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Schismatic family: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings (1/)
Switch to Sintel's badness, WE & CWE tunings (2/)
Line 1,155: Line 1,155:
: mapping generators: ~567/400, ~3
: mapping generators: ~567/400, ~3


[[Optimal tuning]] ([[CTE]]): ~567/400 = 600.0000{{c}}, ~3/2 = 701.5899{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~567/400 = 600.0072{{c}}, ~3/2 = 701.6005{{c}}
: [[error map]]: {{val| +0.014 -0.340 +0.982 -0.629 }}
* [[CWE]]: ~567/400 = 600.0000{{c}}, ~3/2 = 701.5915{{c}}
: error map: {{val| 0.000 -0.364 +0.954 -0.656 }}
<!-- * [[CTE]]: ~567/400 = 600.0000{{c}}, ~3/2 = 701.5899{{c}} -->


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 1,161: Line 1,166:
* [[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, 106d, 118, 130, 248, 378 }}
{{Optimal ET sequence|legend=1| 12, …, 106d, 118, 130, 248, 378 }}


[[Badness]] (Smith): 0.054744
[[Badness]] (Sintel): 1.39


=== 11-limit ===
=== 11-limit ===
Line 1,172: Line 1,177:
Mapping: {{mapping| 2 0 30 69 102 | 0 1 -8 -20 -30 }}
Mapping: {{mapping| 2 0 30 69 102 | 0 1 -8 -20 -30 }}


Optimal tuning (CTE): ~99/70 = 600.0000{{c}}, ~3/2 = 701.6077{{c}}
Optimal tunings:
* WE: ~99/70 = 600.0165{{c}}, ~3/2 = 701.6316{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 701.6110{{c}}
<!-- * CTE: ~99/70 = 600.0000{{c}}, ~3/2 = 701.6077{{c}} -->


{{Optimal ET sequence|legend=0| 12, 106de, 118, 130, 248 }}
{{Optimal ET sequence|legend=0| 12, …, 106de, 118, 130, 248 }}


Badness (Smith): 0.028160
Badness (Sintel): 0.931


==== 13-limit ====
==== 13-limit ====
Line 1,185: Line 1,193:
Mapping: {{mapping| 2 0 30 69 102 -75 | 0 1 -8 -20 -30 26 }}
Mapping: {{mapping| 2 0 30 69 102 -75 | 0 1 -8 -20 -30 26 }}


Optimal tuning (CTE): ~99/70 = 600.0000{{c}}, ~3/2 = 701.5949{{c}}
Optimal tunings:
* WE: ~99/70 = 599.9610{{c}}, ~3/2 = 701.5445{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 701.5908{{c}}
<!-- * CTE: ~99/70 = 600.0000{{c}}, ~3/2 = 701.5949{{c}} -->


{{Optimal ET sequence|legend=0| 12, 106def, 118, 130, 248, 378 }}
{{Optimal ET sequence|legend=0| 12, 118, 130, 248, 378 }}


Badness (Smith): 0.028722
Badness (Sintel): 1.19


===== 17-limit =====
===== 17-limit =====
Line 1,198: Line 1,209:
Mapping: {{mapping| 2 0 30 69 102 -75 5 | 0 1 -8 -20 -30 26 1 }}
Mapping: {{mapping| 2 0 30 69 102 -75 5 | 0 1 -8 -20 -30 26 1 }}


Optimal tuning (CTE): ~99/70 = 600.0000{{c}}, ~3/2 = 701.5959{{c}}
Optimal tunings:
* WE: ~99/70 = 600.0331{{c}}, ~3/2 = 701.6387{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 701.5994{{c}}
<!-- * CTE: ~99/70 = 600.0000{{c}}, ~3/2 = 701.5959{{c}} -->


{{Optimal ET sequence|legend=0| 12, 106def, 118, 130, 248g }}
{{Optimal ET sequence|legend=0| 12, 118, 130, 248g }}


Badness (Smith): 0.029340
Badness (Sintel): 1.49


==== Bischis ====
==== Bischis ====
Line 1,211: Line 1,225:
Mapping: {{mapping| 2 0 30 69 102 131 | 0 1 -8 -20 -30 -39 }}
Mapping: {{mapping| 2 0 30 69 102 131 | 0 1 -8 -20 -30 -39 }}


Optimal tuning (CTE): ~55/39 = 600.0000{{c}}, ~3/2 = 701.5708{{c}}
Optimal tunings:
* WE: ~55/39 = 599.9766{{c}}, ~3/2 = 701.5380{{c}}
* CWE: ~55/39 = 600.0000{{c}}, ~3/2 = 701.5670{{c}}
<!-- * CTE: ~55/39 = 600.0000{{c}}, ~3/2 = 701.5708{{c}} -->


{{Optimal ET sequence|legend=0| 12f, 106deff, 118f, 130 }}
{{Optimal ET sequence|legend=0| 12f, 106deff, 118f, 130 }}


Badness (Smith): 0.029321
Badness (Sintel): 1.21


===== 17-limit =====
===== 17-limit =====
Line 1,224: Line 1,241:
Mapping: {{mapping| 2 0 30 69 102 131 5 | 0 1 -8 -20 -30 -39 1 }}
Mapping: {{mapping| 2 0 30 69 102 131 5 | 0 1 -8 -20 -30 -39 1 }}


