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Schismatic family: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings (1/)
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7187{{c}}
* [[WE]]: ~2 = 1200.0749{{c}}, ~3/2 = 701.7797{{c}}
* [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7359{{c}}
: [[error map]]: {{val| +0.075 -0.100 -0.027 }}
* [[CWE]]: ~2 = 1200.0000{{c]}, ~3/2 = 701.7308{{c}}
: error map: {{val| 0.000 -0.224 -0.160 }}
<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7187{{c}}
* [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7359{{c}} -->


[[Tuning ranges]]:  
[[Tuning ranges]]:  
* 5-odd-limit [[diamond monotone]]: ~3/2 = [685.714, 705.882] (4\7 to 10\17)
* [[5-odd-limit]] [[diamond monotone]]: ~3/2 = [685.714, 705.882] (4\7 to 10\17)
* 5-odd-limit [[diamond tradeoff]]: ~3/2 = [701.711, 701.955] (1/8-comma to untempered)
* 5-odd-limit [[diamond tradeoff]]: ~3/2 = [701.711, 701.955] (1/8-comma to untempered)


{{Optimal ET sequence|legend=1| 12, 29, 41, 53, 118, 171, 289, 460, 749, 3456bc, 4205bc, 4954bc, 5703bbc, 6452bbcc }}
{{Optimal ET sequence|legend=1| 12, 29, 41, 53, 118, 171, 289, 460, 749, 3456bc, 4205bc, 4954bc, 5703bbc, 6452bbcc }}


[[Badness]] (Smith): 0.004259
[[Badness]] (Sintel): 0.0999


=== Overview to extensions ===
=== Overview to extensions ===
The second comma of the [[Normal forms #Normal forms for commas|normal comma list]] defines which 7-limit family member we are looking at.  
The second comma of the [[normal forms #Normal forms for commas|normal comma list]] defines which 7-limit family member we are looking at.  
* [[#Garibaldi|Garibaldi]] adds [[garischisma|{{monzo| 25 -14 0 -1 }}]],  
* [[#Garibaldi|Garibaldi]] adds [[garischisma|{{monzo| 25 -14 0 -1 }}]],  
* [[#Grackle|Grackle]] adds {{monzo| -44 26 0 1 }},  
* [[#Grackle|Grackle]] adds {{monzo| -44 26 0 1 }},  
Line 65: Line 69:
{{Mapping|legend=1| 1 0 15 25 | 0 1 -8 -14 }}
{{Mapping|legend=1| 1 0 15 25 | 0 1 -8 -14 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~3/2 = 702.085{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.1233{{c}}, ~3/2 = 702.1573{{c}}
: [[error map]]: {{val| +0.123 +0.326 -2.709 +2.328 }}
* [[CWE]]: ~2 = 1200.0000{{c]}, ~3/2 = 702.0774{{c}}
: error map: {{val| 0.000 +0.122 -2.933 +2.090 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 702.085{{c}} -->


[[Minimax tuning]]:
[[Minimax tuning]]:
Line 79: Line 88:
* 7- and 9-odd-limit [[diamond tradeoff]]: ~3/2 = [701.711, 702.915]
* 7- and 9-odd-limit [[diamond tradeoff]]: ~3/2 = [701.711, 702.915]


{{Optimal ET sequence|legend=1| 12, 29, 41, 53, 94, 241c, 335cd, 576ccd }}
{{Optimal ET sequence|legend=1| 12, 29, 41, 53, 94 }}


[[Badness]] (Smith): 0.021644
[[Badness]] (Sintel): 0.548


=== Cassandra ===
=== Cassandra ===
Line 92: Line 101:
Mapping: {{mapping| 1 0 15 25 -33 | 0 1 -8 -14 23 }}
Mapping: {{mapping| 1 0 15 25 -33 | 0 1 -8 -14 23 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.157{{c}}
Optimal tunings:
* WE: ~2 = 1200.3089{{c}}, ~3/2 = 702.3377{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.1562{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 702.157{{c}} -->


Minimax tuning:
Minimax tuning:
Line 102: Line 114:
* 11-odd-limit diamond tradeoff: ~3/2 = [701.711, 702.915]
* 11-odd-limit diamond tradeoff: ~3/2 = [701.711, 702.915]


{{Optimal ET sequence|legend=0| 41, 53, 94, 229c, 323c, 417cce }}
{{Optimal ET sequence|legend=0| 12e, 41, 53, 94, 229c }}


Badness (Smith): 0.027396
Badness (Sintel): 0.906


==== 13-limit ====
==== 13-limit ====
Line 113: Line 125:
Mapping: {{mapping| 1 0 15 25 -33 -28 | 0 1 -8 -14 23 20 }}
Mapping: {{mapping| 1 0 15 25 -33 -28 | 0 1 -8 -14 23 20 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.113{{c}}
Optimal tunings:
* WE: ~2 = 1200.1703{{c}}, ~3/2 = 702.2122{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.1135{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 702.113{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 126: Line 141:
{{Optimal ET sequence|legend=0| 41, 53, 94, 429ccdeef, 523ccdeef }}
{{Optimal ET sequence|legend=0| 41, 53, 94, 429ccdeef, 523ccdeef }}


Badness (Sintel): 0.020676
Badness (Sintel): 0.854


===== Cassie =====
===== Cassie =====
Line 135: Line 150:
Mapping: {{mapping| 1 0 15 25 -33 -28 -7 | 0 1 -8 -14 23 20 7 }}
Mapping: {{mapping| 1 0 15 25 -33 -28 -7 | 0 1 -8 -14 23 20 7 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.092{{c}}
Optimal tunings:
* WE: ~2 = 1199.8140{{c}}, ~3/2 = 701.9833{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0909{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 702.092{{c}} -->


{{Optimal ET sequence|legend=0| 41, 53, 94g }}
{{Optimal ET sequence|legend=0| 12e, 41, 53, 94g }}


