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Porcupine family: Difference between revisions

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Restore POTE tuning by request (and correct the tunings for undecimation)
-diamond monotone and tradeoff (trivially derivable and lack of significance); misc. cleanup
Line 37: Line 37:
* 5-odd-limit [[diamond monotone]]: ~10/9 = [150.000, 171.429] (1\8 to 1\7)
* 5-odd-limit [[diamond monotone]]: ~10/9 = [150.000, 171.429] (1\8 to 1\7)
* 5-odd-limit [[diamond tradeoff]]: ~10/9 = [157.821, 166.015]
* 5-odd-limit [[diamond tradeoff]]: ~10/9 = [157.821, 166.015]
* 5-odd-limit diamond monotone and tradeoff: ~10/9 = [157.821, 166.015]


{{Optimal ET sequence|legend=1| 7, 15, 22, 95c }}
{{Optimal ET sequence|legend=1| 7, 15, 22, 95c }}
Line 58: Line 57:
* POTE: ~2 = 1\1, ~11/10 = 164.0777
* POTE: ~2 = 1\1, ~11/10 = 164.0777


{{Optimal ET sequence|legend=1| 7, 15, 22, 73ce, 95ce }}
Optimal ET sequence: {{Optimal ET sequence| 7, 15, 22, 73ce, 95ce }}


Badness: 0.0097
Badness: 0.0097
Line 75: Line 74:
* POTE: ~2 = 1\1, ~88/65 = 518.2094
* POTE: ~2 = 1\1, ~88/65 = 518.2094


{{Optimal ET sequence|legend=1| 7, 23bc, 30, 37, 44 }}
Optimal ET sequence: {{Optimal ET sequence| 7, 23bc, 30, 37, 44 }}


Badness: 0.0305
Badness: 0.0305
Line 106: Line 105:
* 7-odd-limit [[diamond tradeoff]]: ~10/9 = [157.821, 166.015]
* 7-odd-limit [[diamond tradeoff]]: ~10/9 = [157.821, 166.015]
* 9-odd-limit diamond tradeoff: ~10/9 = [157.821, 182.404]
* 9-odd-limit diamond tradeoff: ~10/9 = [157.821, 182.404]
* 7- and 9-odd-limit diamond monotone and tradeoff: ~10/9 = [160.000, 163.636]


{{Optimal ET sequence|legend=1| 7, 15, 22, 37, 59, 81bd }}
{{Optimal ET sequence|legend=1| 7, 15, 22, 37, 59, 81bd }}
Line 125: Line 123:
Minimax tuning:  
Minimax tuning:  
* 11-odd-limit: ~11/10 = {{monzo| 1/6 -1/6 0 1/12 }}
* 11-odd-limit: ~11/10 = {{monzo| 1/6 -1/6 0 1/12 }}
: eigenmonzo basis (unchanged-interval basis): 2.9/7
: eigenmonzo (unchanged-interval) basis: 2.9/7


Tuning ranges:  
Tuning ranges:  
* 11-odd-limit diamond monotone: ~11/10 = [160.000, 163.636] (2\15 to 3\22)
* 11-odd-limit diamond monotone: ~11/10 = [160.000, 163.636] (2\15 to 3\22)
* 11-odd-limit diamond tradeoff: ~11/10 = [150.637, 182.404]
* 11-odd-limit diamond tradeoff: ~11/10 = [150.637, 182.404]
* 11-odd-limit diamond monotone and tradeoff: ~11/10 = [160.000, 163.636]


{{Optimal ET sequence|legend=1| 7, 15, 22, 37, 59 }}
Optimal ET sequence: {{Optimal ET sequence| 7, 15, 22, 37, 59 }}


Badness: 0.021562
Badness: 0.021562
Line 149: Line 146:
Minimax tuning:  
Minimax tuning:  
* 13- and 15-odd-limit: ~10/9 = {{monzo| 1 0 0 0 -1/4 }}
* 13- and 15-odd-limit: ~10/9 = {{monzo| 1 0 0 0 -1/4 }}
: Eigenmonzo basis (unchanged-interval basis): 2.11
: eigenmonzo (unchanged-interval) basis: 2.11


Tuning ranges:  
Tuning ranges:  
Line 155: Line 152:
* 15-odd-limit diamond monotone: ~11/10 = 163.636 (3\22)
* 15-odd-limit diamond monotone: ~11/10 = 163.636 (3\22)
* 13- and 15-odd-limit diamond tradeoff: ~11/10 = [138.573, 182.404]
* 13- and 15-odd-limit diamond tradeoff: ~11/10 = [138.573, 182.404]
* 13-odd-limit diamond monotone and tradeoff: ~11/10 = [160.000, 163.636]
* 15-odd-limit diamond monotone and tradeoff: ~11/10 = 163.636


{{Optimal ET sequence|legend=1| 7, 15, 22f, 37f }}
Optimal ET sequence: {{Optimal ET sequence| 7, 15, 22f, 37f }}


