9 = 752.834{{c}} (~36/35 = 47.166{{c}})
: [[error map]]: {{val| 0.000 +3.712 +13.686 -4.658 }}
* [[POTE]]: ~5/4 = 400.000{{c}}, ~14/9 = 754.882{{c}} (~36/35 = 45.118{{c}})
: error map: {{val| 0.000 +7.808 +13.686 +5.583 }} -->


{{Optimal ET sequence|legend=1| 24, 27 }}
{{Optimal ET sequence|legend=1| 24, 27 }}
Line 463: Line 401:
* WE: ~5/4 = 398.8946{{c}}, ~14/9 = 752.1272{{c}} (~36/35 = 45.6619{{c}})
* WE: ~5/4 = 398.8946{{c}}, ~14/9 = 752.1272{{c}} (~36/35 = 45.6619{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~14/9 = 753.5000{{c}} (~36/35 = 46.5000{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~14/9 = 753.5000{{c}} (~36/35 = 46.5000{{c}})
<!-- * CTE: ~5/4 = 400.000{{c}}, ~14/9 = 752.051{{c}} (~36/35 = 47.949{{c}})
* POTE: ~5/4 = 400.000{{c}}, ~14/9 = 754.212{{c}} (~36/35 = 45.788{{c}}) -->


{{Optimal ET sequence|legend=0| 24, 27e, 51ce }}
{{Optimal ET sequence|legend=0| 24, 27e, 51ce }}
Line 480: Line 416:
* WE: ~5/4 = 399.1053{{c}}, ~14/9 = 752.0643{{c}} (~36/35 = 46.1463{{c}})
* WE: ~5/4 = 399.1053{{c}}, ~14/9 = 752.0643{{c}} (~36/35 = 46.1463{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~14/9 = 753.3806{{c}} (~36/35 = 46.6194{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~14/9 = 753.3806{{c}} (~36/35 = 46.6194{{c}})
<!-- * CTE: ~5/4 = 400.000{{c}}, ~14/9 = 752.128{{c}} (~36/35 = 47.872{{c}})
* POTE: ~5/4 = 400.000{{c}}, ~14/9 = 753.750{{c}} (~36/35 = 46.250{{c}}) -->


{{Optimal ET sequence|legend=0| 24, 27e, 51ce }}
{{Optimal ET sequence|legend=0| 24, 27e, 51ce }}
Line 501: Line 435:
* [[CWE]]: ~5/4 = 400.0000{{c}}, ~32/21 = 747.9138{{c}} (~21/20 = 52.0862{{c}})
* [[CWE]]: ~5/4 = 400.0000{{c}}, ~32/21 = 747.9138{{c}} (~21/20 = 52.0862{{c}})
: error map: {{val| 0.000 -6.127 +13.686 -12.567 }}
: error map: {{val| 0.000 -6.127 +13.686 -12.567 }}
<!-- * [[CTE]]: ~5/4 = 400.000{{c}}, ~32/21 = 747.948{{c}} (~21/20 = 52.052{{c}})
: [[error map]]: {{val| 0.000 -6.058 +13.686 -12.671 }}
* [[POTE]]: ~5/4 = 400.000{{c}}, ~32/21 = 747.907{{c}} (~21/20 = 52.093{{c}})
: error map: {{val| 0.000 -6.143 +13.686 -12.544 }} -->


{{Optimal ET sequence|legend=1| 21, 24, 45c }}
{{Optimal ET sequence|legend=1| 21, 24, 45c }}
Line 520: Line 450:
* WE: ~5/4 = 400.0637{{c}}, ~32/21 = 748.4638{{c}} (~33/32 = 51.6637{{c}})
* WE: ~5/4 = 400.0637{{c}}, ~32/21 = 748.4638{{c}} (~33/32 = 51.6637{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~32/21 = 748.3383{{c}} (~33/32 = 51.6617{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~32/21 = 748.3383{{c}} (~33/32 = 51.6617{{c}})
<!-- * CTE: ~5/4 = 400.000{{c}}, ~32/21 = 748.296{{c}} (~33/32 = 51.704{{c}})
* POTE: ~5/4 = 400.000{{c}}, ~32/21 = 748.345{{c}} (~33/32 = 51.655{{c}}) -->


{{Optimal ET sequence|legend=0| 21, 24 }}
{{Optimal ET sequence|legend=0| 21, 24 }}
Line 537: Line 465:
* WE: ~5/4 = 399.8855{{c}}, ~32/21 = 748.2378{{c}} (~33/32 = 51.5332{{c}})
* WE: ~5/4 = 399.8855{{c}}, ~32/21 = 748.2378{{c}} (~33/32 = 51.5332{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~32/21 = 748.4655{{c}} (~33/32 = 51.5345{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~32/21 = 748.4655{{c}} (~33/32 = 51.5345{{c}})
<!-- * CTE: ~5/4 = 400.000{{c}}, ~32/21 = 748.525{{c}} (~33/32 = 51.475{{c}})
* POTE: ~5/4 = 400.000{{c}}, ~32/21 = 748.452{{c}} (~33/32 = 51.548{{c}}) -->