Badness (Smith): 0.023270
Badness (Sintel): 1.19


====== 19-limit ======
====== 19-limit ======
Line 148: Line 166:
Mapping: {{mapping| 1 0 15 25 -33 -28 -7 9 | 0 1 -8 -14 23 20 7 -3 }}
Mapping: {{mapping| 1 0 15 25 -33 -28 -7 9 | 0 1 -8 -14 23 20 7 -3 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.079{{c}}
Optimal tunings:
* WE: ~2 = 1199.9556{{c}}, ~3/2 = 702.0530{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0787{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 702.079{{c}} -->


{{Optimal ET sequence|legend=0| 41, 53, 94g }}
{{Optimal ET sequence|legend=0| 12e, 41, 53 }}


Badness (Smith): 0.018189
Badness (Sintel): 1.11


===== Cassandric =====
===== Cassandric =====
Line 161: Line 182:
Mapping: {{mapping| 1 0 15 25 -33 -28 77 | 0 1 -8 -14 23 20 -46 }}
Mapping: {{mapping| 1 0 15 25 -33 -28 77 | 0 1 -8 -14 23 20 -46 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.097{{c}}
Optimal tunings:
* WE: ~2 = 1200.0046{{c}}, ~3/2 = 702.2167{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0962{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 702.097{{c}} -->


{{Optimal ET sequence|legend=0| 41g, 53, 94, 241ce, 335cde }}
{{Optimal ET sequence|legend=0| 41g, 53, 94 }}


Badness (Smith): 0.023167
Badness (Sintel): 1.18


====== 19-limit ======
====== 19-limit ======
Line 176: Line 200:
Optimal tunings:
Optimal tunings:
* WE: ~2 = 1200.2910{{c}}, ~3/2 = 702.2681{{c}}
* WE: ~2 = 1200.2910{{c}}, ~3/2 = 702.2681{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 702.0967{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0967{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 702.0978{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 702.0978{{c}} -->


{{Optimal ET sequence|legend=1| 41g, 53, 94, 241ceh, 335cdehh }}
{{Optimal ET sequence|legend=1| 41g, 53, 94 }}


Badness (Smith): 0.017635
Badness (Sintel): 1.07


====== 23-limit ======
====== 23-limit ======
Line 193: Line 217:
* WE: ~2 = 1200.2970{{c}}, ~3/2 = 702.2697{{c}}
* WE: ~2 = 1200.2970{{c}}, ~3/2 = 702.2697{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0943{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0943{{c}}
* POTE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0960{{c}}
<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0960{{c}} -->


{{Optimal ET sequence|legend=0| 41g, 53, 94 }}
{{Optimal ET sequence|legend=0| 41g, 53, 94 }}


Badness (Smith): 0.015072
Badness (Sintel): 1.08


===== Cassander =====
===== Cassander =====
Line 206: Line 230:
Mapping: {{mapping| 1 0 15 25 -33 -28 -72 | 0 1 -8 -14 23 20 48 }}
Mapping: {{mapping| 1 0 15 25 -33 -28 -72 | 0 1 -8 -14 23 20 48 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.144{{c}}
Optimal tunings:
* WE: ~2 = 1200.1986{{c}}, ~3/2 = 702.2598{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.1455{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 702.144{{c}} -->


{{Optimal ET sequence|legend=0| 41, 53g, 94 }}
{{Optimal ET sequence|legend=0| 41, 53g, 94 }}


Badness (Smith): 0.022454
Badness (Sintel): 1.14


====== 19-limit ======
====== 19-limit ======
Line 219: Line 246:
Mapping: {{mapping| 1 0 15 25 -33 -28 -72 9 | 0 1 -8 -14 23 20 48 -3 }}
Mapping: {{mapping| 1 0 15 25 -33 -28 -72 9 | 0 1 -8 -14 23 20 48 -3 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.135{{c}}
Optimal tunings:
* WE: ~2 = 1200.3057{{c}}, ~3/2 = 702.3138{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.1373{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 702.135{{c}} -->


{{Optimal ET sequence|legend=0| 41, 53g, 94 }}
{{Optimal ET sequence|legend=0| 41, 53g, 94 }}


Badness (Smith): 0.017576
Badness (Sintel): 1.07


=== Andromeda ===
=== Andromeda ===
Line 232: Line 262:
Mapping: {{mapping| 1 0 15 25 32 | 0 1 -8 -14 -18 }}
Mapping: {{mapping| 1 0 15 25 32 | 0 1 -8 -14 -18 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.321{{c}}
Optimal tunings:
* WE: ~2 = 1200.1917{{c}}, ~3/2 = 702.4836{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.3599{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 702.321{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 242: Line 275:
* 11-odd-limit diamond tradeoff: ~3/2 = [701.711, 704.377]
* 11-odd-limit diamond tradeoff: ~3/2 = [701.711, 704.377]


{{Optimal ET sequence|legend=0| 12, 29, 41, 217ce, 258ce }}
{{Optimal ET sequence|legend=0| 12, 29, 41 }}


Badness (Smith): 0.023556
Badness (Sintel): 0.779


==== 13-limit ====
==== 13-limit ====
Line 253: Line 286:
Mapping: {{mapping| 1 0 15 25 32 37 | 0 1 -8 -14 -18 -21 }}
Mapping: {{mapping| 1 0 15 25 32 37 | 0 1 -8 -14 -18 -21 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.559{{c}}
Optimal tunings:
* WE: ~2 = 1200.3031{{c}}, ~3/2 = 702.7368{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.5420{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 702.559{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 264: Line 300:
* 15-odd-limit diamond tradeoff: ~3/2 = [701.676, 704.377]
* 15-odd-limit diamond tradeoff: ~3/2 = [701.676, 704.377]


{{Optimal ET sequence|legend=0| 12f, 29, 41, 152cdf, 193cdf, 234cdf }}
{{Optimal ET sequence|legend=0| 12f, 29, 41 }}


Badness (Smith): 0.020749
Badness (Sintel): 0.857


===== 17-limit =====
===== 17-limit =====
Line 275: Line 311:
Mapping: {{mapping| 1 0 15 25 32 37 -7 | 0 1 -8 -14 -18 -21 7 }}
Mapping: {{mapping| 1 0 15 25 32 37 -7 | 0 1 -8 -14 -18 -21 7 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.312{{c}}
Optimal tunings:
* WE: ~2 = 1199.1984{{c}}, ~3/2 = 701.8424{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.3384{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 702.312{{c}} -->


