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Augmented family: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings, per community consensus
Line 16: Line 16:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~5/4 = 400.000, ~3/2 = 701.955 (~16/15 = 98.045)
* [[WE]]: ~5/4 = 399.0128{{c}}, ~3/2 = 704.8937{{c}} (~16/15 = 93.1320{{c}})
: [[error map]]: {{val| -2.962 -0.023 +6.776 }}
* [[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 }}
<!-- * [[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 }}
: [[error map]]: {{val| 0.000 0.000 +13.686 }}
* [[POTE]]: ~5/4 = 400.000, ~3/2 = 706.638 (~16/15 = 93.362)
* [[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 }}
: error map: {{val| 0.000 +4.683 +13.686 }} -->


{{Optimal ET sequence|legend=1| 3, 12, 27, 39, 51c, 90cc }}
{{Optimal ET sequence|legend=1| 3, 9, 12, 27, 39, 51c, 90cc }}


[[Badness]] (Smith): 0.022315
[[Badness]] (Sintel): 0.523


=== Overview to extensions ===
=== Overview to extensions ===
Line 35: Line 39:
{{Mapping|legend=1| 3 0 7 -1 | 0 1 0 2 }}
{{Mapping|legend=1| 3 0 7 -1 | 0 1 0 2 }}


[[Optimal tuning]]s:
[[Optimal tuning]]s:  
* [[CTE]]: ~5/4 = 400.000, ~3/2 = 692.124 (~16/15 = 107.876)
* [[WE]]: ~5/4 = 399.1036{{c}}, ~3/2 = 694.4509{{c}} (~16/15 = 103.7564{{c}})
: [[error map]]: {{val| -2.689 -10.193 +7.412 +15.594 }}
* [[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 }}
<!-- * [[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 }}
: [[error map]]: {{val| 0.000 -9.831 +13.686 +15.422 }}
* [[POTE]]: ~5/4 = 400.000, ~3/2 = 696.011 (~16/15 = 103.989)
* [[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 }}
: 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 }}


[[Badness]] (Smith): 0.026459
[[Badness]] (Sintel): 0.670


=== 11-limit ===
=== 11-limit ===
Line 52: Line 60:
Mapping: {{mapping| 3 0 7 -1 1 | 0 1 0 2 2 }}
Mapping: {{mapping| 3 0 7 -1 1 | 0 1 0 2 2 }}


Optimal tunings:
Optimal tunings:  
* CTE: ~5/4 = 400.000, ~3/2 = 687.685 (~16/15 = 112.315)
* WE: ~5/4 = 398.9225{{c}}, ~3/2 = 690.6486{{c}} (~16/15 = 107.1966{{c}})
* POTE: ~5/4 = 400.000, ~3/2 = 692.514 (~16/15 = 107.486)
* 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, 45cde }}
{{Optimal ET sequence|legend=0| 9, 12, 21, 33e }}


Badness (Smith): 0.020191
Badness (Sintel): 0.668


==== 13-limit ====
==== 13-limit ====
Line 68: Line 78:


Optimal tunings:  
Optimal tunings:  
* CTE: ~5/4 = 400.000, ~3/2 = 685.084 (~16/15 = 114.916)
* WE: ~5/4 = 399.0956{{c}}, ~3/2 = 687.2261{{c}} (~16/15 = 110.9651{{c}})
* POTE: ~5/4 = 400.000, ~3/2 = 688.783 (~16/15 = 111.217)
* 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, 54bceeff }}
{{Optimal ET sequence|legend=0| 9, 12f, 21, 33ef }}


Badness (Smith): 0.018448
Badness (Sintel): 0.762


==== Augustus ====
==== Augustus ====
Line 83: Line 95:


Optimal tunings:  
Optimal tunings:  
* CTE: ~5/4 = 400.000, ~3/2 = 687.685 (~16/15 = 112.315)
* WE: ~5/4 = 400.4230{{c}}, ~3/2 = 686.0809{{c}} (~16/15 = 114.7650{{c}})
* POTE: ~5/4 = 400.000, ~3/2 = 685.356 (~16/15 = 114.644)
* 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, 21f }}
{{Optimal ET sequence|legend=0| 9, 12 }}


