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Augmented family: Difference between revisions

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Line 16: Line 16:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~5/4 = 400.000, ~3/2 = 701.955 (~16/15 = 98.045)
* [[CTE]]: ~5/4 = 400.000, ~3/2 = 701.955 (~16/15 = 98.045)
: [[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, ~3/2 = 706.638 (~16/15 = 93.362)
: 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, 12, 27, 39, 51c, 90cc }}
Line 36: Line 38:
[[Optimal tuning]]s:
[[Optimal tuning]]s:
* [[CTE]]: ~5/4 = 400.000, ~3/2 = 692.124 (~16/15 = 107.876)
* [[CTE]]: ~5/4 = 400.000, ~3/2 = 692.124 (~16/15 = 107.876)
: [[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, ~3/2 = 696.011 (~16/15 = 103.989)
: error map: {{val| 0.000 -5.944 +13.686 +23.195 }}


{{Optimal ET sequence|legend=1| 9, 12, 45cd, 57cd, 69cdd }}
{{Optimal ET sequence|legend=1| 9, 12, 45cd }}


[[Badness]] (Smith): 0.026459
[[Badness]] (Smith): 0.026459
Line 55: Line 59:
* POTE: ~5/4 = 400.000, ~3/2 = 692.514 (~16/15 = 107.486)
* POTE: ~5/4 = 400.000, ~3/2 = 692.514 (~16/15 = 107.486)


Optimal ET sequence: {{Optimal ET sequence| 9, 12, 21, 33e, 45cde }}
Optimal ET sequence: {{optimal ET sequence| 9, 12, 21, 33e, 45cde }}


Badness (Smith): 0.020191
Badness (Smith): 0.020191
Line 70: Line 74:
* POTE: ~5/4 = 400.000, ~3/2 = 688.783 (~16/15 = 111.217)
* POTE: ~5/4 = 400.000, ~3/2 = 688.783 (~16/15 = 111.217)


Optimal ET sequence: {{Optimal ET sequence| 9, 12f, 21, 33ef, 54bceeff }}
Optimal ET sequence: {{optimal ET sequence| 9, 12f, 21, 33ef, 54bceeff }}


Badness (Smith): 0.018448
Badness (Smith): 0.018448
Line 85: Line 89:
* POTE: ~5/4 = 400.000, ~3/2 = 685.356 (~16/15 = 114.644)
* POTE: ~5/4 = 400.000, ~3/2 = 685.356 (~16/15 = 114.644)


Optimal ET sequence: {{Optimal ET sequence| 9, 12, 21f }}
Optimal ET sequence: {{optimal ET sequence| 9, 12, 21f }}


Badness (Smith): 0.022236
Badness (Smith): 0.022236
Line 102: Line 106:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~5/4 = 400.000, ~3/2 = 709.595 (~21/20 = 90.405)
* [[CTE]]: ~5/4 = 400.000, ~3/2 = 709.595 (~21/20 = 90.405)
: [[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, ~3/2 = 709.257 (~21/20 = 90.743)
: 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 121: Line 127:
* POTE: ~5/4 = 400.000, ~3/2 = 711.177 (~21/20 = 88.823)
* POTE: ~5/4 = 400.000, ~3/2 = 711.177 (~21/20 = 88.823)


Optimal ET sequence: {{Optimal ET sequence| 12, 15, 27e }}
Optimal ET sequence: {{optimal ET sequence| 12, 15, 27e }}


Badness (Smith): 0.019613
Badness (Smith): 0.019613
Line 136: Line 142:
* POTE: ~5/4 = 400.000, ~3/2 = 712.013 (~21/20 = 87.987)
* POTE: ~5/4 = 400.000, ~3/2 = 712.013 (~21/20 = 87.987)


Optimal ET sequence: {{Optimal ET sequence| 12f, 15, 27eff }}
Optimal ET sequence: {{optimal ET sequence| 12f, 15, 27eff }}


Badness (Smith): 0.020785
Badness (Smith): 0.020785
Line 151: Line 157:
* POTE: ~5/4 = 400.000, ~3/2 = 712.609 (~21/20 = 87.391)
* POTE: ~5/4 = 400.000, ~3/2 = 712.609 (~21/20 = 87.391)


Optimal ET sequence: {{Optimal ET sequence| 12, 15, 27e, 69bceef }}
Optimal ET sequence: {{optimal ET sequence| 12, 15, 27e, 69bceef }}


Badness (Smith): 0.022890
Badness (Smith): 0.022890
Line 166: Line 172:
* POTE: ~5/4 = 400.000, ~3/2 = 709.677 (~21/20 = 90.323)
* POTE: ~5/4 = 400.000, ~3/2 = 709.677 (~21/20 = 90.323)