Badness: 0.021276
Badness: 0.021276
Line 177: Line 172:
Minimax tuning:  
Minimax tuning:  
* 13- and 15-odd-limit: ~10/9 = {{monzo| 2/13 0 0 0 1/13 -1/13 }}
* 13- and 15-odd-limit: ~10/9 = {{monzo| 2/13 0 0 0 1/13 -1/13 }}
: Eigenmonzo basis (unchanged-interval basis): 2.13/11
: eigenmonzo (unchanged-interval) basis: 2.13/11


Tuning ranges:  
Tuning ranges:  
Line 183: Line 178:
* 15-odd-limit diamond monotone: ~10/9 = 162.162 (5\37)
* 15-odd-limit diamond monotone: ~10/9 = 162.162 (5\37)
* 13- and 15-odd-limit diamond tradeoff: ~10/9 = [150.637, 182.404]
* 13- and 15-odd-limit diamond tradeoff: ~10/9 = [150.637, 182.404]
* 13-odd-limit diamond monotone and tradeoff: ~10/9 = [160.000, 162.162]
* 15-odd-limit diamond monotone and tradeoff: ~10/9 = 162.162


{{Optimal ET sequence|legend=1| 15, 22, 37 }}
Optimal ET sequence: {{Optimal ET sequence| 15, 22, 37 }}


Badness: 0.025314
Badness: 0.025314
Line 203: Line 196:
Minimax tuning:  
Minimax tuning:  
* 13- and 15-odd-limit: ~11/10 = {{monzo| 1/14 0 0 -1/14 0 1/14 }}
* 13- and 15-odd-limit: ~11/10 = {{monzo| 1/14 0 0 -1/14 0 1/14 }}
: Eigenmonzo basis (unchanged-interval basis): 2.13/7
: eigenmonzo (unchanged-interval) basis: 2.13/7


{{Optimal ET sequence|legend=1| 15f, 22f, 37, 59f }}
Optimal ET sequence: {{Optimal ET sequence| 15f, 22f, 37, 59f }}


Badness: 0.035130
Badness: 0.035130
Line 222: Line 215:
Minimax tuning:  
Minimax tuning:  
* 13- and 15-odd-limit: ~11/10 = {{monzo| 1/6 -1/6 0 1/12 }}
* 13- and 15-odd-limit: ~11/10 = {{monzo| 1/6 -1/6 0 1/12 }}
: Eigenmonzo basis (unchanged-interval basis): 2.9/7
: eigenmonzo (unchanged-interval) basis: 2.9/7


{{Optimal ET sequence|legend=1| 7, 15f, 22 }}
Optimal ET sequence: {{Optimal ET sequence| 7, 15f, 22 }}


Badness: 0.026043
Badness: 0.026043
Line 260: Line 253:
* 11-odd-limit eigenmonzo (unchanged-interval) basis: 2.7
* 11-odd-limit eigenmonzo (unchanged-interval) basis: 2.7


{{Optimal ET sequence|legend=1| 7d, 8d, 15 }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 8d, 15 }}


Badness: 0.022325
Badness: 0.022325
Line 276: Line 269:
* 13- and 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.7
* 13- and 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.7


{{Optimal ET sequence|legend=1| 7d, 8d, 15, 38bceff }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 8d, 15, 38bceff }}


Badness: 0.019389
Badness: 0.019389
Line 316: Line 309:
Minimax tuning:  
Minimax tuning:  
* 11-odd-limit: ~11/10 = {{monzo| 2/11 0 1/11 -1/11 }}
* 11-odd-limit: ~11/10 = {{monzo| 2/11 0 1/11 -1/11 }}
: eigenmonzo basis (unchanged-interval basis): 2.7/5
: eigenmonzo (unchanged-interval) basis: 2.7/5


{{Optimal ET sequence|legend=1| 7d, 15d, 22, 51 }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 15d, 22, 51 }}


Badness: 0.027268
Badness: 0.027268
Line 333: Line 326:
* POTE: ~2 = 1\1, ~11/10 = 164.953
* POTE: ~2 = 1\1, ~11/10 = 164.953


{{Optimal ET sequence|legend=1| 7d, 22, 29, 51f, 80cdeff }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 22, 29, 51f, 80cdeff }}


Badness: 0.026543
Badness: 0.026543
Line 373: Line 366:
Minimax tuning:  
Minimax tuning:  
* 11-odd-limit: ~11/10 = {{monzo| 2/3 -1/3 }}
* 11-odd-limit: ~11/10 = {{monzo| 2/3 -1/3 }}
: eigenmonzo basis (unchanged-interval basis): 2.3
: eigenmonzo (unchanged-interval) basis: 2.3


{{Optimal ET sequence|legend=1| 7, 22d, 29, 65ce }}
Optimal ET sequence: {{Optimal ET sequence| 7, 22d, 29, 65ce }}


Badness: 0.049669
Badness: 0.049669
Line 392: Line 385:
Minimax tuning:  
Minimax tuning:  
* 13- and 15-odd-limit: ~11/10 = {{monzo| 2/3 -1/3 }}
* 13- and 15-odd-limit: ~11/10 = {{monzo| 2/3 -1/3 }}
: eigenmonzo basis (unchanged-interval basis): 2.3
: eigenmonzo (unchanged-interval) basis: 2.3