Badness (Smith): 0.022236
Badness (Sintel): 0.919


== Augene ==
== Augene ==
Line 100: Line 114:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~5/4 = 400.000, ~3/2 = 709.595 (~21/20 = 90.405)
* [[WE]]: ~5/4 = 398.7461{{c}}, ~3/2 = 707.0335{{c}} (~21/20 = 90.4587{{c}})
: [[error map]]: {{val| -3.762 +1.317 +4.909 +2.060 }}
* [[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 }}
<!-- * [[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 }}
: [[error map]]: {{val| 0.000 +7.640 +13.686 +11.984 }}
* [[POTE]]: ~5/4 = 400.000, ~3/2 = 709.257 (~21/20 = 90.743)
* [[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 }}
: 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 }}


[[Badness]] (Smith): 0.024816
[[Badness]] (Sintel): 0.628


=== 11-limit ===
=== 11-limit ===
Line 117: Line 135:


Optimal tunings:  
Optimal tunings:  
* CTE: ~5/4 = 400.000, ~3/2 = 713.570 (~21/20 = 86.430)
* WE: ~5/4 = 398.4962{{c}}, ~3/2 = 708.5030{{c}} (~21/20 = 88.4895{{c}})
* POTE: ~5/4 = 400.000, ~3/2 = 711.177 (~21/20 = 88.823)
* 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 }}


Badness (Smith): 0.019613
Badness (Sintel): 0.648


==== 13-limit ====
==== 13-limit ====
Line 132: Line 152:


Optimal tunings:  
Optimal tunings:  
* CTE: ~5/4 = 400.000, ~3/2 = 716.123 (~21/20 = 83.877)
* WE: ~5/4 = 398.0488{{c}}, ~3/2 = 708.5402{{c}} (~21/20 = 87.5574{{c}})
* POTE: ~5/4 = 400.000, ~3/2 = 712.013 (~21/20 = 87.987)
* 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 }}


Badness (Smith): 0.020785
Badness (Sintel): 0.859


==== Ogene ====
==== Ogene ====
Line 147: Line 169:


Optimal tunings:  
Optimal tunings:  
* CTE: ~5/4 = 400.000, ~3/2 = 711.902 (~21/20 = 88.098)
* WE: ~5/4 = 398.6473{{c}}, ~3/2 = 710.1987{{c}} (~21/20 = 87.0959{{c}})
* POTE: ~5/4 = 400.000, ~3/2 = 712.609 (~21/20 = 87.391)
* 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 }}


Badness (Smith): 0.022890
Badness (Sintel): 0.946


==== Agene ====
==== Agene ====
Line 162: Line 186:


Optimal tunings:  
Optimal tunings:  
* CTE: ~5/4 = 400.000, ~3/2 = 712.572 (~21/20 = 87.428)
* WE: ~5/4 = 398.5229{{c}}, ~3/2 = 707.0562{{c}} (~21/20 = 89.9897{{c}})
* POTE: ~5/4 = 400.000, ~3/2 = 709.677 (~21/20 = 90.323)
* 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 }}
{{Optimal ET sequence|legend=0| 12f, 27e, 66cdeeef }}


Badness (Smith): 0.023113
Badness (Sintel): 0.955


=== Eugene ===
=== Eugene ===
Line 177: Line 203:


Optimal tunings:  
Optimal tunings:  
* CTE: ~5/4 = 400.000, ~3/2 = 713.002 (~21/20 = 86.998)
* WE: ~5/4 = 399.1743{{c}}, ~3/2 = 712.6763{{c}} (~21/20 = 85.6723{{c}})
* POTE: ~5/4 = 400.000, ~3/2 = 714.150 (~21/20 = 85.850)
* 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 }}


Badness (Smith): 0.035554
Badness (Sintel): 1.18


== Inflated ==
== Inflated ==
Line 192: Line 220:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~5/4 = 400.000, ~3/2 = 717.517 (~25/24 = 82.483)
* [[WE]]: ~5/4 = 398.4023{{c}}, ~3/2 = 719.8327{{c}} (~25/24 = 76.9719{{c}})
: [[error map]]: {{val| -3.762 +1.317 +4.909 +2.060 }}
* [[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 }}
<!-- * [[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 }}
: [[error map]]: {{val| 0.000 +15.562 +13.686 -16.274 }}
* [[POTE]]: ~5/4 = 400.000, ~3/2 = 722.719 (~25/24 = 77.281)
* [[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 }}
: 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 }}