Optimal tuning (CTE): ~55/39 = 600.0000{{c}}, ~3/2 = 701.5717{{c}}
Optimal tunings:
* WE: ~55/39 = 600.0997{{c}}, ~3/2 = 701.7114{{c}}
* CWE: ~55/39 = 600.0000{{c}}, ~3/2 = 701.5899{{c}}
<!-- * CTE: ~55/39 = 600.0000{{c}}, ~3/2 = 701.5717{{c}} -->


{{Optimal ET sequence|legend=0| 12f, 106deff, 118f, 130, 248fg }}
{{Optimal ET sequence|legend=0| 12f, 106deff, 118f, 130, 248fg }}


Badness (Smith): 0.026894
Badness (Sintel): 1.37


== Kleischismic ==
== Kleischismic ==
Line 1,238: Line 1,258:
: mapping generators: ~1225/864, ~35/24
: mapping generators: ~1225/864, ~35/24


[[Optimal tuning]] ([[POTE]]): ~1225/864 = 600.000{{c}}, ~35/24 = 650.920{{c}} (~36/35 = 50.920{{c}})
[[Optimal tuning]]s:
* [[WE]]: ~1225/864 = 600.1246{{c}}, ~35/24 = 651.0550{{c}} (~36/35 = 50.9304{{c}})
: [[error map]]: {{val| +0.249 +0.280 -0.453 -0.650 }}
* [[CWE]]: ~1225/864 = 600.0000{{c}}, ~35/24 = 650.9204{{c}} (~36/35 = 50.9204{{c}})
: error map: {{val| 0.000 -0.114 -1.041 -1.338 }}
<!-- * [[POTE]]: ~1225/864 = 600.000{{c}}, ~35/24 = 650.920{{c}} (~36/35 = 50.920{{c}}) -->


{{Optimal ET sequence|legend=1| 24, 70c, 94, 118, 212, 330, 542d, 872cd }}
{{Optimal ET sequence|legend=1| 24, 94, 118, 212, 330, 542d, 872cdd, 1414ccddd }}


[[Badness]] (Smith): 0.110583
[[Badness]] (Sintel): 2.80


=== 11-limit ===
=== 11-limit ===
Line 1,251: Line 1,276:
Mapping: {{mapping| 2 1 22 -15 8 | 0 2 -16 19 -1 }}
Mapping: {{mapping| 2 1 22 -15 8 | 0 2 -16 19 -1 }}


Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~35/24 = 650.918{{c}} (~36/35 = 50.918{{c}})
Optimal tunings:
* WE: ~99/70 = 600.1645{{c}}, ~35/24 = 651.0963{{c}} (~36/35 = 50.9319{{c}})
* CWE: ~99/70 = 600.0000{{c}}, ~35/24 = 650.9184{{c}} (~36/35 = 50.9184{{c}})
<!-- * POTE: ~99/70 = 600.000{{c}}, ~35/24 = 650.918{{c}} (~36/35 = 50.918{{c}}) -->


{{Optimal ET sequence|legend=0| 24, 70c, 94, 118, 212, 330e, 542de }}
{{Optimal ET sequence|legend=0| 24, 94, 118, 212, 330e, 542dee, 872cddeee }}


Badness (Smith): 0.036749
Badness (Sintel): 1.21


==== 13-limit ====
==== 13-limit ====
Line 1,264: Line 1,292:
Mapping: {{mapping| 2 1 22 -15 8 15 | 0 2 -16 19 -1 -7 }}
Mapping: {{mapping| 2 1 22 -15 8 15 | 0 2 -16 19 -1 -7 }}


Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~35/24 = 650.938{{c}} (~36/35 = 50.938{{c}})
Optimal tunings:
* WE: ~99/70 = 600.0696{{c}}, ~35/24 = 651.0136{{c}} (~36/35 = 50.9440{{c}})
* CWE: ~99/70 = 600.0000{{c}}, ~35/24 = 650.9378{{c}} (~36/35 = 50.9378{{c}})
<!-- * POTE: ~99/70 = 600.000{{c}}, ~35/24 = 650.938{{c}} (~36/35 = 50.938{{c}}) -->


{{Optimal ET sequence|legend=0| 24, 70c, 94, 118, 212f }}
{{Optimal ET sequence|legend=0| 24, 94, 118, 212f }}


Badness (Smith): 0.037640
Badness (Sintel): 1.56


===== 17-limit =====
===== 17-limit =====
Line 1,277: Line 1,308:
Mapping: {{mapping| 2 1 22 -15 8 15 6 | 0 2 -16 19 -1 -7 2 }}
Mapping: {{mapping| 2 1 22 -15 8 15 6 | 0 2 -16 19 -1 -7 2 }}


Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~35/24 = 650.942{{c}} (~36/35 = 50.942{{c}})
Optimal tunings:
* WE: ~99/70 = 600.1134{{c}}, ~35/24 = 651.0646{{c}} (~36/35 = 50.9512{{c}})
* CWE: ~99/70 = 600.0000{{c}}, ~35/24 = 650.9414{{c}} (~36/35 = 50.9414{{c}})
<!-- * POTE: ~99/70 = 600.000{{c}}, ~35/24 = 650.942{{c}} (~36/35 = 50.942{{c}}) -->