Optimal ET sequence: {{Optimal ET sequence| 12f, 27e }}
Optimal ET sequence: {{optimal ET sequence| 12f, 27e }}


Badness (Smith): 0.023113
Badness (Smith): 0.023113
Line 181: Line 187:
* POTE: ~5/4 = 400.000, ~3/2 = 714.150 (~21/20 = 85.850)
* POTE: ~5/4 = 400.000, ~3/2 = 714.150 (~21/20 = 85.850)


Optimal ET sequence: {{Optimal ET sequence| 12e, 15, 27, 42 }}
Optimal ET sequence: {{optimal ET sequence| 12e, 15, 27, 42 }}


Badness (Smith): 0.035554
Badness (Smith): 0.035554
Line 196: Line 202:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~5/4 = 400.000, ~3/2 = 717.517 (~25/24 = 82.483)
* [[CTE]]: ~5/4 = 400.000, ~3/2 = 717.517 (~25/24 = 82.483)
: [[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, ~3/2 = 722.719 (~25/24 = 77.281)
: 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 213: Line 221:
* POTE: ~5/4 = 400.000, ~3/2 = 722.663 (~25/24 = 77.337)
* POTE: ~5/4 = 400.000, ~3/2 = 722.663 (~25/24 = 77.337)


Optimal ET sequence: {{Optimal ET sequence| 3de, 12de, 15 }}
Optimal ET sequence: {{optimal ET sequence| 3de, 12de, 15 }}


Badness (Smith): 0.031171
Badness (Smith): 0.031171
Line 228: Line 236:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~5/4 = 400.000, ~3/2 = 684.847 (~16/15 = 115.153)
* [[CTE]]: ~5/4 = 400.000, ~3/2 = 684.847 (~16/15 = 115.153)
: [[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, ~3/2 = 681.629 (~16/15 = 118.371)
: error map: {{val| 0.000 -20.326 +13.686 -50.455 }}


{{Optimal ET sequence|legend=1| 3, 9 }}
{{Optimal ET sequence|legend=1| 3, 6b, 9 }}


[[Badness]] (Smith): 0.059079
[[Badness]] (Smith): 0.059079
Line 245: Line 255:
* POTE: ~5/4 = 400.000, ~3/2 = 680.042 (~16/15 = 119.958)
* POTE: ~5/4 = 400.000, ~3/2 = 680.042 (~16/15 = 119.958)


Optimal ET sequence: {{Optimal ET sequence| 3, 9 }}
Optimal ET sequence: {{optimal ET sequence| 3, 9 }}


Badness (Smith): 0.037183
Badness (Smith): 0.037183
Line 262: Line 272:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~28/25 = 200.000, ~3/2 = 701.955 (~16/15 = 98.045)
* [[CTE]]: ~28/25 = 200.000, ~3/2 = 701.955 (~16/15 = 98.045)
: [[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, ~3/2 = 710.963 (~16/15 = 89.037)
: 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 279: Line 291:
* POTE: ~28/25 = 200.000, ~3/2 = 714.304 (~16/15 = 85.696)
* POTE: ~28/25 = 200.000, ~3/2 = 714.304 (~16/15 = 85.696)


Optimal ET sequence: {{Optimal ET sequence| 6, 12, 30dee, 42ddeee }}
Optimal ET sequence: {{optimal ET sequence| 6, 12, 30dee, 42ddeee }}


Badness (Smith): 0.038412
Badness (Smith): 0.038412
Line 294: Line 306:
* POTE: ~28/25 = 200.000, ~3/2 = 710.005 (~16/15 = 89.995)
* POTE: ~28/25 = 200.000, ~3/2 = 710.005 (~16/15 = 89.995)


Optimal ET sequence: {{Optimal ET sequence| 6f, 12f }}
Optimal ET sequence: {{optimal ET sequence| 6f, 12f }}


Badness (Smith): 0.035946
Badness (Smith): 0.035946
Line 313: Line 325:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~5/4 = 400.000, ~7/4 = 952.295 (~35/32 = 152.295)
* [[CTE]]: ~5/4 = 400.000, ~7/4 = 952.295 (~35/32 = 152.295)
: [[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, ~7/4 = 952.951 (~35/32 = 152.951)
: error map: {{val| 0.000 +3.947 +13.686 -15.875 }}


{{Optimal ET sequence|legend=1| 6, 9, 15, 24, 39, 63cd, 102ccdd }}
{{Optimal ET sequence|legend=1| 6, 9, 15, 24, 39 }}