{{Optimal ET sequence|legend=1| 7, 22d, 29, 65cef }}
Optimal ET sequence: {{Optimal ET sequence| 7, 22d, 29, 65cef }}


Badness: 0.030233
Badness: 0.030233
Line 432: Line 425:
* POTE: ~2 = 1\1, ~11/10 = 158.750
* POTE: ~2 = 1\1, ~11/10 = 158.750


{{Optimal ET sequence|legend=1| 7, 8d, 15d }}
Optimal ET sequence: {{Optimal ET sequence| 7, 8d, 15d }}


Badness: 0.026790
Badness: 0.026790
Line 490: Line 483:
* POTE: ~7/5 = 1\2, ~9/7 = 435.386
* POTE: ~7/5 = 1\2, ~9/7 = 435.386


{{Optimal ET sequence|legend=1| 8d, 14c, 22, 58ce }}
Optimal ET sequence: {{Optimal ET sequence| 8d, 14c, 22, 58ce }}


Badness: 0.023095
Badness: 0.023095
Line 505: Line 498:
* POTE: ~7/5 = 1\2, ~9/7 = 435.861
* POTE: ~7/5 = 1\2, ~9/7 = 435.861


{{Optimal ET sequence|legend=1| 8d, 14cf, 22 }}
Optimal ET sequence: {{Optimal ET sequence| 8d, 14cf, 22 }}


Badness: 0.021516
Badness: 0.021516
Line 520: Line 513:
* POTE: ~7/5 = 1\2, ~9/7 = 437.078
* POTE: ~7/5 = 1\2, ~9/7 = 437.078


{{Optimal ET sequence|legend=1| 14c, 22f }}
Optimal ET sequence: {{Optimal ET sequence| 14c, 22f }}


Badness: 0.025233
Badness: 0.025233
Line 535: Line 528:
* POTE: ~7/5 = 1\2, ~9/7 = 435.425
* POTE: ~7/5 = 1\2, ~9/7 = 435.425


{{Optimal ET sequence|legend=1| 22 }}
Optimal ET sequence: {{Optimal ET sequence| 22 }}


Badness: 0.068406
Badness: 0.068406
Line 572: Line 565:
* POTE: ~2 = 1\1, ~21/20 = 82.504
* POTE: ~2 = 1\1, ~21/20 = 82.504


{{Optimal ET sequence|legend=1| 14c, 15, 29, 44d }}
Optimal ET sequence: {{Optimal ET sequence| 14c, 15, 29, 44d }}


Badness: 0.026023
Badness: 0.026023
Line 587: Line 580:
* POTE: ~2 = 1\1, ~21/20 = 82.530
* POTE: ~2 = 1\1, ~21/20 = 82.530


{{Optimal ET sequence|legend=1| 14cf, 15, 29, 44d }}
Optimal ET sequence: {{Optimal ET sequence| 14cf, 15, 29, 44d }}


Badness: 0.022285
Badness: 0.022285
Line 602: Line 595:
* POTE: ~2 = 1\1, ~21/20 = 81.759
* POTE: ~2 = 1\1, ~21/20 = 81.759


{{Optimal ET sequence|legend=1| 14c, 15, 29f, 44dff }}
Optimal ET sequence: {{Optimal ET sequence| 14c, 15, 29f, 44dff }}


Badness: 0.029816
Badness: 0.029816
Line 639: Line 632:
* POTE: ~2 = 1\1, ~9/7 = 454.512
* POTE: ~2 = 1\1, ~9/7 = 454.512


{{Optimal ET sequence|legend=1| 8d, 21cde, 29, 37, 66 }}
Optimal ET sequence: {{Optimal ET sequence| 8d, 21cde, 29, 37, 66 }}


Badness: 0.045694
Badness: 0.045694
Line 654: Line 647:
* POTE: ~2 = 1\1, ~13/10 = 454.529
* POTE: ~2 = 1\1, ~13/10 = 454.529


{{Optimal ET sequence|legend=1| 8d, 21cdef, 29, 37, 66 }}
Optimal ET sequence: {{Optimal ET sequence| 8d, 21cdef, 29, 37, 66 }}


Badness: 0.027168
Badness: 0.027168
Line 688: Line 681:
* POTE: ~2 = 1\1, ~36/35 = 54.376
* POTE: ~2 = 1\1, ~36/35 = 54.376


{{Optimal ET sequence|legend=1| 1ce, 21ce, 22 }}
Optimal ET sequence: {{Optimal ET sequence| 1ce, 21ce, 22 }}


Badness: 0.051319
Badness: 0.051319
Line 703: Line 696:
* POTE: ~2 = 1\1, ~36/35 = 54.665
* POTE: ~2 = 1\1, ~36/35 = 54.665


{{Optimal ET sequence|legend=1| 1ce, 21cef, 22 }}
Optimal ET sequence: {{Optimal ET sequence| 1ce, 21cef, 22 }}


Badness: 0.044739
Badness: 0.044739
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