[[Badness]] (Smith): 0.054729
[[Badness]] (Sintel): 1.39


=== 11-limit ===
=== 11-limit ===
Line 209: Line 241:


Optimal tunings:  
Optimal tunings:  
* CTE: ~5/4 = 400.000, ~3/2 = 717.382 (~25/24 = 82.618)
* WE: ~5/4 = 398.4016{{c}}, ~3/2 = 719.7758{{c}} (~25/24 = 77.0275{{c}})
* POTE: ~5/4 = 400.000, ~3/2 = 722.663 (~25/24 = 77.337)
* 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 }}


Badness (Smith): 0.031171
Badness (Sintel): 1.03


== Deflated ==
== Deflated ==
Line 224: Line 258:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~5/4 = 400.000, ~3/2 = 684.847 (~16/15 = 115.153)
* [[WE]]: ~5/4 = 401.9566{{c}}, ~3/2 = 684.9634{{c}} (~16/15 = 118.9497{{c}})
: [[error map]]: {{val| +5.870 -11.122 +27.382 -34.224 }}
* [[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 }}
<!-- * [[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 }}
: [[error map]]: {{val| 0.000 -17.108 +13.686 -53.673 }}
* [[POTE]]: ~5/4 = 400.000, ~3/2 = 681.629 (~16/15 = 118.371)
* [[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 }}
: 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 }}


[[Badness]] (Smith): 0.059079
[[Badness]] (Sintel): 1.50


=== 11-limit ===
=== 11-limit ===
Line 241: Line 279:


Optimal tunings:  
Optimal tunings:  
* CTE: ~5/4 = 400.000, ~3/2 = 679.881 (~16/15 = 120.119)
* WE: ~5/4 = 402.1799{{c}}, ~3/2 = 683.7477{{c}} (~16/15 = 120.6120{{c}})
* POTE: ~5/4 = 400.000, ~3/2 = 680.042 (~16/15 = 119.958)
* 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, 9 }}
{{Optimal ET sequence|legend=0| 3, 6b, 9 }}


Badness (Smith): 0.037183
Badness (Sintel): 1.23


== Hexe ==
== Hexe ==
Line 258: Line 298:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~28/25 = 200.000, ~3/2 = 701.955 (~16/15 = 98.045)
* [[WE]]: ~28/25 = 199.0488{{c}}, ~3/2 = 707.5815{{c}} (~25/24 = 88.6137{{c}})
: [[error map]]: {{val| +5.870 -11.122 +27.382 -34.224 }}
* [[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 }}
<!-- * [[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 }}
: [[error map]]: {{val| 0.000 0.000 +13.686 +31.174 }}
* [[POTE]]: ~28/25 = 200.000, ~3/2 = 710.963 (~16/15 = 89.037)
* [[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 }}
: 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 }}


[[Badness]] (Smith): 0.057730
[[Badness]] (Sintel): 1.46


=== 11-limit ===
=== 11-limit ===
Line 275: Line 319:


Optimal tunings:  
Optimal tunings:  
* CTE: ~28/25 = 200.000, ~3/2 = 701.955 (~16/15 = 98.045)
* WE: ~28/25 = 198.6942{{c}}, ~3/2 = 709.6404{{c}} (~25/24 = 85.1362{{c}})
* POTE: ~28/25 = 200.000, ~3/2 = 714.304 (~16/15 = 85.696)
* 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 }}


Badness (Smith): 0.038412
Badness (Sintel): 1.27


=== 13-limit ===
=== 13-limit ===
Line 290: Line 336:


Optimal tunings:  
Optimal tunings:  
* CTE: ~28/25 = 200.000, ~3/2 = 692.433 (~21/20 = 92.433)
* WE: ~28/25 = 198.4492{{c}}, ~3/2 = 704.4994{{c}} (~25/24 = 89.2973{{c}})
* POTE: ~28/25 = 200.000, ~3/2 = 710.005 (~16/15 = 89.995)
* 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 }}