[[Badness]] (Smith): 0.054988
[[Badness]] (Smith): 0.054988
Line 332: Line 346:
* POTE: ~5/4 = 400.000, ~7/4 = 952.932 (~12/11 = 152.932)
* POTE: ~5/4 = 400.000, ~7/4 = 952.932 (~12/11 = 152.932)


Optimal ET sequence: {{Optimal ET sequence| 6, 9, 15, 24, 39 }}
Optimal ET sequence: {{optimal ET sequence| 6, 9, 15, 24, 39 }}


Badness (Smith): 0.026152
Badness (Smith): 0.026152
Line 351: Line 365:
* POTE: ~5/4 = 400.000, ~7/4 = 951.687 (~12/11 = 151.687)
* POTE: ~5/4 = 400.000, ~7/4 = 951.687 (~12/11 = 151.687)


Optimal ET sequence: {{Optimal ET sequence| 6, 9, 15, 24 }}
Optimal ET sequence: {{optimal ET sequence| 6, 9, 15, 24 }}


Badness (Smith): 0.020248
Badness (Smith): 0.020248


; Scales
; Scales
* [[triphi]], triforce[9] with L:s = phi
* [[triphi]], Triforce[9] with L:s = phi


==== Semitriforce ====
==== Semitriforce ====
Line 371: Line 385:
* POTE: ~44/39 = 200.000, ~7/4 = 953.358 (~40/39 = 46.642)
* POTE: ~44/39 = 200.000, ~7/4 = 953.358 (~40/39 = 46.642)


Optimal ET sequence: {{Optimal ET sequence| 6, 18bd, 24 }}
Optimal ET sequence: {{optimal ET sequence| 6, 18bd, 24 }}


Badness (Smith): 0.059160
Badness (Smith): 0.059160
Line 388: Line 402:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~5/4 = 400.000, ~14/9 = 752.834 (~36/35 = 47.166)
* [[CTE]]: ~5/4 = 400.000, ~14/9 = 752.834 (~36/35 = 47.166)
: [[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, ~14/9 = 754.882 (~36/35 = 45.118)
: 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 405: Line 421:
* POTE: ~5/4 = 400.000, ~14/9 = 754.212 (~36/35 = 45.788)
* POTE: ~5/4 = 400.000, ~14/9 = 754.212 (~36/35 = 45.788)


Optimal ET sequence: {{Optimal ET sequence| 24, 27e, 51ce }}
Optimal ET sequence: {{optimal ET sequence| 24, 27e, 51ce }}


Badness (Smith): 0.038232
Badness (Smith): 0.038232
Line 420: Line 436:
* POTE: ~5/4 = 400.000, ~14/9 = 753.750 (~36/35 = 46.250)
* POTE: ~5/4 = 400.000, ~14/9 = 753.750 (~36/35 = 46.250)


Optimal ET sequence: {{Optimal ET sequence| 24, 27e, 51ce }}
Optimal ET sequence: {{optimal ET sequence| 24, 27e, 51ce }}


Badness (Smith): 0.030159
Badness (Smith): 0.030159
Line 437: Line 453:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~5/4 = 400.000, ~32/21 = 747.948 (~21/20 = 52.052)
* [[CTE]]: ~5/4 = 400.000, ~32/21 = 747.948 (~21/20 = 52.052)
: [[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, ~32/21 = 747.907 (~21/20 = 52.093)
: 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 454: Line 472:
* POTE: ~5/4 = 400.000, ~32/21 = 748.345 (~33/32 = 51.655)
* POTE: ~5/4 = 400.000, ~32/21 = 748.345 (~33/32 = 51.655)


Optimal ET sequence: {{Optimal ET sequence| 21, 24 }}
Optimal ET sequence: {{optimal ET sequence| 21, 24 }}


Badness (Smith): 0.068062
Badness (Smith): 0.068062
Line 469: Line 487:
* POTE: ~5/4 = 400.000, ~32/21 = 748.452 (~33/32 = 51.548)
* POTE: ~5/4 = 400.000, ~32/21 = 748.452 (~33/32 = 51.548)


Optimal ET sequence: {{Optimal ET sequence| 21, 24 }}
Optimal ET sequence: {{optimal ET sequence| 21, 24 }}


Badness (Smith): 0.042289
Badness (Smith): 0.042289
Line 486: Line 504:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~5/4 = 400.000, ~28/25 = 175.359
* [[CTE]]: ~5/4 = 400.000, ~28/25 = 175.359
: [[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, ~28/25 = 176.646
: 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 503: Line 523:
* POTE: ~5/4 = 400.000, ~11/10 = 176.981
* POTE: ~5/4 = 400.000, ~11/10 = 176.981