{{Optimal ET sequence|legend=0| 24, 70c, 94, 118, 212fg }}
{{Optimal ET sequence|legend=0| 24, 94, 118 }}


Badness (Smith): 0.025615
Badness (Sintel): 1.30


==== Kleischis ====
==== Kleischis ====
Line 1,290: Line 1,324:
Mapping: {{mapping| 2 1 22 -15 8 -36 | 0 2 -16 19 -1 40 }}
Mapping: {{mapping| 2 1 22 -15 8 -36 | 0 2 -16 19 -1 40 }}


Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~35/24 = 650.951{{c}} (~36/35 = 50.951{{c}})
Optimal tunings:
* WE: ~99/70 = 600.1909{{c}}, ~35/24 = 651.1578{{c}} (~36/35 = 50.9670{{c}})
* CWE: ~99/70 = 600.0000{{c}}, ~35/24 = 650.9541{{c}} (~36/35 = 50.9541{{c}})
<!-- * POTE: ~99/70 = 600.000{{c}}, ~35/24 = 650.951{{c}} (~36/35 = 50.951{{c}}) -->


{{Optimal ET sequence|legend=0| 24f, 70cf, 94, 118f, 212 }}
{{Optimal ET sequence|legend=0| 24f, 94, 118f, 212 }}


Badness (Smith): 0.037607
Badness (Sintel): 1.55


===== 17-limit =====
===== 17-limit =====
Line 1,303: Line 1,340:
Mapping: {{mapping| 2 1 22 -15 8 -36 6 | 0 2 -16 19 -1 40 2 }}
Mapping: {{mapping| 2 1 22 -15 8 -36 6 | 0 2 -16 19 -1 40 2 }}


Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~35/24 = 650.948{{c}} (~36/35 = 50.948{{c}})
Optimal tunings:
* WE: ~99/70 = 600.2190{{c}}, ~35/24 = 651.1578{{c}} (~36/35 = 50.9670{{c}})
* CWE: ~99/70 = 600.0000{{c}}, ~35/24 = 650.9518{{c}} (~36/35 = 50.9518{{c}})
<!-- * POTE: ~99/70 = 600.000{{c}}, ~35/24 = 650.948{{c}} (~36/35 = 50.948{{c}}) -->


{{Optimal ET sequence|legend=0| 24f, 70cf, 94, 118f, 212g }}
{{Optimal ET sequence|legend=0| 24f, 94, 118f, 212g }}


Badness (Smith): 0.024734
Badness (Sintel): 1.26


== Salsa ==
== Salsa ==
Line 1,365: Line 1,405:
: mapping generators: ~2, ~140/81
: mapping generators: ~2, ~140/81


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~140/81 = 950.797{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.8579{{c}}, ~140/81 = 951.6847{{c}}
: [[error map]]: {{val| -0.142 -0.586 +0.600 +0.708 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~140/81 = 951.7966{{c}}
: error map: {{val| 0.000 -0.362 +0.941 +1.088 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~140/81 = 950.797{{c}} -->


{{Optimal ET sequence|legend=1| 24, 53, 130, 183, 313 }}
{{Optimal ET sequence|legend=1| 24, 53, 130, 183, 313 }}


[[Badness]] (Smith): 0.045817
[[Badness]] (Sintel): 1.16


=== 11-limit ===
=== 11-limit ===
Line 1,378: Line 1,423:
Mapping: {{mapping| 1 0 15 -17 51 | 0 2 -16 25 -60 }}
Mapping: {{mapping| 1 0 15 -17 51 | 0 2 -16 25 -60 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~140/81 = 950.801{{c}}
Optimal tunings:
* WE: ~2 = 1199.8482{{c}}, ~140/81 = 950.6809{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~140/81 = 950.8020{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~140/81 = 950.801{{c}} -->


{{Optimal ET sequence|legend=0| 24e, 53, 130, 183, 313 }}
{{Optimal ET sequence|legend=0| 53, 130, 183, 313, 809cd }}


Badness (Smith): 0.036289
Badness (Sintel): 1.20


=== 13-limit ===
=== 13-limit ===
Line 1,393: Line 1,441:
Mapping: {{mapping| 1 0 15 -17 51 14 | 0 2 -16 25 -60 -13 }}
Mapping: {{mapping| 1 0 15 -17 51 14 | 0 2 -16 25 -60 -13 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~26/15 = 950.801{{c}}
Optimal tunings:
* WE: ~2 = 1199.9140{{c}}, ~140/81 = 950.7324{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~140/81 = 950.8010{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~26/15 = 950.801{{c}} -->


{{Optimal ET sequence|legend=0| 24e, 53, 130, 183, 313 }}
{{Optimal ET sequence|legend=0| 53, 130, 183, 313 }}


Badness (Smith): 0.020816
Badness (Sintel): 0.860


=== 17-limit ===
=== 17-limit ===
Line 1,406: Line 1,457:
Mapping: {{mapping| 1 0 15 -17 51 14 -49 | 0 2 -16 25 -60 -13 67 }}
Mapping: {{mapping| 1 0 15 -17 51 14 -49 | 0 2 -16 25 -60 -13 67 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~26/15 = 950.810{{c}}
Optimal tunings:
* WE: ~2 = 1199.9740{{c}}, ~26/15 = 950.7894{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 950.8100{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~26/15 = 950.810{{c}} -->