{{Optimal ET sequence|legend=0| 21, 24 }}
{{Optimal ET sequence|legend=0| 21, 24 }}
Line 558: Line 484:
* [[CWE]]: ~5/4 = 400.0000{{c}}, ~28/25 = 176.2984{{c}} (~49/48 = 47.4031{{c}})
* [[CWE]]: ~5/4 = 400.0000{{c}}, ~28/25 = 176.2984{{c}} (~49/48 = 47.4031{{c}})
: error map: {{val| 0.000 +3.239 +13.686 +7.473 }}
: error map: {{val| 0.000 +3.239 +13.686 +7.473 }}
<!-- * [[CTE]]: ~5/4 = 400.000{{c}}, ~28/25 = 175.359{{c}}
: [[error map]]: {{val| 0.000 -0.521 +13.686 +6.533 }}
* [[POTE]]: ~5/4 = 400.000{{c}}, ~28/25 = 176.646{{c}}
: error map: {{val| 0.000 +4.629 +13.686 +7.820 }} -->


{{Optimal ET sequence|legend=1| 6, 21, 27, 75c, 102ccd, 129bccd }}
{{Optimal ET sequence|legend=1| 6, 21, 27, 75c, 102ccd, 129bccd }}
Line 577: Line 499:
* WE: ~5/4 = 398.6615{{c}}, ~11/10 = 176.3886{{c}} (~49/48 = 45.8843{{c}})
* WE: ~5/4 = 398.6615{{c}}, ~11/10 = 176.3886{{c}} (~49/48 = 45.8843{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~11/10 = 176.5471{{c}} (~49/48 = 46.9059{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~11/10 = 176.5471{{c}} (~49/48 = 46.9059{{c}})
<!-- * CTE: ~5/4 = 400.000{{c}}, ~11/10 = 175.053{{c}}
* POTE: ~5/4 = 400.000{{c}}, ~11/10 = 176.981{{c}} -->


{{Optimal ET sequence|legend=0| 6, 21, 27e }}
{{Optimal ET sequence|legend=0| 6, 21, 27e }}
Line 594: Line 514:
* WE: ~5/4 = 398.8612{{c}}, ~11/10 = 176.0486{{c}} (~49/48 = 46.7640{{c}})
* WE: ~5/4 = 398.8612{{c}}, ~11/10 = 176.0486{{c}} (~49/48 = 46.7640{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~11/10 = 176.3326{{c}} (~49/48 = 47.3348{{c}})
* CWE: ~5/4 = 400.0000{{c}}, ~11/10 = 176.3326{{c}} (~49/48 = 47.3348{{c}})
<!-- * CTE: ~5/4 = 400.000{{c}}, ~11/10 = 175.252{{c}}
* POTE: ~5/4 = 400.000{{c}}, ~11/10 = 176.551{{c}} -->


{{Optimal ET sequence|legend=0| 6, 21, 27e }}
{{Optimal ET sequence|legend=0| 6, 21, 27e }}
Line 615: Line 533:
* [[CWE]]: ~54/49 = 200.0000{{c}}, ~45/28 = 854.7144{{c}} (~36/35 = 54.7144{{c}})
* [[CWE]]: ~54/49 = 200.0000{{c}}, ~45/28 = 854.7144{{c}} (~36/35 = 54.7144{{c}})
: error map: {{val| 0.000 +7.474 +13.686 -4.683 }}
: error map: {{val| 0.000 +7.474 +13.686 -4.683 }}
<!-- * [[CTE]]: ~54/49 = 200.000{{c}}, ~45/28 = 853.190{{c}} (~36/35 = 53.190{{c}})
: [[error map]]: {{val| 0.000 +4.425 +13.686 -9.256 }}
* [[POTE]]: ~54/49 = 200.000{{c}}, ~45/28 = 855.485{{c}} (~36/35 = 55.485{{c}})
: error map: {{val| 0.000 +9.015 +13.686 -2.371 }} -->


{{Optimal ET sequence|legend=1| 18, 24, 42 }}
{{Optimal ET sequence|legend=1| 18, 24, 42 }}
Line 634: Line 548:
* WE: ~54/49 = 199.5188{{c}}, ~18/11 = 853.1623{{c}} (~36/35 = 55.0872{{c}})
* WE: ~54/49 = 199.5188{{c}}, ~18/11 = 853.1623{{c}} (~36/35 = 55.0872{{c}})
* CWE: ~54/49 = 200.0000{{c}}, ~18/11 = 854.3545{{c}} (~36/35 = 54.3545{{c}})
* CWE: ~54/49 = 200.0000{{c}}, ~18/11 = 854.3545{{c}} (~36/35 = 54.3545{{c}})
<!-- * CTE: ~54/49 = 200.000{{c}}, ~18/11 = 852.597{{c}} (~36/35 = 52.597{{c}})
* POTE: ~54/49 = 200.000{{c}}, ~18/11 = 855.220{{c}} (~36/35 = 55.220{{c}}) -->