Badness (Smith): 0.035946
Badness (Sintel): 1.49


== Triforce ==
== Triforce ==
Line 309: Line 357:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~5/4 = 400.000, ~7/4 = 952.295 (~35/32 = 152.295)
* [[WE]]: ~5/4 = 399.7480{{c}}, ~7/4 = 952.3507{{c}} (~35/32 = 152.8547{{c}})
: [[error map]]: {{val| -0.756 +2.746 +11.922 -17.987 }}
* [[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 }}
<!-- * [[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 }}
: [[error map]]: {{val| 0.000 +2.635 +13.686 -16.531 }}
* [[POTE]]: ~5/4 = 400.000, ~7/4 = 952.951 (~35/32 = 152.951)
* [[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 }}
: 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 }}


[[Badness]] (Smith): 0.054988
[[Badness]] (Sintel): 1.39


=== 11-limit ===
=== 11-limit ===
Line 326: Line 378:


Optimal tunings:  
Optimal tunings:  
* CTE: ~5/4 = 400.000, ~7/4 = 952.250 (~12/11 = 152.250)
* WE: ~5/4 = 399.7654{{c}}, ~7/4 = 952.3730{{c}} (~12/11 = 152.8421{{c}})
* POTE: ~5/4 = 400.000, ~7/4 = 952.932 (~12/11 = 152.932)
* 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 }}


Badness (Smith): 0.026152
Badness (Sintel): 0.865


; Music
; Music
Line 345: Line 399:


Optimal tunings:  
Optimal tunings:  
* CTE: ~5/4 = 400.000, ~7/4 = 950.805 (~12/11 = 150.805)
* WE: ~5/4 = 399.7107{{c}}, ~7/4 = 950.9983{{c}} (~12/11 = 151.5768{{c}})
* POTE: ~5/4 = 400.000, ~7/4 = 951.687 (~12/11 = 151.687)
* 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| 6, 9, 15, 24 }}
{{Optimal ET sequence|legend=0| 6f, 9, 15, 24 }}


Badness (Smith): 0.020248
Badness (Sintel): 0.837


; Scales
; Scales
Line 365: Line 421:


Optimal tunings:  
Optimal tunings:  
* CTE: ~44/39 = 200.000, ~7/4 = 952.531 (~40/39 = 47.469)
* WE: ~44/39 = 199.8321{{c}}, ~7/4 = 952.5580{{c}} (~40/39 = 46.6024{{c}})
* POTE: ~44/39 = 200.000, ~7/4 = 953.358 (~40/39 = 46.642)
* 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 }}


Badness (Smith): 0.059160
Badness (Sintel): 2.44


== Hemiaug ==
== Hemiaug ==
Line 382: Line 440:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~5/4 = 400.000, ~14/9 = 752.834 (~36/35 = 47.166)
* [[WE]]: ~5/4 = 398.9278{{c}}, ~14/9 = 752.8583{{c}} (~36/35 = 44.9973{{c}})
: [[error map]]: {{val| -3.217 +2.689 +6.181 -3.462 }}
* [[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 }}
<!-- * [[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 }}
: [[error map]]: {{val| 0.000 +3.712 +13.686 -4.658 }}
* [[POTE]]: ~5/4 = 400.000, ~14/9 = 754.882 (~36/35 = 45.118)
* [[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 }}
: 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 }}


[[Badness]] (Smith): 0.070463
[[Badness]] (Sintel): 1.78


=== 11-limit ===
=== 11-limit ===
Line 399: Line 461:


Optimal tunings:  
Optimal tunings:  
* CTE: ~5/4 = 400.000, ~14/9 = 752.051 (~36/35 = 47.949)
* WE: ~5/4 = 398.8946{{c}}, ~14/9 = 752.1272{{c}} (~36/35 = 45.6619{{c}})
* POTE: ~5/4 = 400.000, ~14/9 = 754.212 (~36/35 = 45.788)
* 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 }}


Badness (Smith): 0.038232
Badness (Sintel): 1.26


=== 13-limit ===
=== 13-limit ===
Line 414: Line 478:


Optimal tunings:  
Optimal tunings:  
* CTE: ~5/4 = 400.000, ~14/9 = 752.128 (~36/35 = 47.872)
* WE: ~5/4 = 399.1053{{c}}, ~14/9 = 752.0643{{c}} (~36/35 = 46.1463{{c}})
* POTE: ~5/4 = 400.000, ~14/9 = 753.750 (~36/35 = 46.250)
* 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 }}