{{Optimal ET sequence|legend=0| 12f, 29, 41 }}
{{Optimal ET sequence|legend=0| 12f, 29, 41 }}


Badness (Smith): 0.023406
Badness (Sintel): 1.19


====== 19-limit ======
====== 19-limit ======
Line 288: Line 327:
Mapping: {{mapping| 1 0 15 25 32 37 -7 9 | 0 1 -8 -14 -18 -21 7 -3 }}
Mapping: {{mapping| 1 0 15 25 32 37 -7 9 | 0 1 -8 -14 -18 -21 7 -3 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.357{{c}}
Optimal tunings:
* WE: ~2 = 1199.5242{{c}}, ~3/2 = 702.0783{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.3711{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 702.357{{c}} -->


{{Optimal ET sequence|legend=0| 12f, 29, 41 }}
{{Optimal ET sequence|legend=0| 12f, 29, 41 }}


Badness (Smith): 0.019154
Badness (Sintel): 1.17


===== Schisicosiennic =====
===== Schisicosiennic =====
Line 301: Line 343:
Mapping: {{mapping| 1 0 15 25 32 37 58 | 0 1 -8 -14 -18 -21 -34 }}
Mapping: {{mapping| 1 0 15 25 32 37 58 | 0 1 -8 -14 -18 -21 -34 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.725{{c}}
Optimal tunings:
* WE: ~2 = 1200.6122{{c}}, ~3/2 = 703.0830{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.6968{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 702.725{{c}} -->


{{Optimal ET sequence|legend=0| 12fg, 29g, 41, 70cd, 111cd }}
{{Optimal ET sequence|legend=0| 12fg, 29g, 41, 70cd }}


Badness (Smith): 0.021758
Badness (Sintel): 1.11


====== 19-limit ======
====== 19-limit ======
Line 314: Line 359:
Mapping: {{mapping| 1 0 15 25 32 37 58 9 | 0 1 -8 -14 -18 -21 -34 -3 }}
Mapping: {{mapping| 1 0 15 25 32 37 58 9 | 0 1 -8 -14 -18 -21 -34 -3 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.753{{c}}
Optimal tunings:
* WE: ~2 = 1200.7981{{c}}, ~3/2 = 703.2199{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.7221{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 702.753{{c}} -->


{{Optimal ET sequence|legend=0| 12fg, 29g, 41, 70cd, 111cdh, 181ccddh }}
{{Optimal ET sequence|legend=0| 12fg, 29g, 41, 70cd }}


Badness (Smith): 0.017902
Badness (Sintel): 1.09


===== Schisicosiennoid =====
===== Schisicosiennoid =====
Line 327: Line 375:
Mapping: {{mapping| 1 0 15 25 32 37 12 | 0 1 -8 -14 -18 -21 -5 }}
Mapping: {{mapping| 1 0 15 25 32 37 12 | 0 1 -8 -14 -18 -21 -5 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.717{{c}}
Optimal tunings:
* WE: ~2 = 1201.3146{{c}}, ~3/2 = 703.4864{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.6491{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 702.717{{c}} -->


{{Optimal ET sequence|legend=0| 12f, 29g, 41g, 70cdgg }}
{{Optimal ET sequence|legend=0| 12f, 29g, 41g }}


Badness (Smith): 0.020895
Badness (Sintel): 1.06


====== 19-limit ======
====== 19-limit ======
Line 340: Line 391:
Mapping: {{mapping| 1 0 15 25 32 37 12 9 | 0 1 -8 -14 -18 -21 -5 -3 }}
Mapping: {{mapping| 1 0 15 25 32 37 12 9 | 0 1 -8 -14 -18 -21 -5 -3 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.716{{c}}
Optimal tunings:
* WE: ~2 = 1201.3140{{c}}, ~3/2 = 703.4860{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.6578{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 702.716{{c}} -->


{{Optimal ET sequence|legend=1| 12f, 29g, 41g, 70cdgg }}
{{Optimal ET sequence|legend=1| 12f, 29g, 41g }}


Badness (Smith): 0.016773
Badness (Sintel): 1.02


=== Helenus ===
=== Helenus ===
Line 353: Line 407:
Mapping: {{mapping| 1 0 15 25 51 | 0 1 -8 -14 -30 }}
Mapping: {{mapping| 1 0 15 25 51 | 0 1 -8 -14 -30 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.725{{c}}
Optimal tunings:
* WE: ~2 = 1199.7097{{c}}, ~3/2 = 701.5554{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7370{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 701.725{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 359: Line 416:
: unchanged-interval (eigenmonzo) basis: 2.11/9
: unchanged-interval (eigenmonzo) basis: 2.11/9


{{Optimal ET sequence|legend=0| 12, 41e, 53, 118d, 171de }}
{{Optimal ET sequence|legend=0| 12, 41e, 53, 118d }}


Badness (Smith): 0.035637
Badness (Sintel): 1.18


==== 13-limit ====
==== 13-limit ====
Line 370: Line 427:
Mapping: {{mapping| 1 0 15 25 51 56 | 0 1 -8 -14 -30 -33 }}
Mapping: {{mapping| 1 0 15 25 51 56 | 0 1 -8 -14 -30 -33 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.747{{c}}
Optimal tunings:
* WE: ~2 = 1199.7370{{c}}, ~3/2 = 701.5937{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7570{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 701.747{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 376: Line 436:
: unchanged-interval (eigenmonzo) basis: 2.11/9
: unchanged-interval (eigenmonzo) basis: 2.11/9


{{Optimal ET sequence|legend=0| 12f, 41ef, 53, 118d, 171de }}
{{Optimal ET sequence|legend=0| 12f, …, 41ef, 53, 118d }}


Badness (Smith): 0.026284
Badness (Sintel): 1.09


==== 17-limit ====
==== 17-limit ====
Line 387: Line 447:
Mapping: {{mapping| 1 0 15 25 51 56 -7 | 0 1 -8 -14 -30 -33 7 }}
Mapping: {{mapping| 1 0 15 25 51 56 -7 | 0 1 -8 -14 -30 -33 7 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.680{{c}}
Optimal tunings:
* WE: ~2 = 1199.2895{{c}}, ~3/2 = 701.2643{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.6967{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 701.680{{c}} -->