{{Optimal ET sequence|legend=0| 18e, 24, 42e, 66ce, 108bccee }}
{{Optimal ET sequence|legend=0| 18e, 24, 42e, 66ce, 108bccee }}
Line 657: Line 569:
* [[CWE]]: ~49/45 = 133.3333{{c}}, ~3/2 = 705.5157{{c}} (~36/35 = 38.8490{{c}})
* [[CWE]]: ~49/45 = 133.3333{{c}}, ~3/2 = 705.5157{{c}} (~36/35 = 38.8490{{c}})
: error map: {{val| 0.000 +3.561 +13.686 +3.356 }}
: error map: {{val| 0.000 +3.561 +13.686 +3.356 }}
<!-- * [[CTE]]: ~49/45 = 133.333{{c}}, ~3/2 = 702.004{{c}} (~36/35 = 35.338{{c}})
: [[error map]]: {{val| 0.000 +0.049 +13.686 -0.155 }}
* [[POTE]]: ~49/45 = 133.333{{c}}, ~3/2 = 707.167{{c}} (~36/35 = 40.501{{c}})
: error map: {{val| 0.000 +5.212 +13.686 +5.008 }} -->


{{Optimal ET sequence|legend=1| 9, 18, 27, 63c, 90cc }}
{{Optimal ET sequence|legend=1| 9, 18, 27, 63c, 90cc }}
Line 676: Line 584:
* WE: ~12/11 = 132.9553{{c}}, ~3/2 = 704.7217{{c}} (~36/35 = 39.9453{{c}})
* WE: ~12/11 = 132.9553{{c}}, ~3/2 = 704.7217{{c}} (~36/35 = 39.9453{{c}})
* CWE: ~12/11 = 133.3333{{c}}, ~3/2 = 704.5723{{c}} (~36/35 = 37.9056{{c}})
* CWE: ~12/11 = 133.3333{{c}}, ~3/2 = 704.5723{{c}} (~36/35 = 37.9056{{c}})
<!-- * CTE: ~12/11 = 133.333{{c}}, ~3/2 = 699.622{{c}} (~36/35 = 32.955{{c}})
* POTE: ~12/11 = 133.333{{c}}, ~3/2 = 706.726{{c}} (~36/35 = 40.059{{c}}) -->


{{Optimal ET sequence|legend=0| 9, 18e, 27e, 63cee }}
{{Optimal ET sequence|legend=0| 9, 18e, 27e, 63cee }}
Line 693: Line 599:
* WE: ~14/13 = 133.0143{{c}}, ~3/2 = 705.1969{{c}} (~36/35 = 40.1256{{c}})
* WE: ~14/13 = 133.0143{{c}}, ~3/2 = 705.1969{{c}} (~36/35 = 40.1256{{c}})
* CWE: ~14/13 = 133.3333{{c}}, ~3/2 = 705.0176{{c}} (~36/35 = 38.3510{{c}})
* CWE: ~14/13 = 133.3333{{c}}, ~3/2 = 705.0176{{c}} (~36/35 = 38.3510{{c}})
<!-- * CTE: ~14/13 = 133.333{{c}}, ~3/2 = 700.433{{c}} (~36/35 = 33.766{{c}})
* POTE: ~14/13 = 133.333{{c}}, ~3/2 = 706.889{{c}} (~36/35 = 40.222{{c}}) -->


{{Optimal ET sequence|legend=0| 9, 18e, 27e }}
{{Optimal ET sequence|legend=0| 9, 18e, 27e }}
Line 714: Line 618:
* [[CWE]]: ~5/4 = 400.0000{{c}}, ~48/35 = 500.9654{{c}} (~15/14 = 100.9654{{c}})
* [[CWE]]: ~5/4 = 400.0000{{c}}, ~48/35 = 500.9654{{c}} (~15/14 = 100.9654{{c}})
: error map: {{val| 0.000 +3.561 +13.686 +3.356 }}
: error map: {{val| 0.000 +3.561 +13.686 +3.356 }}
<!-- * [[CTE]]: ~5/4 = 400.000{{c}}, ~48/35 = 498.637{{c}} (~15/14 = 98.637{{c}})
: [[error map]]: {{val| 0.000 -6.045 +13.686 +28.447 }}
* [[POTE]]: ~5/4 = 400.000{{c}}, ~48/35 = 501.980{{c}} (~15/14 = 101.980{{c}})
: error map: {{val| 0.000 +3.986 +13.686 +35.134 }} -->


{{Optimal ET sequence|legend=1| 3b, 9bd, 12 }}
{{Optimal ET sequence|legend=1| 3b, 9bd, 12 }}

Revision as of 16:02, 21 August 2025

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The 5-limit parent comma for the augmented family is 128/125, the diesis. The period is 1/3 octave, and this is what is used for 5/4, the classical major third. The generator can be taken as a fifth or a semitone, and 12edo, with its excellent fifth, is an obvious tuning for 5-limit augmented, though a sharper fifth might be preferred to go with the sharp third.