{{Optimal ET sequence|legend=0| 53, 130, 183, 496d }}
{{Optimal ET sequence|legend=0| 53, 130, 183, 496d }}


Badness (Smith): 0.021073
Badness (Sintel): 1.07


=== 19-limit ===
=== 19-limit ===
Line 1,419: Line 1,473:
Mapping: {{mapping| 1 0 15 -17 51 14 -49 9 | 0 2 -16 25 -60 -13 67 -6 }}
Mapping: {{mapping| 1 0 15 -17 51 14 -49 9 | 0 2 -16 25 -60 -13 67 -6 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~26/15 = 950.809{{c}}
Optimal tunings:
* WE: ~2 = 1200.0464{{c}}, ~26/15 = 950.8459{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 950.8091{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~26/15 = 950.809{{c}} -->


{{Optimal ET sequence|legend=0| 53, 130, 183, 313h }}
{{Optimal ET sequence|legend=0| 53, 130, 183, 313h }}


Badness (Smith): 0.018262
Badness (Sintel): 1.11


=== 23-limit ===
=== 23-limit ===
Line 1,432: Line 1,489:
Mapping: {{mapping| 1 0 15 -17 51 14 -49 9 -24 | 0 2 -16 25 -60 -13 67 -6 36 }}
Mapping: {{mapping| 1 0 15 -17 51 14 -49 9 -24 | 0 2 -16 25 -60 -13 67 -6 36 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~26/15 = 950.807{{c}}
Optimal tunings:
* WE: ~2 = 1200.0215{{c}}, ~26/15 = 950.8239{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 950.8069{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~26/15 = 950.807{{c}} -->


{{Optimal ET sequence|legend=0| 53, 130, 183, 313h }}
{{Optimal ET sequence|legend=0| 53, 130, 183, 313h }}


Badness (Smith): 0.014819
Badness (Sintel): 1.06


; Music
; Music
Line 1,450: Line 1,510:
{{Mapping|legend=1| 1 2 -1 1 | 0 -3 24 13 }}
{{Mapping|legend=1| 1 2 -1 1 | 0 -3 24 13 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~160/147 = 166.140{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.7408{{c}}, ~160/147 = 166.2424{{c}}
: [[error map]]: {{val| +0.741 +0.799 +2.763 -6.934 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~160/147 = 166.1597{{c}}
: error map: {{val| 0.000 -0.434 +1.518 -8.750 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~160/147 = 166.140{{c}} -->


{{Optimal ET sequence|legend=1| 29, 36, 65 }}
{{Optimal ET sequence|legend=1| 29, 36, 65 }}


[[Badness]] (Smith): 0.174705
[[Badness]] (Sintel): 4.42


=== 11-limit ===
=== 11-limit ===
Line 1,463: Line 1,528:
Mapping: {{mapping| 1 2 -1 1 0 | 0 -3 24 13 25 }}
Mapping: {{mapping| 1 2 -1 1 0 | 0 -3 24 13 25 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/10 = 166.097{{c}}
Optimal tunings:
* WE: ~2 = 1200.6379{{c}}, ~11/10 = 166.1853{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 166.1157{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~11/10 = 166.097{{c}} -->


{{Optimal ET sequence|legend=0| 29, 36, 65 }}
{{Optimal ET sequence|legend=0| 29, 36, 65 }}


Badness (Smith): 0.068310
Badness (Sintel): 2.26


=== 13-limit ===
=== 13-limit ===
Line 1,476: Line 1,544:
Mapping: {{mapping| 1 2 -1 1 0 3 | 0 -3 24 13 25 5 }}
Mapping: {{mapping| 1 2 -1 1 0 3 | 0 -3 24 13 25 5 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/10 = 166.054{{c}}
Optimal tunings:
* WE: ~2 = 1201.1361{{c}}, ~11/10 = 166.2110{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 166.0833{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~11/10 = 166.054{{c}} -->


{{Optimal ET sequence|legend=0| 29, 36, 65f, 94df, 159df }}
{{Optimal ET sequence|legend=0| 29, 65f, 94df }}


Badness (Smith): 0.043750
Badness (Sintel): 1.81


== Tertiaschis ==
== Tertiaschis ==
Line 1,491: Line 1,562:
{{Mapping|legend=1| 1 2 -1 10 | 0 -3 24 -52 }}
{{Mapping|legend=1| 1 2 -1 10 | 0 -3 24 -52 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~192/175 = 166.019{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.3627{{c}}, ~192/175 = 166.0691{{c}}
: [[error map]]: {{val| +0.363 +0.563 -1.019 -0.790 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~192/175 = 166.0172{{c}}
: error map: {{val| 0.000 -0.007 -1.901 -1.720 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~192/175 = 166.019{{c}} -->


{{Optimal ET sequence|legend=1| 65, 94, 159, 253, 412cd }}
{{Optimal ET sequence|legend=1| 65, 94, 159, 253, 412cd }}


[[Badness]] (Smith): 0.211859
[[Badness]] (Sintel): 5.36


=== 11-limit ===
=== 11-limit ===
Line 1,504: Line 1,580:
Mapping: {{mapping| 1 2 -1 10 0 | 0 -3 24 -52 25 }}
Mapping: {{mapping| 1 2 -1 10 0 | 0 -3 24 -52 25 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/10 = 166.017{{c}}
Optimal tunings:
* WE: ~2 = 1200.3379{{c}}, ~11/10 = 166.0638{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 166.0167{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~11/10 = 166.017{{c}} -->