{{Optimal ET sequence|legend=0| 12f, 41ef, 53, 65d, 118dg }}
{{Optimal ET sequence|legend=0| 12f, 53, 65d, 118dg }}


Badness (Smith): 0.023732
Badness (Sintel): 1.21


==== 19-limit ====
==== 19-limit ====
Line 400: Line 463:
Mapping: {{mapping| 1 0 15 25 51 56 -7 9 | 0 1 -8 -14 -30 -33 7 -3 }}
Mapping: {{mapping| 1 0 15 25 51 56 -7 9 | 0 1 -8 -14 -30 -33 7 -3 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.705{{c}}
Optimal tunings:
* WE: ~2 = 1199.5280{{c}}, ~3/2 = 701.4290{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7149{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 701.705{{c}} -->


{{Optimal ET sequence|legend=1| 12f, 41ef, 53, 65d, 118dg }}
{{Optimal ET sequence|legend=0| 12f, 53, 65d }}


Badness (Smith): 0.019411
Badness (Sintel): 1.18


=== Hemigari ===
=== Hemigari ===
Line 414: Line 480:
: mapping generators: ~2, ~110/63
: mapping generators: ~2, ~110/63


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~110/63 = 951.082{{c}}
Optimal tunings:
* WE: ~2 = 1200.7303{{c}}, ~110/63 = 951.6605{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~110/63 = 951.0604{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~110/63 = 951.082{{c}} -->


{{Optimal ET sequence|legend=0| 29, 53, 82e, 135e, 188ce }}
{{Optimal ET sequence|legend=0| 24d, 29, 53, 82e, 135ee }}


Badness (Smith): 0.050681
Badness (Sintel): 1.68


==== 13-limit ====
==== 13-limit ====
Line 427: Line 496:
Mapping: {{mapping| 1 0 15 25 9 14 | 0 2 -16 -28 -7 -13 }}
Mapping: {{mapping| 1 0 15 25 9 14 | 0 2 -16 -28 -7 -13 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~26/15 = 951.082{{c}}
Optimal tunings:
* WE: ~2 = 1200.8146{{c}}, ~26/15 = 951.7273{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.0574{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~26/15 = 951.082{{c}} -->


{{Optimal ET sequence|legend=0| 29, 53, 82e, 135ef, 188cef }}
{{Optimal ET sequence|legend=0| 24d, 29, 53, 82e, 135eef }}


Badness (Smith): 0.027464
Badness (Sintel): 1.13


=== Karadeniz ===
=== Karadeniz ===
Line 443: Line 515:
: mapping generators: ~2, ~11/9
: mapping generators: ~2, ~11/9


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/9 = 350.994{{c}}
Optimal tunings:
* WE: ~2 = 1199.7351{{c}}, ~11/9 = 350.9167{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 350.9995{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~11/9 = 350.994{{c}} -->


{{Optimal ET sequence|legend=0| 41, 106, 147 }}
{{Optimal ET sequence|legend=0| 24d, 41, 65d, 106, 147 }}


Badness (Smith): 0.041562
Badness (Sintel): 1.37


==== 13-limit ====
==== 13-limit ====
Line 456: Line 531:
Mapping: {{mapping| 1 1 7 11 2 -8 | 0 2 -16 -28 5 40 }}
Mapping: {{mapping| 1 1 7 11 2 -8 | 0 2 -16 -28 5 40 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/9 = 351.014{{c}}
Optimal tunings:
* WE: ~2 = 1199.3042{{c}}, ~11/9 = 350.7533{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 350.9686{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~11/9 = 351.014{{c}} -->


{{Optimal ET sequence|legend=0| 41, 106, 147 }}
{{Optimal ET sequence|legend=0| 24d, 41, 65d, 106f }}


Badness (Smith): 0.042564
Badness (Sintel): 1.34


=== Sanjaab ===
=== Sanjaab ===
Line 470: Line 548:
: mapping generators: ~2, ~11/10
: mapping generators: ~2, ~11/10


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/10 = 165.974{{c}}
Optimal tunings:
* WE: ~2 = 1200.1997{{c}}, ~11/10 = 166.0018{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 165.9786{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~11/10 = 165.974{{c}} -->


{{Optimal ET sequence|legend=1| 29, 65d, 94, 441cde, 535cde, 629cde }}
{{Optimal ET sequence|legend=0| 29, 65d, 94 }}


Badness (Smith): 0.058040
Badness (Sintel): 1.92


==== 13-limit ====
==== 13-limit ====
Line 483: Line 564:
Mapping: {{mapping| 1 2 -1 -3 0 -1 | 0 -3 24 42 25 34 }}
Mapping: {{mapping| 1 2 -1 -3 0 -1 | 0 -3 24 42 25 34 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/10 = 165.963{{c}}
Optimal tunings:
* WE: ~2 = 1200.1224{{c}}, ~11/10 = 165.9800{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 165.9659{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~11/10 = 165.963{{c}} -->


{{Optimal ET sequence|legend=0| 29, 65d, 94 }}
{{Optimal ET sequence|legend=0| 29, 65d, 94 }}


Badness (Smith): 0.033849
Badness (Sintel): 1.40


== Schism ==
== Schism ==
Line 505: Line 589:
{{Mapping|legend=1| 1 0 15 -59 | 0 1 -8 39 }}
{{Mapping|legend=1| 1 0 15 -59 | 0 1 -8 39 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~3/2 = 701.757{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.0989{{c}}, ~3/2 = 701.8145{{c}}
: [[error map]]: {{val| +0.099 -0.042 -0.138 -0.038 }}
* [[CWE]]: ~2 = 1200.0000{{c]}, ~3/2 = 701.7579{{c}}
: error map: {{val| 0.000 -0.197 -0.377 -0.268 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 701.757{{c}} -->


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 519: Line 608:
* 7- and 9-odd-limit [[diamond tradeoff]]: ~3/2 = [701.711, 701.955]
* 7- and 9-odd-limit [[diamond tradeoff]]: ~3/2 = [701.711, 701.955]