Augmented

Subgroup: 2.3.5

Comma list: 128/125

Mapping: [⟨3 0 7], ⟨0 1 0]]

mapping generators: ~5/4, ~3

Optimal tunings:

  • WE: ~5/4 = 399.0128 ¢, ~3/2 = 704.8937 ¢ (~16/15 = 93.1320 ¢)
error map: ⟨-2.962 -0.023 +6.776]
  • CWE: ~5/4 = 400.0000 ¢, ~3/2 = 705.0691 ¢ (~16/15 = 94.9309 ¢)
error map: ⟨0.000 +3.114 +13.686]

Optimal ET sequence: 3, 9, 12, 27, 39, 51c, 90cc

Badness (Sintel): 0.523

Overview to extensions

The second comma of the normal comma list defines which 7-limit family member we are looking at. August adds 36/35, augene 64/63, hexe 256/245, hemiaug 245/243, and triforce 49/48. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quartertones instead of semitones.

August

Subgroup: 2.3.5.7

Comma list: 36/35, 128/125

Mapping: [⟨3 0 7 -1], ⟨0 1 0 2]]

Optimal tunings:

  • WE: ~5/4 = 399.1036 ¢, ~3/2 = 694.4509 ¢ (~16/15 = 103.7564 ¢)
error map: ⟨-2.689 -10.193 +7.412 +15.594]
  • CWE: ~5/4 = 400.0000 ¢, ~3/2 = 694.6812 ¢ (~16/15 = 105.3188 ¢)
error map: ⟨0.000 -7.274 +13.686 +20.537]

Optimal ET sequence: 9, 12, 45cd

Badness (Sintel): 0.670

11-limit

Subgroup: 2.3.5.7.11

Comma list: 36/35, 45/44, 56/55

Mapping: [⟨3 0 7 -1 1], ⟨0 1 0 2 2]]

Optimal tunings:

  • WE: ~5/4 = 398.9225 ¢, ~3/2 = 690.6486 ¢ (~16/15 = 107.1966 ¢)
  • CWE: ~5/4 = 400.0000 ¢, ~3/2 = 690.8519 ¢ (~16/15 = 109.1481 ¢)

Optimal ET sequence: 9, 12, 21, 33e

Badness (Sintel): 0.668

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 27/26, 36/35, 45/44, 56/55

Mapping: [⟨3 0 7 -1 1 -3], ⟨0 1 0 2 2 3]]

Optimal tunings:

  • WE: ~5/4 = 399.0956 ¢, ~3/2 = 687.2261 ¢ (~16/15 = 110.9651 ¢)
  • CWE: ~5/4 = 400.0000 ¢, ~3/2 = 687.5057 ¢ (~16/15 = 112.4943 ¢)

Optimal ET sequence: 9, 12f, 21, 33ef

Badness (Sintel): 0.762

Augustus

Subgroup: 2.3.5.7.11.13

Comma list: 26/25, 36/35, 45/44, 56/55

Mapping: [⟨3 0 7 -1 1 11], ⟨0 1 0 2 2 0]]

Optimal tunings:

  • WE: ~5/4 = 400.4230 ¢, ~3/2 = 686.0809 ¢ (~16/15 = 114.7650 ¢)
  • CWE: ~5/4 = 400.0000 ¢, ~3/2 = 685.8446 ¢ (~16/15 = 114.1554 ¢)

Optimal ET sequence: 9, 12

Badness (Sintel): 0.919

Augene

Main article: Augene

Subgroup: 2.3.5.7

Comma list: 64/63, 126/125

Mapping: [⟨3 0 7 18], ⟨0 1 0 -2]]

Optimal tunings:

  • WE: ~5/4 = 398.7461 ¢, ~3/2 = 707.0335 ¢ (~21/20 = 90.4587 ¢)
error map: ⟨-3.762 +1.317 +4.909 +2.060]
  • CWE: ~5/4 = 400.0000 ¢, ~3/2 = 709.3249 ¢ (~21/20 = 90.6751 ¢)
error map: ⟨0.000 +7.370 +13.686 +12.524]

Optimal ET sequence: 12, 27, 39d, 66cd

Badness (Sintel): 0.628

11-limit

Subgroup: 2.3.5.7.11

Comma list: 56/55, 64/63, 100/99

Mapping: [⟨3 0 7 18 20], ⟨0 1 0 -2 -2]]

Optimal tunings:

  • WE: ~5/4 = 398.4962 ¢, ~3/2 = 708.5030 ¢ (~21/20 = 88.4895 ¢)
  • CWE: ~5/4 = 400.0000 ¢, ~3/2 = 711.6031 ¢ (~21/20 = 88.3969 ¢)