{{Optimal ET sequence|legend=0| 65, 94, 159, 253, 412cd }}
{{Optimal ET sequence|legend=0| 65, 94, 159, 253, 412cd, 665ccde }}


Badness (Smith): 0.061336
Badness (Sintel): 2.07


=== 13-limit ===
=== 13-limit ===
Line 1,517: Line 1,596:
Mapping: {{mapping| 1 2 -1 10 0 12 | 0 -3 24 -52 25 -60 }}
Mapping: {{mapping| 1 2 -1 10 0 12 | 0 -3 24 -52 25 -60 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/10 = 166.016{{c}}
Optimal tunings:
* WE: ~2 = 1200.3467{{c}}, ~11/10 = 166.0635{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 166.0142{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~11/10 = 166.016{{c}} -->


{{Optimal ET sequence|legend=0| 65f, 94, 159, 253, 412cdf, 665ccdef }}
{{Optimal ET sequence|legend=0| 65f, 94, 159, 253, 412cdf, 665ccdef }}


Badness (Smith): 0.036700
Badness (Sintel): 1.52


=== 17-limit ===
=== 17-limit ===
Line 1,530: Line 1,612:
Mapping: {{mapping| 1 2 -1 10 0 12 -2 | 0 -3 24 -52 25 -60 44 }}
Mapping: {{mapping| 1 2 -1 10 0 12 -2 | 0 -3 24 -52 25 -60 44 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/10 = 166.012{{c}}
Optimal tunings:
* WE: ~2 = 1200.3019{{c}}, ~11/10 = 166.0535{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 166.0114{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~11/10 = 166.012{{c}} -->


{{Optimal ET sequence|legend=1| 65f, 94, 159, 253 }}
{{Optimal ET sequence|legend=1| 65f, 94, 159, 253 }}


Badness (Smith): 0.026504
Badness (Sintel): 1.35


== Countertertiaschis ==
== Countertertiaschis ==
Line 1,545: Line 1,630:
{{Mapping|legend=1| 1 2 -1 -12 | 0 -3 24 107 }}
{{Mapping|legend=1| 1 2 -1 -12 | 0 -3 24 107 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~625/567 = 166.0621{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.1265{{c}}, ~625/567 = 166.0797{{c}}
: [[error map]]: {{val| +0.127 +0.059 -0.529 +0.178 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~625/567 = 166.0632{{c}}
: error map: {{val| 0.000 -0.145 -0.797 -0.065 }}
<!-- * [[POTE]]: ~2 = 1200.000{{c}}, ~625/567 = 166.0621{{c}} -->


{{Optimal ET sequence|legend=1| 65d, 159, 224, 383, 607 }}
{{Optimal ET sequence|legend=1| 65d, 159, 224, 383, 607 }}


[[Badness]] (Smith): 0.188043
[[Badness]] (Sintel): 4.76


=== 11-limit ===
=== 11-limit ===
Line 1,558: Line 1,648:
Mapping: {{mapping| 1 2 -1 -12 0 | 0 -3 24 107 25 }}
Mapping: {{mapping| 1 2 -1 -12 0 | 0 -3 24 107 25 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/10 = 166.0628{{c}}
Optimal tunings:
* WE: ~2 = 1200.0804{{c}}, ~11/10 = 166.0739{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 166.0634{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~11/10 = 166.0628{{c}} -->


{{Optimal ET sequence|legend=0| 65d, 159, 224, 383, 607 }}
{{Optimal ET sequence|legend=0| 65d, 159, 224, 383, 607 }}


Badness (Smith): 0.048943
Badness (Sintel): 1.62


=== 13-limit ===
=== 13-limit ===
Line 1,571: Line 1,664:
Mapping: {{mapping| 1 2 -1 -12 0 -10 | 0 -3 24 107 25 99 }}
Mapping: {{mapping| 1 2 -1 -12 0 -10 | 0 -3 24 107 25 99 }}


Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/10 = 166.0628{{c}}
Optimal tunings:
* WE: ~2 = 1200.0805{{c}}, ~11/10 = 166.0740{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 166.0635{{c}}
<!-- * POTE: ~2 = 1200.000{{c}}, ~11/10 = 166.0628{{c}} -->


{{Optimal ET sequence|legend=0| 65d, 159, 224, 383, 607 }}
{{Optimal ET sequence|legend=0| 65d, 159, 224, 383, 607 }}


Badness (Smith): 0.024506
Badness (Sintel): 1.01


== Term ==
== Term ==
Term tempers out the [[landscape comma]], mapping ~63/50 to the 1/3-octave period. It can be described as {{nowrap|12 & 171}}, and is the unique temperament that equates a syntonic~Pythagorean comma with a stack of three [[marvel comma]]s. A [[septimal comma]] is then found as a stack of four marvel commas. In some 7-limit adaptive-tuning practice, the marvel comma corresponds to a melodic unit called a [[kleisma]], with three kleismas making a comma, so this temperament may be useful for modeling that. [[171edo]] makes for an excellent tuning.  
Term tempers out the [[landscape comma]], mapping ~63/50 to the 1/3-octave period. It can be described as {{nowrap| 12 & 171 }}, and is the unique temperament that equates a syntonic~Pythagorean comma with a stack of three [[marvel comma]]s. A [[septimal comma]] is then found as a stack of four marvel commas. In some 7-limit adaptive-tuning practice, the marvel comma corresponds to a melodic unit called a [[kleisma]], with three kleismas making a comma, so this temperament may be useful for modeling that. [[171edo]] makes for an excellent tuning.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 1,587: Line 1,683:
: mapping generators: ~63/50, ~3
: mapping generators: ~63/50, ~3