{{Optimal ET sequence|legend=1| 53, 118, 171, 1592c, 1763c, 1934c, 2105c, 2276cd, 2447cd, 2618cd, 2789cd, 2960cd, 3131bcd }}
{{Optimal ET sequence|legend=1| 53, 118, 171, 1592c, 1763c, …, 2960cd, 3131bcd }}


[[Badness]] (Smith): 0.014133
[[Badness]] (Sintel): 0.358


=== Helenoid ===
=== Helenoid ===
Line 532: Line 621:
Mapping: {{mapping| 1 0 15 -59 51 | 0 1 -8 39 -30 }}
Mapping: {{mapping| 1 0 15 -59 51 | 0 1 -8 39 -30 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.722{{c}}
Optimal tunings:
* WE: ~2 = 1200.3277{{c}}, ~3/2 = 701.9135{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7223{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 701.722{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 540: Line 632:
{{Optimal ET sequence|legend=0| 53, 118, 289e, 407de }}
{{Optimal ET sequence|legend=0| 53, 118, 289e, 407de }}


Badness (Smith): 0.038863
Badness (Sintel): 1.28


==== 13-limit ====
==== 13-limit ====
Line 549: Line 641:
Mapping: {{mapping| 1 0 15 -59 51 56 | 0 1 -8 39 -30 -33 }}
Mapping: {{mapping| 1 0 15 -59 51 56 | 0 1 -8 39 -30 -33 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.745{{c}}
Optimal tunings:
* WE: ~2 = 1200.1780{{c}}, ~3/2 = 701.8491{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7446{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 701.745{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 557: Line 652:
{{Optimal ET sequence|legend=0| 53, 118, 171e }}
{{Optimal ET sequence|legend=0| 53, 118, 171e }}


Badness (Smith): 0.033677
Badness (Sintel): 1.39


===== 17-limit =====
===== 17-limit =====
Line 566: Line 661:
Mapping: {{mapping| 1 0 15 -59 51 56 -91 | 0 1 -8 39 -30 -33 60 }}
Mapping: {{mapping| 1 0 15 -59 51 56 -91 | 0 1 -8 39 -30 -33 60 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.742{{c}}
Optimal tunings:
* WE: ~2 = 1200.1645{{c}}, ~3/2 = 701.8385{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7425{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 701.742{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 572: Line 670:
: unchanged-interval (eigenmonzo) basis: 2.17/13
: unchanged-interval (eigenmonzo) basis: 2.17/13


{{Optimal ET sequence|legend=0| 53, 118, 171e, 289ef, 460eef }}
{{Optimal ET sequence|legend=0| 53, 118, 171e }}


Badness (Smith): 0.028891
Badness (Sintel): 1.47


==== Helena ====
==== Helena ====
Line 583: Line 681:
Mapping: {{mapping| 1 0 15 -59 51 -28 | 0 1 -8 39 -30 20 }}
Mapping: {{mapping| 1 0 15 -59 51 -28 | 0 1 -8 39 -30 20 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.740{{c}}
Optimal tunings:
* WE: ~2 = 1200.5227{{c}}, ~3/2 = 702.0456{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7418{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 701.740{{c}} -->


{{Optimal ET sequence|legend=0| 53, 118f, 171ef }}
{{Optimal ET sequence|legend=0| 53, 118f, 171ef }}


Badness (Smith): 0.036281
Badness (Sintel): 1.50


===== 17-limit =====
===== 17-limit =====
Line 596: Line 697:
Mapping: {{mapping| 1 0 15 -59 51 -28 -91 | 0 1 -8 39 -30 20 60 }}
Mapping: {{mapping| 1 0 15 -59 51 -28 -91 | 0 1 -8 39 -30 20 60 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.730{{c}}
Optimal tunings:
* WE: ~2 = 1200.4988{{c}}, ~3/2 = 702.0218{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7332{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 701.730{{c}} -->


{{Optimal ET sequence|legend=0| 53, 118f, 171ef, 289eff }}
{{Optimal ET sequence|legend=0| 53, 118f, 171ef }}


Badness (Smith): 0.030688
Badness (Sintel): 1.56


===== 19-limit =====
===== 19-limit =====
Line 609: Line 713:
Mapping: {{mapping| 1 0 15 -59 51 -28 -91 9 | 0 1 -8 39 -30 20 60 -3 }}
Mapping: {{mapping| 1 0 15 -59 51 -28 -91 9 | 0 1 -8 39 -30 20 60 -3 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.729{{c}}
Optimal tunings:
* WE: ~2 = 1200.5185{{c}}, ~3/2 = 702.0323{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7318{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 701.729{{c}} -->


{{Optimal ET sequence|legend=0| 53, 118f, 171ef, 289effh }}
{{Optimal ET sequence|legend=0| 53, 118f, 171ef }}


Badness (Smith): 0.021892
Badness (Sintel): 1.33


=== Ponta ===
=== Ponta ===
Line 624: Line 731:
Mapping: {{mapping| 1 0 15 -59 135 | 0 1 -8 39 -83 }}
Mapping: {{mapping| 1 0 15 -59 135 | 0 1 -8 39 -83 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.783{{c}}
Optimal tunings:
* WE: ~2 = 1199.9814{{c}}, ~3/2 = 701.7725{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7834{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 701.783{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 630: Line 740:
: unchanged-interval (eigenmonzo) basis: 2.11/7
: unchanged-interval (eigenmonzo) basis: 2.11/7


{{Optimal ET sequence|legend=0| 53, 171, 224, 1291cde, 1515cde, 1739cddee, 1963cddee, 2187ccddee }}
{{Optimal ET sequence|legend=0| 53, 171, 224 }}


Badness (Smith): 0.048692
Badness (Sintel): 1.61


==== 13-limit ====
==== 13-limit ====
Line 641: Line 751:
Mapping: {{mapping| 1 0 15 -59 135 56 | 0 1 -8 39 -83 -33 }}
Mapping: {{mapping| 1 0 15 -59 135 56 | 0 1 -8 39 -83 -33 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.784{{c}}
Optimal tunings:
* WE: ~2 = 1199.9601{{c}}, ~3/2 = 701.7610{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7845{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 701.784{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 649: Line 762:
{{Optimal ET sequence|legend=0| 53, 171, 224 }}
{{Optimal ET sequence|legend=0| 53, 171, 224 }}