Optimal ET sequence: 12, 15, 27e

Badness (Sintel): 0.648

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 40/39, 56/55, 64/63, 66/65

Mapping: [⟨3 0 7 18 20 16], ⟨0 1 0 -2 -2 -1]]

Optimal tunings:

  • WE: ~5/4 = 398.0488 ¢, ~3/2 = 708.5402 ¢ (~21/20 = 87.5574 ¢)
  • CWE: ~5/4 = 400.0000 ¢, ~3/2 = 712.6704 ¢ (~21/20 = 87.3296 ¢)

Optimal ET sequence: 12f, 15, 27eff

Badness (Sintel): 0.859

Ogene

Subgroup: 2.3.5.7.11.13

Comma list: 56/55, 64/63, 91/90, 100/99

Mapping: [⟨3 0 7 18 20 -8], ⟨0 1 0 -2 -2 4]]

Optimal tunings:

  • WE: ~5/4 = 398.6473 ¢, ~3/2 = 710.1987 ¢ (~21/20 = 87.0959 ¢)
  • CWE: ~5/4 = 400.0000 ¢, ~3/2 = 712.5057 ¢ (~21/20 = 87.4943 ¢)

Optimal ET sequence: 12, 15, 27e, 69bceef

Badness (Sintel): 0.946

Agene

Subgroup: 2.3.5.7.11.13

Comma list: 56/55, 64/63, 78/77, 100/99

Mapping: [⟨3 0 7 18 20 35], ⟨0 1 0 -2 -2 -5]]

Optimal tunings:

  • WE: ~5/4 = 398.5229 ¢, ~3/2 = 707.0562 ¢ (~21/20 = 89.9897 ¢)
  • CWE: ~5/4 = 400.0000 ¢, ~3/2 = 710.1903 ¢ (~21/20 = 89.8097 ¢)

Optimal ET sequence: 12f, 27e, 66cdeeef

Badness (Sintel): 0.955

Eugene

Subgroup: 2.3.5.7.11

Comma list: 55/54, 64/63, 77/75

Mapping: [⟨3 0 7 18 -4], ⟨0 1 0 -2 3]]

Optimal tunings:

  • WE: ~5/4 = 399.1743 ¢, ~3/2 = 712.6763 ¢ (~21/20 = 85.6723 ¢)
  • CWE: ~5/4 = 400.0000 ¢, ~3/2 = 713.9414 ¢ (~21/20 = 86.0586 ¢)

Optimal ET sequence: 12e, 15, 27, 42

Badness (Sintel): 1.18

Inflated

Subgroup: 2.3.5.7

Comma list: 28/27, 128/125

Mapping: [⟨3 0 7 -6], ⟨0 1 0 3]]

Optimal tunings:

  • WE: ~5/4 = 398.4023 ¢, ~3/2 = 719.8327 ¢ (~25/24 = 76.9719 ¢)
error map: ⟨-3.762 +1.317 +4.909 +2.060]
  • CWE: ~5/4 = 400.0000 ¢, ~3/2 = 721.0196 ¢ (~25/24 = 78.9804 ¢)
error map: ⟨0.000 +19.065 +13.686 -5.767]

Optimal ET sequence: 3d, 12d, 15

Badness (Sintel): 1.39

11-limit

Subgroup: 2.3.5.7.11

Comma list: 28/27, 55/54, 128/125

Mapping: [⟨3 0 7 -6 -4], ⟨0 1 0 3 3]]

Optimal tunings:

  • WE: ~5/4 = 398.4016 ¢, ~3/2 = 719.7758 ¢ (~25/24 = 77.0275 ¢)
  • CWE: ~5/4 = 400.0000 ¢, ~3/2 = 720.9386 ¢ (~25/24 = 79.0614 ¢)

Optimal ET sequence: 3de, 12de, 15

Badness (Sintel): 1.03

Deflated

Subgroup: 2.3.5.7

Comma list: 21/20, 128/125

Mapping: [⟨3 0 7 13], ⟨0 1 0 -1]]

Optimal tunings:

  • WE: ~5/4 = 401.9566 ¢, ~3/2 = 684.9634 ¢ (~16/15 = 118.9497 ¢)
error map: ⟨+5.870 -11.122 +27.382 -34.224]
  • CWE: ~5/4 = 400.0000 ¢, ~3/2 = 682.2587 ¢ (~16/15 = 117.7413 ¢)
error map: ⟨0.000 -19.696 +13.686 -51.085]

Optimal ET sequence: 3, 6b, 9

Badness (Sintel): 1.50

11-limit

Subgroup: 2.3.5.7.11

Comma list: 21/20, 33/32, 128/125

Mapping: [⟨3 0 7 13 15], ⟨0 1 0 -1 -1]]

Optimal tunings:

  • WE: ~5/4 = 402.1799 ¢, ~3/2 = 683.7477 ¢ (~16/15 = 120.6120 ¢)
  • CWE: ~5/4 = 400.0000 ¢, ~3/2 = 680.0162 ¢ (~16/15 = 119.9838 ¢)

Optimal ET sequence: 3, 6b, 9

Badness (Sintel): 1.23

Hexe

Subgroup: 2.3.5.7

Comma list: 50/49, 128/125

Mapping: [⟨6 0 14 17], ⟨0 1 0 0]]

mapping generators: ~28/25, ~3

Optimal tunings:

  • WE: ~28/25 = 199.0488 ¢, ~3/2 = 707.5815 ¢ (~25/24 = 88.6137 ¢)
error map: ⟨+5.870 -11.122 +27.382 -34.224]
  • CWE: ~28/25 = 200.0000 ¢, ~3/2 = 708.6907 ¢ (~25/24 = 91.3093 ¢)
error map: ⟨0.000 +6.735 +13.686 +31.174]

Optimal ET sequence: 6, 12, 30d, 42dd, 54cdd

Badness (Sintel): 1.46

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 56/55, 125/121

Mapping: [⟨6 0 14 17 21], ⟨0 1 0 0 0]]

Optimal tunings:

  • WE: ~28/25 = 198.6942 ¢, ~3/2 = 709.6404 ¢ (~25/24 = 85.1362 ¢)
  • CWE: ~28/25 = 200.0000 ¢, ~3/2 = 711.8043 ¢ (~25/24 = 88.1957 ¢)

Optimal ET sequence: 6, 12, 30dee, 42ddeee

Badness (Sintel): 1.27

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 50/49, 56/55, 66/65, 105/104

Mapping: [⟨6 0 14 17 21 13], ⟨0 1 0 0 0 1]]

Optimal tunings:

  • WE: ~28/25 = 198.4492 ¢, ~3/2 = 704.4994 ¢ (~25/24 = 89.2973 ¢)
  • CWE: ~28/25 = 200.0000 ¢, ~3/2 = 706.6050 ¢ (~16/15 = 93.3950 ¢)

Optimal ET sequence: 6f, 12f

Badness (Sintel): 1.49

Triforce

triforce9.jpg
Lattice of triforce

Subgroup: 2.3.5.7

Comma list: 49/48, 128/125

Mapping: [⟨3 0 7 6], ⟨0 2 0 1]]

mapping generators: ~5/4, ~7/4

Optimal tunings:

  • WE: ~5/4 = 399.7480 ¢, ~7/4 = 952.3507 ¢ (~35/32 = 152.8547 ¢)
error map: ⟨-0.756 +2.746 +11.922 -17.987]
  • CWE: ~5/4 = 400.0000 ¢, ~7/4 = 952.7463 ¢ (~35/32 = 152.7463 ¢)
error map: ⟨0.000 +3.538 +13.686 -16.080]

Optimal ET sequence: 6, 9, 15, 24, 39

Badness (Sintel): 1.39

11-limit

Subgroup: 2.3.5.7.11

Comma list: 49/48, 56/55, 77/75

Mapping: [⟨3 0 7 6 8], ⟨0 2 0 1 1]]

Optimal tunings:

  • WE: ~5/4 = 399.7654 ¢, ~7/4 = 952.3730 ¢ (~12/11 = 152.8421 ¢)
  • CWE: ~5/4 = 400.0000 ¢, ~7/4 = 952.7447 ¢ (~12/11 = 152.7447 ¢)

Optimal ET sequence: 6, 9, 15, 24, 39

Badness (Sintel): 0.865

Music

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 56/55, 66/65, 77/75

Mapping: [⟨3 0 7 6 8 4], ⟨0 2 0 1 1 3]]

Optimal tunings:

  • WE: ~5/4 = 399.7107 ¢, ~7/4 = 950.9983 ¢ (~12/11 = 151.5768 ¢)
  • CWE: ~5/4 = 400.0000 ¢, ~7/4 = 951.4465 ¢ (~12/11 = 151.4465 ¢)

Optimal ET sequence: 6f, 9, 15, 24

Badness (Sintel): 0.837

Scales
  • triphi, Triforce[9] with L:s = phi

Semitriforce

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 56/55, 77/75, 507/500

Mapping: [⟨6 0 14 12 16 27], ⟨0 2 0 1 1 -1]]

mapping generators: ~44/39, ~7/4

Optimal tunings:

  • WE: ~44/39 = 199.8321 ¢, ~7/4 = 952.5580 ¢ (~40/39 = 46.6024 ¢)
  • CWE: ~44/39 = 200.0000 ¢, ~7/4 = 953.2005 ¢ (~40/39 = 46.7995 ¢)

Optimal ET sequence: 6, 18bd, 24

Badness (Sintel): 2.44

Hemiaug

Subgroup: 2.3.5.7

Comma list: 128/125, 245/243

Mapping: [⟨3 1 7 -1], ⟨0 2 0 5]]

mapping generators: ~5/4, ~14/9

Optimal tunings:

  • WE: ~5/4 = 398.9278 ¢, ~14/9 = 752.8583 ¢ (~36/35 = 44.9973 ¢)
error map: ⟨-3.217 +2.689 +6.181 -3.462]
  • CWE: ~5/4 = 400.0000 ¢, ~14/9 = 754.2078 ¢ (~36/35 = 45.7922 ¢)
error map: ⟨0.000 +6.461 +13.686 +2.213]

Optimal ET sequence: 24, 27

Badness (Sintel): 1.78

11-limit

Subgroup: 2.3.5.7.11

Comma list: 56/55, 128/125, 243/242

Mapping: [⟨3 1 7 -1 1], ⟨0 2 0 5 5]]

Optimal tunings:

  • WE: ~5/4 = 398.8946 ¢, ~14/9 = 752.1272 ¢ (~36/35 = 45.6619 ¢)
  • CWE: ~5/4 = 400.0000 ¢, ~14/9 = 753.5000 ¢ (~36/35 = 46.5000 ¢)

Optimal ET sequence: 24, 27e, 51ce

Badness (Sintel): 1.26

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 56/55, 91/90, 128/125, 245/243

Mapping: [⟨3 1 7 -1 1 13], ⟨0 2 0 5 5 -1]]

Optimal tunings:

  • WE: ~5/4 = 399.1053 ¢, ~14/9 = 752.0643 ¢ (~36/35 = 46.1463 ¢)
  • CWE: ~5/4 = 400.0000 ¢, ~14/9 = 753.3806 ¢ (~36/35 = 46.6194 ¢)

Optimal ET sequence: 24, 27e, 51ce

Badness (Sintel): 1.25

Hemiug

Subgroup: 2.3.5.7

Comma list: 128/125, 1323/1250

Mapping: [⟨3 1 7 14], ⟨0 2 0 -3]]

mapping generators: ~5/4, ~32/21

Optimal tunings:

  • WE: ~5/4 = 400.1805 ¢, ~32/21 = 748.2436 ¢ (~21/20 = 52.1174 ¢)
error map: ⟨+0.542 -5.287 +14.950 -11.030]
  • CWE: ~5/4 = 400.0000 ¢, ~32/21 = 747.9138 ¢ (~21/20 = 52.0862 ¢)
error map: ⟨0.000 -6.127 +13.686 -12.567]

Optimal ET sequence: 21, 24, 45c

Badness (Sintel): 3.49

11-limit

Subgroup: 2.3.5.7.11

Comma list: 56/55, 128/125, 1323/1250

Mapping: [⟨3 1 7 14 16], ⟨0 2 0 -3 -3]]

Optimal tunings:

  • WE: ~5/4 = 400.0637 ¢, ~32/21 = 748.4638 ¢ (~33/32 = 51.6637 ¢)
  • CWE: ~5/4 = 400.0000 ¢, ~32/21 = 748.3383 ¢ (~33/32 = 51.6617 ¢)

Optimal ET sequence: 21, 24

Badness (Sintel): 2.25

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 56/55, 66/65, 105/104, 507/500

Mapping: [⟨3 1 7 14 16 13], ⟨0 2 0 -3 -3 -1]]

Optimal tunings:

  • WE: ~5/4 = 399.8855 ¢, ~32/21 = 748.2378 ¢ (~33/32 = 51.5332 ¢)
  • CWE: ~5/4 = 400.0000 ¢, ~32/21 = 748.4655 ¢ (~33/32 = 51.5345 ¢)

Optimal ET sequence: 21, 24

Badness (Sintel): 1.75

Oodako

Subgroup: 2.3.5.7

Comma list: 128/125, 2401/2400

Mapping: [⟨3 3 7 8], ⟨0 4 0 1]]

mapping generators: ~5/4, ~28/25

Optimal tunings:

  • WE: ~5/4 = 399.0296 ¢, ~28/25 = 176.2174 ¢ (~49/48 = 46.5949 ¢)
error map: ⟨-2.911 +0.004 +6.894 -0.371]
  • CWE: ~5/4 = 400.0000 ¢, ~28/25 = 176.2984 ¢ (~49/48 = 47.4031 ¢)
error map: ⟨0.000 +3.239 +13.686 +7.473]

Optimal ET sequence: 6, 21, 27, 75c, 102ccd, 129bccd

Badness (Sintel): 2.86

11-limit

Subgroup: 2.3.5.7.11

Comma list: 56/55, 128/125, 2401/2400

Mapping: [⟨3 3 7 8 10], ⟨0 4 0 1 1]]

Optimal tunings:

  • WE: ~5/4 = 398.6615 ¢, ~11/10 = 176.3886 ¢ (~49/48 = 45.8843 ¢)
  • CWE: ~5/4 = 400.0000 ¢, ~11/10 = 176.5471 ¢ (~49/48 = 46.9059 ¢)