Badness (Smith): 0.030159
Badness (Sintel): 1.25


== Hemiug ==
== Hemiug ==
Line 431: Line 497:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~5/4 = 400.000, ~32/21 = 747.948 (~21/20 = 52.052)
* [[WE]]: ~5/4 = 400.1805{{c}}, ~32/21 = 748.2436{{c}} (~21/20 = 52.1174{{c}})
: [[error map]]: {{val| +0.542 -5.287 +14.950 -11.030 }}
* [[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 }}
<!-- * [[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 }}
: [[error map]]: {{val| 0.000 -6.058 +13.686 -12.671 }}
* [[POTE]]: ~5/4 = 400.000, ~32/21 = 747.907 (~21/20 = 52.093)
* [[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 }}
: 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 }}


[[Badness]] (Smith): 0.137764
[[Badness]] (Sintel): 3.49


=== 11-limit ===
=== 11-limit ===
Line 448: Line 518:


Optimal tunings:  
Optimal tunings:  
* CTE: ~5/4 = 400.000, ~32/21 = 748.296 (~33/32 = 51.704)
* WE: ~5/4 = 400.0637{{c}}, ~32/21 = 748.4638{{c}} (~33/32 = 51.6637{{c}})
* POTE: ~5/4 = 400.000, ~32/21 = 748.345 (~33/32 = 51.655)
* 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 }}


Badness (Smith): 0.068062
Badness (Sintel): 2.25


=== 13-limit ===
=== 13-limit ===
Line 463: Line 535:


Optimal tunings:  
Optimal tunings:  
* CTE: ~5/4 = 400.000, ~32/21 = 748.525 (~33/32 = 51.475)
* WE: ~5/4 = 399.8855{{c}}, ~32/21 = 748.2378{{c}} (~33/32 = 51.5332{{c}})
* POTE: ~5/4 = 400.000, ~32/21 = 748.452 (~33/32 = 51.548)
* 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 }}


Badness (Smith): 0.042289
Badness (Sintel): 1.75


== Oodako ==
== Oodako ==
Line 480: Line 554:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~5/4 = 400.000, ~28/25 = 175.359
* [[WE]]: ~5/4 = 399.0296{{c}}, ~28/25 = 176.2174{{c}} (~49/48 = 46.5949{{c}})
: [[error map]]: {{val| -2.911 +0.004 +6.894 -0.371 }}
* [[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 }}
<!-- * [[CTE]]: ~5/4 = 400.000{{c}}, ~28/25 = 175.359{{c}}
: [[error map]]: {{val| 0.000 -0.521 +13.686 +6.533 }}
: [[error map]]: {{val| 0.000 -0.521 +13.686 +6.533 }}
* [[POTE]]: ~5/4 = 400.000, ~28/25 = 176.646
* [[POTE]]: ~5/4 = 400.000{{c}}, ~28/25 = 176.646{{c}}
: error map: {{val| 0.000 +4.629 +13.686 +7.820 }}
: 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 }}


[[Badness]] (Smith): 0.113209
[[Badness]] (Sintel): 2.86


=== 11-limit ===
=== 11-limit ===
Line 497: Line 575:


Optimal tunings:  
Optimal tunings:  
* CTE: ~5/4 = 400.000, ~11/10 = 175.053
* WE: ~5/4 = 398.6615{{c}}, ~11/10 = 176.3886{{c}} (~49/48 = 45.8843{{c}})
* POTE: ~5/4 = 400.000, ~11/10 = 176.981
* 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 }}


Badness (Smith): 0.059192
Badness (Sintel): 1.96


=== 13-limit ===
=== 13-limit ===
Line 512: Line 592:


Optimal tunings:  
Optimal tunings:  
* CTE: ~5/4 = 400.000, ~11/10 = 175.252
* WE: ~5/4 = 398.8612{{c}}, ~11/10 = 176.0486{{c}} (~49/48 = 46.7640{{c}})
* POTE: ~5/4 = 400.000, ~11/10 = 176.551
* 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 }}