Badness (Smith): 0.023616
Badness (Sintel): 0.976


==== 17-limit ====
==== 17-limit ====
Line 658: Line 771:
Mapping: {{mapping| 1 0 15 -59 135 56 -91 | 0 1 -8 39 -83 -33 60 }}
Mapping: {{mapping| 1 0 15 -59 135 56 -91 | 0 1 -8 39 -83 -33 60 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.777{{c}}
Optimal tunings:
* WE: ~2 = 1199.8850{{c}}, ~3/2 = 701.7101{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7775{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 701.777{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 666: Line 782:
{{Optimal ET sequence|legend=0| 53, 171, 224, 395e, 619eg }}
{{Optimal ET sequence|legend=0| 53, 171, 224, 395e, 619eg }}


Badness (Smith): 0.022853
Badness (Sintel): 1.16


=== Pontic ===
=== Pontic ===
Line 677: Line 793:
Mapping: {{mapping| 1 0 15 -59 -136 | 0 1 -8 39 88 }}
Mapping: {{mapping| 1 0 15 -59 -136 | 0 1 -8 39 88 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.724{{c}}
Optimal tunings:
* WE: ~2 = 1200.1259{{c}}, ~3/2 = 701.7980{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7256{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 701.724{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 683: Line 802:
: unchanged-interval (eigenmonzo) basis: 2.11
: unchanged-interval (eigenmonzo) basis: 2.11


{{Optimal ET sequence|legend=0| 53e, 118, 289, 407d, 696d }}
{{Optimal ET sequence|legend=0| 53e, 118, 289, 407d }}


Badness (Smith): 0.049573
Badness (Sintel): 1.64


==== 13-limit ====
==== 13-limit ====
Line 694: Line 813:
Mapping: {{mapping| 1 0 15 -59 -136 56 | 0 1 -8 39 88 -33 }}
Mapping: {{mapping| 1 0 15 -59 -136 56 | 0 1 -8 39 88 -33 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.738{{c}}
Optimal tunings:
* WE: ~2 = 1199.9254{{c}}, ~3/2 = 701.6945{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7378{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 701.738{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 700: Line 822:
: unchanged-interval (eigenmonzo) basis: 2.13/11
: unchanged-interval (eigenmonzo) basis: 2.13/11


{{Optimal ET sequence|legend=0| 53e, 118, 171, 289f, 460ef }}
{{Optimal ET sequence|legend=0| 53e, 118, 171, 289f }}


Badness (Smith): 0.045308
Badness (Sintel): 1.87


===== 17-limit =====
===== 17-limit =====
Line 711: Line 833:
Mapping: {{mapping| 1 0 15 -59 -136 56 -91 | 0 1 -8 39 88 -33 60 }}
Mapping: {{mapping| 1 0 15 -59 -136 56 -91 | 0 1 -8 39 88 -33 60 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.740{{c}}
Optimal tunings:
* WE: ~2 = 1199.9454{{c}}, ~3/2 = 701.7085{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7401{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 701.740{{c}} -->


Minimax tuning:  
Minimax tuning:  
Line 717: Line 842:
: unchanged-interval (eigenmonzo) basis: 2.13/11
: unchanged-interval (eigenmonzo) basis: 2.13/11


{{Optimal ET sequence|legend=0| 53e, 118, 171, 289f, 460ef }}
{{Optimal ET sequence|legend=0| 53e, 118, 171, 289f }}


Badness (Smith): 0.029618
Badness (Sintel): 1.51


==== Pontoid ====
==== Pontoid ====
Line 728: Line 853:
Mapping: {{mapping| 1 0 15 -59 -136 -215 | 0 1 -8 39 88 138 }}
Mapping: {{mapping| 1 0 15 -59 -136 -215 | 0 1 -8 39 88 138 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.735{{c}}
Optimal tunings:
* WE: ~2 = 1200.0897{{c}}, ~3/2 = 701.7874{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7356{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 701.735{{c}} -->


{{Optimal ET sequence|legend=0| 53ef, 118f, 171, 289, 460e, 749def }}
{{Optimal ET sequence|legend=0| 53ef, 118f, 171, 289 }}


Badness (Smith): 0.050188
Badness (Sintel): 2.07


===== 17-limit =====
===== 17-limit =====
Line 741: Line 869:
Mapping: {{mapping| 1 0 15 -59 -136 -215 -91 | 0 1 -8 39 88 138 60 }}
Mapping: {{mapping| 1 0 15 -59 -136 -215 -91 | 0 1 -8 39 88 138 60 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.735{{c}}
Optimal tunings:
* WE: ~2 = 1200.1045{{c}}, ~3/2 = 701.7962{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.7359{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 701.735{{c}} -->


{{Optimal ET sequence|legend=0| 53ef, 118f, 171, 289, 460e, 749defg }}
{{Optimal ET sequence|legend=0| 53ef, 118f, 171, 289, 460e, 749defg }}


Badness (Smith): 0.029383
Badness (Sintel): 1.50


=== Bipont ===
=== Bipont ===
Line 757: Line 888:
: mapping generators: ~99/70, ~3
: mapping generators: ~99/70, ~3


Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~3/2 = 701.757{{c}}
Optimal tunings:
* WE: ~99/70 = 600.0500{{c}}, ~3/2 = 701.8153{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 701.7584{{c}}
<!-- * POTE: ~99/70 = 600.000{{c}}, ~3/2 = 701.757{{c}} -->


{{Optimal ET sequence|legend=0| 106, 118, 224, 342, 1592c, 1934ce, 2276cde, 2618cde, 2960cde }}
{{Optimal ET sequence|legend=0| 106, 118, 224, 342, 1592c, 1934ce, 2276cde, 2618cde, 2960cde }}