Optimal ET sequence: {{Optimal ET sequence| 6, 21, 27e }}
Optimal ET sequence: {{optimal ET sequence| 6, 21, 27e }}


Badness (Smith): 0.059192
Badness (Smith): 0.059192
Line 518: Line 538:
* POTE: ~5/4 = 400.000, ~11/10 = 176.551
* POTE: ~5/4 = 400.000, ~11/10 = 176.551


Optimal ET sequence: {{Optimal ET sequence| 6, 21, 27e }}
Optimal ET sequence: {{optimal ET sequence| 6, 21, 27e }}


Badness (Smith): 0.042323
Badness (Smith): 0.042323
Line 535: Line 555:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~54/49 = 200.000, ~45/28 = 853.190 (~36/35 = 53.190)
* [[CTE]]: ~54/49 = 200.000, ~45/28 = 853.190 (~36/35 = 53.190)
: [[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, ~45/28 = 855.485 (~36/35 = 55.485)
: 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 552: Line 574:
* POTE: ~54/49 = 200.000, ~18/11 = 855.220 (~36/35 = 55.220)
* POTE: ~54/49 = 200.000, ~18/11 = 855.220 (~36/35 = 55.220)


Optimal ET sequence: {{Optimal ET sequence| 24, 42e, 66ce, 108bccee }}
Optimal ET sequence: {{optimal ET sequence| 24, 42e, 66ce, 108bccee }}


Badness (Smith): 0.080738
Badness (Smith): 0.080738
Line 571: Line 593:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~49/45 = 133.333, ~3/2 = 702.004 (~36/35 = 35.338)
* [[CTE]]: ~49/45 = 133.333, ~3/2 = 702.004 (~36/35 = 35.338)
: [[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, ~3/2 = 707.167 (~36/35 = 40.501)
: 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 588: Line 612:
* POTE: ~12/11 = 133.333, ~3/2 = 706.726 (~36/35 = 40.059)
* POTE: ~12/11 = 133.333, ~3/2 = 706.726 (~36/35 = 40.059)


Optimal ET sequence: {{Optimal ET sequence| 9, 18e, 27e, 63cee }}
Optimal ET sequence: {{optimal ET sequence| 9, 18e, 27e, 63cee }}


Badness (Smith): 0.034861
Badness (Smith): 0.034861
Line 603: Line 627:
* POTE: ~14/13 = 133.333, ~3/2 = 706.889 (~36/35 = 40.222)
* POTE: ~14/13 = 133.333, ~3/2 = 706.889 (~36/35 = 40.222)


Optimal ET sequence: {{Optimal ET sequence| 9, 18e, 27e }}
Optimal ET sequence: {{optimal ET sequence| 9, 18e, 27e }}


Badness (Smith): 0.024143
Badness (Smith): 0.024143
Line 618: Line 642:
[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~5/4 = 400.000, ~48/35 = 498.637 (~15/14 = 98.637)
* [[CTE]]: ~5/4 = 400.000, ~48/35 = 498.637 (~15/14 = 98.637)
: [[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, ~48/35 = 501.980 (~15/14 = 101.980)
: error map: {{val| 0.000 +3.986 +13.686 +35.134 }}


{{Optimal ET sequence|legend=1| 9bd, 12 }}
{{Optimal ET sequence|legend=1| 9bd, 12 }}
Line 636: Line 662:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~5/4 = 400.000, ~7/4 = 968.826 (~28/25 = 168.826)
: [[error map]]: {{val| 0.000 +98.045 +13.686 0.000 }}
* [[POTE]]: ~5/4 = 400.000, ~7/4 = 1034.013 (~15/14 = 165.987)
* [[POTE]]: ~5/4 = 400.000, ~7/4 = 1034.013 (~15/14 = 165.987)
: error map: {{val| 0.000 +98.045 +13.686 +65.187 }}


{{Optimal ET sequence|legend=1| 3d, 6, 9bd, 15bbd }}
{{Optimal ET sequence|legend=1| 3d, 6, 9bd }}


[[Badness]] (Smith): 0.028673
[[Badness]] (Smith): 0.028673
Line 650: Line 679:


Optimal tunings:  
Optimal tunings:  
* CTE: ~5/4 = 400.000, ~7/4 = 961.874 (~11/10 = 161.874)
* POTE: ~5/4 = 400.000, ~7/4 = 1033.153 (~12/11 = 166.847)
* POTE: ~5/4 = 400.000, ~7/4 = 1033.153 (~12/11 = 166.847)


Optimal ET sequence: {{Optimal ET sequence| 3de, 6, 15bbdee }}
Optimal ET sequence: {{optimal ET sequence| 3de, 6 }}


Badness (Smith): 0.025592
Badness (Smith): 0.025592
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