Badness (Smith): 0.042323
Badness (Sintel): 1.75


== Hemisemiaug ==
== Hemisemiaug ==
Line 529: Line 611:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~54/49 = 200.000, ~45/28 = 853.190 (~36/35 = 53.190)
* [[WE]]: ~54/49 = 199.5469{{c}}, ~45/28 = 853.5468{{c}} (~36/35 = 55.3594{{c}})
: [[error map]]: {{val| -2.719 +4.686 +7.342 -9.998 }}
* [[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 }}
<!-- * [[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 }}
: [[error map]]: {{val| 0.000 +4.425 +13.686 -9.256 }}
* [[POTE]]: ~54/49 = 200.000, ~45/28 = 855.485 (~36/35 = 55.485)
* [[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 }}
: 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 }}


[[Badness]] (Smith): 0.210984
[[Badness]] (Sintel): 5.34


=== 11-limit ===
=== 11-limit ===
Line 546: Line 632:


Optimal tunings:  
Optimal tunings:  
* CTE: ~54/49 = 200.000, ~18/11 = 852.597 (~36/35 = 52.597)
* WE: ~54/49 = 199.5188{{c}}, ~18/11 = 853.1623{{c}} (~36/35 = 55.0872{{c}})
* POTE: ~54/49 = 200.000, ~18/11 = 855.220 (~36/35 = 55.220)
* 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| 24, 42e, 66ce, 108bccee }}
{{Optimal ET sequence|legend=0| 18e, 24, 42e, 66ce, 108bccee }}


Badness (Smith): 0.080738
Badness (Sintel): 2.67


== Niner ==
== Niner ==
Line 565: Line 653:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~49/45 = 133.333, ~3/2 = 702.004 (~36/35 = 35.338)
* [[WE]]: ~49/45 = 133.0272{{c}}, ~3/2 = 705.5438{{c}} (~36/35 = 40.4075{{c}})
: [[error map]]: {{val| -2.755 +0.834 +7.259 -2.737 }}
* [[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 }}
<!-- * [[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 }}
: [[error map]]: {{val| 0.000 +0.049 +13.686 -0.155 }}
* [[POTE]]: ~49/45 = 133.333, ~3/2 = 707.167 (~36/35 = 40.501)
* [[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 }}
: 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 }}


[[Badness]] (Smith): 0.067157
[[Badness]] (Sintel): 1.70


=== 11-limit ===
=== 11-limit ===
Line 582: Line 674:


Optimal tunings:  
Optimal tunings:  
* CTE: ~12/11 = 133.333, ~3/2 = 699.622 (~36/35 = 32.955)
* WE: ~12/11 = 132.9553{{c}}, ~3/2 = 704.7217{{c}} (~36/35 = 39.9453{{c}})
* POTE: ~12/11 = 133.333, ~3/2 = 706.726 (~36/35 = 40.059)
* 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 }}


Badness (Smith): 0.034861
Badness (Sintel): 1.15


=== 13-limit ===
=== 13-limit ===
Line 597: Line 691:


Optimal tunings:  
Optimal tunings:  
* CTE: ~14/13 = 133.333, ~3/2 = 700.433 (~36/35 = 33.766)
* WE: ~14/13 = 133.0143{{c}}, ~3/2 = 705.1969{{c}} (~36/35 = 40.1256{{c}})
* POTE: ~14/13 = 133.333, ~3/2 = 706.889 (~36/35 = 40.222)
* 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 }}


Badness (Smith): 0.024143
Badness (Sintel): 0.998


== Trug ==
== Trug ==
Line 614: Line 710:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~5/4 = 400.000, ~48/35 = 498.637 (~15/14 = 98.637)
* [[WE]]: ~5/4 = 398.2337{{c}}, ~48/35 = 499.7635{{c}} (~15/14 = 101.5299{{c}})
: [[error map]]: {{val| -2.755 +0.834 +7.259 -2.737 }}
* [[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 }}
<!-- * [[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 }}
: [[error map]]: {{val| 0.000 -6.045 +13.686 +28.447 }}
* [[POTE]]: ~5/4 = 400.000, ~48/35 = 501.980 (~15/14 = 101.980)
* [[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 }}
: error map: {{val| 0.000 +3.986 +13.686 +35.134 }} -->


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


[[Badness]] (Smith): 0.138279
[[Badness]] (Sintel): 3.50


== External links ==
== External links ==
Retrieved from "https://en.xen.wiki/w/Augmented_family"