Badness (Smith): 0.014629
Badness (Sintel): 0.484


==== 13-limit ====
==== 13-limit ====
Line 770: Line 904:
Mapping: {{mapping| 2 0 30 -118 -85 112 | 0 1 -8 39 29 -33 }}
Mapping: {{mapping| 2 0 30 -118 -85 112 | 0 1 -8 39 29 -33 }}


Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~3/2 = 701.773{{c}}
Optimal tunings:
* WE: ~99/70 = 599.9939{{c}}, ~3/2 = 701.7657{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 701.7728{{c}}
<!-- * POTE: ~99/70 = 600.000{{c}}, ~3/2 = 701.773{{c}} -->


{{Optimal ET sequence|legend=0| 106, 118, 224, 566f, 790f }}
{{Optimal ET sequence|legend=0| 106, 118, 224, 566f, 790f }}


Badness (Smith): 0.030172
Badness (Sintel): 1.25


===== 17-limit =====
===== 17-limit =====
Line 783: Line 920:
Mapping: {{mapping| 2 0 30 -118 -85 112 -182 | 0 1 -8 39 29 -33 60 }}
Mapping: {{mapping| 2 0 30 -118 -85 112 -182 | 0 1 -8 39 29 -33 60 }}


Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~3/2 = 701.765{{c}}
Optimal tunings:
* WE: ~99/70 = 599.9839{{c}}, ~3/2 = 701.7463{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 701.7649{{c}}
<!-- * POTE: ~99/70 = 600.000{{c}}, ~3/2 = 701.765{{c}} -->


{{Optimal ET sequence|legend=0| 106g, 118, 224, 342, 566f }}
{{Optimal ET sequence|legend=0| 106g, 118, 224, 342, 566f }}


Badness (Smith): 0.027051
Badness (Sintel): 1.38


==== Counterbipont ====
==== Counterbipont ====
Line 796: Line 936:
Mapping: {{mapping| 2 0 30 -118 -85 -243 | 0 1 -8 39 29 79 }}
Mapping: {{mapping| 2 0 30 -118 -85 -243 | 0 1 -8 39 29 79 }}


Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~3/2 = 701.769{{c}}
Optimal tunings:
* WE: ~99/70 = 600.0405{{c}}, ~3/2 = 701.8160{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 701.7697{{c}}
<!-- * POTE: ~99/70 = 600.000{{c}}, ~3/2 = 701.769{{c}} -->


{{Optimal ET sequence|legend=0| 106f, 118f, 224, 342f, 566, 1356cf, 1922cff }}
{{Optimal ET sequence|legend=0| 106f, 118f, 224, 342f, 566, 1356cf }}


Badness (Smith): 0.025547
Badness (Sintel): 1.06


===== 17-limit =====
===== 17-limit =====
Line 809: Line 952:
Mapping: {{mapping| 2 0 30 -118 -85 -243 -182 | 0 1 -8 39 29 79 60 }}
Mapping: {{mapping| 2 0 30 -118 -85 -243 -182 | 0 1 -8 39 29 79 60 }}


Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~3/2 = 701.764{{c}}
Optimal tunings:
* WE: ~99/70 = 600.0336{{c}}, ~3/2 = 701.8031{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 701.7647{{c}}
<!-- * POTE: ~99/70 = 600.000{{c}}, ~3/2 = 701.764{{c}} -->


{{Optimal ET sequence|legend=0| 106fg, 118f, 224, 342f, 566, 908fg, 1474cffgg }}
{{Optimal ET sequence|legend=0| 106fg, 118f, 224, 342f, 566 }}


Badness (Smith): 0.025251
Badness (Sintel): 1.29


===== 19-limit =====
===== 19-limit =====
Line 822: Line 968:
Mapping: {{mapping| 2 0 30 -118 -85 -243 -182 -169 | 0 1 -8 39 29 79 60 56 }}
Mapping: {{mapping| 2 0 30 -118 -85 -243 -182 -169 | 0 1 -8 39 29 79 60 56 }}


Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~3/2 = 701.761{{c}}
Optimal tunings:
* WE: ~99/70 = 600.0243{{c}}, ~3/2 = 701.7891{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 701.7613{{c}}
<!-- * POTE: ~99/70 = 600.000{{c}}, ~3/2 = 701.761{{c}} -->


{{Optimal ET sequence|legend=0| 106fgh, 118f, 224, 342f, 566h, 908fgh }}
{{Optimal ET sequence|legend=0| 106fgh, 118f, 224, 342f, 566h, 908fgh }}


Badness (Smith): 0.022267
Badness (Sintel): 1.35


==== Quadrapont ====
==== Quadrapont ====
Line 836: Line 985:
: mapping generators: ~208/175, ~3
: mapping generators: ~208/175, ~3


Optimal tuning (POTE): ~208/175 = 300.000{{c}}, ~3/2 = 701.756{{c}}
Optimal tunings:
* WE: ~208/175 = 300.0229{{c}}, ~3/2 = 701.8097{{c}}
* CWE: ~208/175 = 300.0000{{c}}, ~3/2 = 701.7578{{c}}
<!-- * POTE: ~208/175 = 300.000{{c}}, ~3/2 = 701.756{{c}} -->


{{Optimal ET sequence|legend=0| 224, 460, 684, 2276cde, 2960cde, 3644bccddee }}
{{Optimal ET sequence|legend=0| 224, 460, 684, 2276cde, 2960cde }}


Badness (Smith): 0.021025
Badness (Sintel): 0.869


== Grackle ==
== Grackle ==
Line 852: Line 1,004:
: mapping generators: ~2, ~3
: mapping generators: ~2, ~3


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~3/2 = 701.239{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.7974{{c}}, ~3/2 = 701.1210{{c}}
: [[error map]]: {{val| -0.203 -1.037 +3.300 -1.618 }}
* [[CWE]]: ~2 = 1200.0000{{c]}, ~3/2 = 701.2465{{c}}
: error map: {{val| 0.000 -0.709 +3.715 -1.234 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 701.239{{c}} -->


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 858: Line 1,015:
* [[9-odd-limit]] unchanged-interval (eigenmonzo) basis: 2.9/7
* [[9-odd-limit]] unchanged-interval (eigenmonzo) basis: 2.9/7