[[Optimal tuning]] ([[POTE]]): ~63/50 = 400.000{{c}}, ~3/2 = 701.742{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~63/50 = 400.0257{{c}}, ~3/2 = 701.7873{{c}}
: [[error map]]: {{val| +0.077 -0.091 -0.072 +0.031 }}
* [[CWE]]: ~63/50 = 400.0000{{c}}, ~3/2 = 701.7383{{c}}
: error map: {{val| 0.000 -0.217 -0.220 -0.115 }}
<!-- * [[POTE]]: ~63/50 = 400.000{{c}}, ~3/2 = 701.742{{c}} -->


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 1,593: Line 1,694:
* [[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, 147d, 159, 171, 867, 1038, 1209, 1380, 1551, 1722 }}
{{Optimal ET sequence|legend=1| 12, …, 159, 171, 867, 1038, 1209, 1380, 1551, 1722 }}


[[Badness]] (Smith): 0.019950
[[Badness]] (Sintel): 0.505


=== Terminal ===
=== Terminal ===
Line 1,606: Line 1,707:
Mapping: {{mapping| 3 0 45 94 134 | 0 1 -8 -18 -26 }}
Mapping: {{mapping| 3 0 45 94 134 | 0 1 -8 -18 -26 }}


Optimal tuning (POTE): ~44/35 = 400.000{{c}}, ~3/2 = 701.824{{c}}
Optimal tunings:
* WE: ~44/35 = 400.0464{{c}}, ~3/2 = 701.9053{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~3/2 = 701.8178{{c}}
<!-- * POTE: ~44/35 = 400.000{{c}}, ~3/2 = 701.824{{c}} -->


{{Optimal ET sequence|legend=0| 12, 147de, 159, 330 }}
{{Optimal ET sequence|legend=0| 12, …, 159, 330 }}


Badness (Smith): 0.059502
Badness (Sintel): 1.97


==== 13-limit ====
==== 13-limit ====
Line 1,619: Line 1,723:
Mapping: {{mapping| 3 0 45 94 134 168 | 0 1 -8 -18 -26 -33 }}
Mapping: {{mapping| 3 0 45 94 134 168 | 0 1 -8 -18 -26 -33 }}


Optimal tuning (POTE): ~44/35 = 400.000{{c}}, ~3/2 = 701.821{{c}}
Optimal tunings:
* WE: ~44/35 = 400.0449{{c}}, ~3/2 = 701.8995{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~3/2 = 701.8156{{c}}
<!-- * POTE: ~44/35 = 400.000{{c}}, ~3/2 = 701.821{{c}} -->


{{Optimal ET sequence|legend=0| 12f, 147def, 159, 330 }}
{{Optimal ET sequence|legend=0| 12f, …, 159, 330 }}


Badness (Smith): 0.037082
Badness (Sintel): 1.53


==== 17-limit ====
==== 17-limit ====
Line 1,632: Line 1,739:
Mapping: {{mapping| 3 0 45 94 134 168 -2 | 0 1 -8 -18 -26 -33 3 }}
Mapping: {{mapping| 3 0 45 94 134 168 -2 | 0 1 -8 -18 -26 -33 3 }}


Optimal tuning (POTE): ~34/27 = 400.000{{c}}, ~3/2 = 701.810{{c}}
Optimal tunings:
* WE: ~34/27 = 400.0195{{c}}, ~3/2 = 701.8439{{c}}
* CWE: ~34/27 = 400.0000{{c}}, ~3/2 = 701.8081{{c}}
<!-- * POTE: ~34/27 = 400.000{{c}}, ~3/2 = 701.810{{c}} -->


{{Optimal ET sequence|legend=0| 12f, 147def, 159, 171, 330 }}
{{Optimal ET sequence|legend=0| 12f, 159, 171, 330 }}


Badness (Smith): 0.027073
Badness (Sintel): 1.38


=== Terminator ===
=== Terminator ===
Line 1,645: Line 1,755:
Mapping: {{mapping| 3 0 45 94 -137 | 0 1 -8 -18 31 }}
Mapping: {{mapping| 3 0 45 94 -137 | 0 1 -8 -18 31 }}


Optimal tuning (POTE): ~63/50 = 400.000{{c}}, ~3/2 = 701.685{{c}}
Optimal tunings:
* WE: ~63/50 = 399.9677{{c}}, ~3/2 = 701.6278{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~3/2 = 701.6846{{c}}
<!-- * POTE: ~63/50 = 400.000{{c}}, ~3/2 = 701.685{{c}} -->


{{Optimal ET sequence|legend=0| 12e, 159e, 171, 183, 354, 537, 891de }}
{{Optimal ET sequence|legend=0| 12e, 171, 183, 354, 537, 891de }}