Optimal ET sequence: 6, 21, 27e

Badness (Sintel): 1.96

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 56/55, 78/77, 128/125, 507/500

Mapping: [⟨3 3 7 8 10 12], ⟨0 4 0 1 1 -2]]

Optimal tunings:

  • WE: ~5/4 = 398.8612 ¢, ~11/10 = 176.0486 ¢ (~49/48 = 46.7640 ¢)
  • CWE: ~5/4 = 400.0000 ¢, ~11/10 = 176.3326 ¢ (~49/48 = 47.3348 ¢)

Optimal ET sequence: 6, 21, 27e

Badness (Sintel): 1.75

Hemisemiaug

Subgroup: 2.3.5.7

Comma list: 128/125, 12005/11664

Mapping: [⟨6 1 14 4], ⟨0 2 0 3]]

mapping generators: ~54/49, ~45/28

Optimal tunings:

  • WE: ~54/49 = 199.5469 ¢, ~45/28 = 853.5468 ¢ (~36/35 = 55.3594 ¢)
error map: ⟨-2.719 +4.686 +7.342 -9.998]
  • CWE: ~54/49 = 200.0000 ¢, ~45/28 = 854.7144 ¢ (~36/35 = 54.7144 ¢)
error map: ⟨0.000 +7.474 +13.686 -4.683]

Optimal ET sequence: 18, 24, 42

Badness (Sintel): 5.34

11-limit

Subgroup: 2.3.5.7.11

Comma list: 56/55, 128/125, 3773/3645

Mapping: [⟨6 1 14 4 8], ⟨0 2 0 3 3]]

Optimal tunings:

  • WE: ~54/49 = 199.5188 ¢, ~18/11 = 853.1623 ¢ (~36/35 = 55.0872 ¢)
  • CWE: ~54/49 = 200.0000 ¢, ~18/11 = 854.3545 ¢ (~36/35 = 54.3545 ¢)

Optimal ET sequence: 18e, 24, 42e, 66ce, 108bccee

Badness (Sintel): 2.67

Niner

Niner gives 9 as the complexity of an otonal tetrad, tying it with augene as a temperament supported by 27edo. Niner[18], therefore, has nine such tetrads.

Subgroup: 2.3.5.7

Comma list: 128/125, 686/675

Mapping: [⟨9 0 21 11], ⟨0 1 0 1]]

mapping generators: ~49/45, ~3

Optimal tunings:

  • WE: ~49/45 = 133.0272 ¢, ~3/2 = 705.5438 ¢ (~36/35 = 40.4075 ¢)
error map: ⟨-2.755 +0.834 +7.259 -2.737]
  • CWE: ~49/45 = 133.3333 ¢, ~3/2 = 705.5157 ¢ (~36/35 = 38.8490 ¢)
error map: ⟨0.000 +3.561 +13.686 +3.356]

Optimal ET sequence: 9, 18, 27, 63c, 90cc

Badness (Sintel): 1.70

11-limit

Subgroup: 2.3.5.7.11

Comma list: 56/55, 128/125, 540/539

Mapping: [⟨9 0 21 11 17], ⟨0 1 0 1 1]]

Optimal tunings:

  • WE: ~12/11 = 132.9553 ¢, ~3/2 = 704.7217 ¢ (~36/35 = 39.9453 ¢)
  • CWE: ~12/11 = 133.3333 ¢, ~3/2 = 704.5723 ¢ (~36/35 = 37.9056 ¢)

Optimal ET sequence: 9, 18e, 27e, 63cee

Badness (Sintel): 1.15

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 56/55, 78/77, 91/90, 128/125

Mapping: [⟨9 0 21 11 17 19], ⟨0 1 0 1 1 1]]

Optimal tunings:

  • WE: ~14/13 = 133.0143 ¢, ~3/2 = 705.1969 ¢ (~36/35 = 40.1256 ¢)
  • CWE: ~14/13 = 133.3333 ¢, ~3/2 = 705.0176 ¢ (~36/35 = 38.3510 ¢)

Optimal ET sequence: 9, 18e, 27e

Badness (Sintel): 0.998

Trug

Subgroup: 2.3.5.7

Comma list: 128/125, 360/343

Mapping: [⟨3 1 7 6], ⟨0 3 0 2]]

mapping generators: ~5/4, ~48/35

Optimal tunings:

  • WE: ~5/4 = 398.2337 ¢, ~48/35 = 499.7635 ¢ (~15/14 = 101.5299 ¢)
error map: ⟨-2.755 +0.834 +7.259 -2.737]
  • CWE: ~5/4 = 400.0000 ¢, ~48/35 = 500.9654 ¢ (~15/14 = 100.9654 ¢)
error map: ⟨0.000 +3.561 +13.686 +3.356]

Optimal ET sequence: 3b, 9bd, 12

Badness (Sintel): 3.50

External links

Retrieved from "https://en.xen.wiki/index.php?title=Augmented_family&oldid=207913"