{{Optimal ET sequence|legend=1| 12, 53d, 65, 77, 166c, 243c }}
{{Optimal ET sequence|legend=1| 12, …, 65, 77, 166c }}


[[Badness]] (Smith): 0.070407
[[Badness]] (Sintel): 1.78


=== 11-limit ===
=== 11-limit ===
Line 869: Line 1,026:
Mapping: {{mapping| 1 0 15 44 70 | 0 1 -8 -26 -42 }}
Mapping: {{mapping| 1 0 15 44 70 | 0 1 -8 -26 -42 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.172{{c}}
Optimal tunings:
* WE: ~2 = 1199.7077{{c}}, ~3/2 = 701.0017{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.1804{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 701.172{{c}} -->


{{Optimal ET sequence|legend=0| 12, 53dee, 65e, 77, 89, 166c, 255c }}
{{Optimal ET sequence|legend=0| 12, 65e, 77, 89, 166c }}


Badness (Smith): 0.048887
Badness (Sintel): 1.62


==== 13-limit ====
==== 13-limit ====
Line 882: Line 1,042:
Mapping: {{mapping| 1 0 15 44 70 75 | 0 1 -8 -26 -42 -45 }}
Mapping: {{mapping| 1 0 15 44 70 75 | 0 1 -8 -26 -42 -45 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.226{{c}}
Optimal tunings:
* WE: ~2 = 1199.7782{{c}}, ~3/2 = 701.0966{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.2319{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 701.226{{c}} -->


{{Optimal ET sequence|legend=0| 12f, 53deeff, 65ef, 77, 166cf, 243cf }}
{{Optimal ET sequence|legend=0| 12f, 65ef, 77, 166cf }}


Badness (Smith): 0.037859
Badness (Sintel): 1.56


===== 17-limit =====
===== 17-limit =====
Line 895: Line 1,058:
Mapping: {{mapping| 1 0 15 44 70 75 -7 | 0 1 -8 -26 -42 -45 7 }}
Mapping: {{mapping| 1 0 15 44 70 75 -7 | 0 1 -8 -26 -42 -45 7 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.206{{c}}
Optimal tunings:
* WE: ~2 = 1199.5839{{c}}, ~3/2 = 700.9632{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.2137{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 701.206{{c}} -->


{{Optimal ET sequence|legend=0| 12f, 53deeff, 65ef, 77, 89f, 166cf }}
{{Optimal ET sequence|legend=0| 12f, 77, 89f, 166cf }}


Badness (Smith): 0.029864
Badness (Sintel): 1.52


===== 19-limit =====
===== 19-limit =====
Line 908: Line 1,074:
Mapping: {{mapping| 1 0 15 44 70 75 -7 9 | 0 1 -8 -26 -42 -45 7 -3 }}
Mapping: {{mapping| 1 0 15 44 70 75 -7 9 | 0 1 -8 -26 -42 -45 7 -3 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.217{{c}}
Optimal tunings:
* WE: ~2 = 1199.7146{{c}}, ~3/2 = 701.0500{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.2212{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 701.217{{c}} -->


{{Optimal ET sequence|legend=0| 12f, 53deeff, 65ef, 77, 166cf }}
{{Optimal ET sequence|legend=0| 12f, 77, 166cf }}


Badness (Smith): 0.023096
Badness (Sintel): 1.40


==== Grackloid ====
==== Grackloid ====
Line 921: Line 1,090:
Mapping: {{mapping| 1 0 15 44 70 -47 | 0 1 -8 -26 -42 32 }}
Mapping: {{mapping| 1 0 15 44 70 -47 | 0 1 -8 -26 -42 32 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.217{{c}}
Optimal tunings:
* WE: ~2 = 1200.0060{{c}}, ~3/2 = 701.2202{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.2167{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 701.217{{c}} -->


{{Optimal ET sequence|legend=0| 12, 53deef, 65e, 77, 166c }}
{{Optimal ET sequence|legend=0| 12, 77, 166c }}


Badness (Smith): 0.048511
Badness (Sintel): 2.00


=== Grack ===
=== Grack ===
Line 934: Line 1,106:
Mapping: {{mapping| 1 0 15 44 51 | 0 1 -8 -26 -30 }}
Mapping: {{mapping| 1 0 15 44 51 | 0 1 -8 -26 -30 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.401{{c}}
Optimal tunings:
* WE: ~2 = 1199.8388{{c}}, ~3/2 = 701.3071{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.4068{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 701.401{{c}} -->


{{Optimal ET sequence|legend=0| 12, 53d, 65, 77e, 142de }}
{{Optimal ET sequence|legend=0| 12, 53d, 65, 77e }}


Badness (Smith): 0.055908
Badness (Sintel): 1.85


==== 13-limit ====
==== 13-limit ====
Line 947: Line 1,122:
Mapping: {{mapping| 1 0 15 44 51 75 | 0 1 -8 -26 -30 -45 }}
Mapping: {{mapping| 1 0 15 44 51 75 | 0 1 -8 -26 -30 -45 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.348{{c}}
Optimal tunings:
* WE: ~2 = 1199.7329{{c}}, ~3/2 = 701.1918{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.3555{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 701.348{{c}} -->


{{Optimal ET sequence|legend=0| 12f, 53dff, 65f, 77e }}
{{Optimal ET sequence|legend=0| 12f, 53dff, 65f, 77e }}


Badness (Smith): 0.044458
Badness (Sintel): 1.84


==== Catahelenic ====
==== Catahelenic ====
Line 960: Line 1,138:
Mapping: {{mapping| 1 0 15 44 51 56 | 0 1 -8 -26 -30 -33 }}
Mapping: {{mapping| 1 0 15 44 51 56 | 0 1 -8 -26 -30 -33 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.529{{c}}
Optimal tunings:
* WE: ~2 = 1199.8928{{c}}, ~3/2 = 701.4664{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.5327{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~3/2 = 701.529{{c}} -->


{{Optimal ET sequence|legend=0| 12f, 53df, 65 }}
{{Optimal ET sequence|legend=0| 12f, …, 53d, 65 }}


Badness (Smith): 0.048524
Badness (Sintel): 2.01


== Bischismic ==
== Bischismic ==
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