Badness (Smith): 0.066968
Badness (Sintel): 2.21


==== 13-limit ====
==== 13-limit ====
Line 1,658: Line 1,771:
Mapping: {{mapping| 3 0 45 94 -137 -103 | 0 1 -8 -18 31 24 }}
Mapping: {{mapping| 3 0 45 94 -137 -103 | 0 1 -8 -18 31 24 }}


Optimal tuning (POTE): ~63/50 = 400.000{{c}}, ~3/2 = 701.689{{c}}
Optimal tunings:
* WE: ~63/50 = 399.9731{{c}}, ~3/2 = 701.6414{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~3/2 = 701.6881{{c}}
<!-- * POTE: ~63/50 = 400.000{{c}}, ~3/2 = 701.689{{c}} -->


{{Optimal ET sequence|legend=0| 171, 183, 354, 891de, 1245dee, 1599ddee }}
{{Optimal ET sequence|legend=0| 12e, 171, 183, 354, 891de }}


Badness (Smith): 0.035487
Badness (Sintel): 1.47


==== 17-limit ====
==== 17-limit ====
Line 1,671: Line 1,787:
Mapping: {{mapping| 3 0 45 94 -137 -103 -2 | 0 1 -8 -18 31 24 3 }}
Mapping: {{mapping| 3 0 45 94 -137 -103 -2 | 0 1 -8 -18 31 24 3 }}


Optimal tuning (POTE): ~63/50 = 400.000{{c}}, ~3/2 = 701.688{{c}}
Optimal tunings:
* WE: ~63/50 = 399.9757{{c}}, ~3/2 = 701.6458{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~3/2 = 701.6881{{c}}
<!-- * POTE: ~63/50 = 400.000{{c}}, ~3/2 = 701.688{{c}} -->


{{Optimal ET sequence|legend=0| 171, 183, 354, 891de, 1245dee, 1599ddee }}
{{Optimal ET sequence|legend=0| 12e, 171, 183, 354, 891de }}


Badness (Smith): 0.020434
Badness (Sintel): 1.04


=== Semiterm ===
=== Semiterm ===
Line 1,687: Line 1,806:
: mapping generators: ~55/49, ~3
: mapping generators: ~55/49, ~3


Optimal tuning (POTE): ~55/49 = 200.0000{{c}}, ~3/2 = 701.7460{{c}}
Optimal tunings:
* WE: ~55/49 = 200.0134{{c}}, ~3/2 = 701.7931{{c}}
* CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 701.7426{{c}}
<!-- * POTE: ~55/49 = 200.0000{{c}}, ~3/2 = 701.7460{{c}} -->


{{Optimal ET sequence|legend=0| 12, 330e, 342, 1380, 1722, 2064, 2406c }}
{{Optimal ET sequence|legend=0| 12, …, 330e, 342, 1380, 1722, 2064, 2406c, 5154bccdde }}


Badness (Smith): 0.029438
Badness (Sintel): 0.973


==== 13-limit ====
==== 13-limit ====
Line 1,700: Line 1,822:
Mapping: {{mapping| 6 0 90 188 287 355 | 0 1 -8 -18 -28 -35 }}
Mapping: {{mapping| 6 0 90 188 287 355 | 0 1 -8 -18 -28 -35 }}


Optimal tuning (POTE): ~55/49 = 200.0000{{c}}, ~3/2 = 701.7256{{c}}
Optimal tunings:
* WE: ~55/49 = 200.0083{{c}}, ~3/2 = 701.7549{{c}}
* CWE: ~55/49 = 200.0000{{c}}, ~3/2 = 701.7238{{c}}
<!-- * POTE: ~55/49 = 200.0000{{c}}, ~3/2 = 701.7256{{c}} -->


{{Optimal ET sequence|legend=0| 12f, 330eff, 342f, 696f }} *
{{Optimal ET sequence|legend=0| 12f, 330eff, 342f, 696f }} *
Line 1,706: Line 1,831:
<nowiki>*</nowiki> optimal patent val: [[354edo|354]]
<nowiki>*</nowiki> optimal patent val: [[354edo|354]]


Badness (Smith): 0.044657
Badness (Sintel): 1.85


=== Hemiterm ===
=== Hemiterm ===
Line 1,716: Line 1,841:
: mapping generators: ~63/50, ~693/400
: mapping generators: ~63/50, ~693/400


Optimal tuning (POTE): ~63/50 = 400.000{{c}}, ~693/400 = 950.872{{c}} (~12/11 = 150.872{{c}})
Optimal tunings:
* WE: ~63/50 = 400.0309{{c}}, ~693/400 = 950.9458{{c}} (~12/11 = 150.8841{{c}})
* CWE: ~63/50 = 400.0000{{c}}, ~693/400 = 950.8707{{c}} (~12/11 = 150.8707{{c}})
<!-- * POTE: ~63/50 = 400.000{{c}}, ~693/400 = 950.872{{c}} (~12/11 = 150.872{{c}}) -->


{{Optimal ET sequence|legend=0| 24d, 159, 183, 342, 1209, 1551, 1893e, 2235ce }}
{{Optimal ET sequence|legend=0| 24d, 159, 183, 342, 1209, 1551, 1893e, 2235ce }}


Badness (Smith): 0.020687
Badness (Sintel): 0.684


==== 13-limit ====
==== 13-limit ====
Line 1,729: Line 1,857:
Mapping: {{mapping| 3 0 45 94 8 42 | 0 2 -16 -36 1 -13 }}
Mapping: {{mapping| 3 0 45 94 8 42 | 0 2 -16 -36 1 -13 }}


Optimal tuning (POTE): ~63/50 = 400.000{{c}}, ~26/15 = 950.873{{c}} (~12/11 = 150.873{{c}})
Optimal tunings:
* WE: ~63/50 = 400.0541{{c}}, ~26/15 = 951.0013{{c}} (~12/11 = 150.8932{{c}})
* CWE: ~63/50 = 400.0000{{c}}, ~26/15 = 950.8696{{c}} (~12/11 = 150.8696{{c}})
<!-- * POTE: ~63/50 = 400.000{{c}}, ~26/15 = 950.873{{c}} (~12/11 = 150.873{{c}}) -->


{{Optimal ET sequence|legend=0| 24d, 159, 183, 342f }}
{{Optimal ET sequence|legend=0| 24d, 159, 183, 342f }}


Badness (Smith): 0.031362
Badness (Sintel): 1.30


==== 17-limit ====
==== 17-limit ====
Line 1,742: Line 1,873:
Mapping: {{mapping| 3 0 45 94 8 42 -2 | 0 2 -16 -36 1 -13 6 }}
Mapping: {{mapping| 3 0 45 94 8 42 -2 | 0 2 -16 -36 1 -13 6 }}


Optimal tuning (POTE): ~34/27 = 400.000{{c}}, ~26/15 = 950.867{{c}} (~12/11 = 150.867{{c}})
Optimal tunings:
* WE: ~34/27 = 400.0373{{c}}, ~26/15 = 950.9556{{c}} (~12/11 = 150.8809{{c}})
* CWE: ~34/27 = 400.0000{{c}}, ~26/15 = 950.8652{{c}} (~12/11 = 150.8652{{c}})
<!-- * POTE: ~34/27 = 400.000{{c}}, ~26/15 = 950.867{{c}} (~12/11 = 150.867{{c}}) -->


{{Optimal ET sequence|legend=0| 24d, 159, 183, 342f, 525f, 867ff }}
{{Optimal ET sequence|legend=0| 24d, 159, 183, 342f, 525f }}


Badness (Smith): 0.022316
Badness (Sintel): 1.14


== Altinex ==
== Altinex ==
Line 1,756: Line 1,890:
: mapping generators: ~1536/1225, ~34300/19683
: mapping generators: ~1536/1225, ~34300/19683


[[Optimal tuning]] ([[CTE]]): ~1536/1225 = 400.000{{c}}, ~34300/19683 = 950.9654{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~1536/1225 = 400.1360{{c}}, ~34300/19683 = 951.2867{{c}}
: [[error map]]: {{val| +0.408 +0.618 -0.781 -1.304 }}
* [[CWE]]: ~1536/1225 = 400.0000{{c}}, ~34300/19683 = 950.9638{{c}}
: error map: {{val| 0.000 -0.027 -1.735 -2.441 }}
<!-- * [[CTE]]: ~1536/1225 = 400.000{{c}}, ~34300/19683 = 950.9654{{c}} -->


{{Optimal ET sequence|legend=1| 24, …, 111c, 135, 159, 612ccdd, 771ccdd }}
{{Optimal ET sequence|legend=1| 24, 135, 159, 612ccdd }}


[[Badness]] (Smith): 0.422026
[[Badness]] (Sintel): 10.7


=== 11-limit ===
=== 11-limit ===
Line 1,769: Line 1,908:
Mapping: {{mapping| 3 0 45 -32 8 | 0 2 -16 17 1 }}
Mapping: {{mapping| 3 0 45 -32 8 | 0 2 -16 17 1 }}


Optimal tuning (CTE): ~44/35 = 400.000{{c}}, ~121/70 = 950.9658{{c}}
Optimal tunings:
* WE: ~44/35 = 400.1156{{c}}, ~121/70 = 951.2377{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~121/70 = 950.9634{{c}}
<!-- * CTE: ~44/35 = 400.000{{c}}, ~121/70 = 950.9658{{c}} -->


{{Optimal ET sequence|legend=0| 24, …, 111c, 135, 159, 612ccdd, 771ccdd }}
{{Optimal ET sequence|legend=0| 24, 135, 159 }}


Badness (Smith): 0.101224
Badness (Sintel): 3.35


=== 13-limit ===
=== 13-limit ===
Line 1,782: Line 1,924:
Mapping: {{mapping| 3 0 45 -32 8 42 | 0 2 -16 17 1 -13 }}
Mapping: {{mapping| 3 0 45 -32 8 42 | 0 2 -16 17 1 -13 }}


Optimal tuning (CTE): ~44/35 = 400.000{{c}}, ~26/15 = 950.9360{{c}}
Optimal tunings:
* WE: ~44/35 = 400.1396{{c}}, ~26/15 = 951.2799{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~26/15 = 950.9462{{c}}
<!-- * CTE: ~44/35 = 400.000{{c}}, ~26/15 = 950.9360{{c}} -->


{{Optimal ET sequence|legend=0| 24, …, 111cf, 135f, 159 }}
{{Optimal ET sequence|legend=0| 24, 135f, 159 }}


Badness (Smith): 0.054894
Badness (Sintel): 2.27


== Sesquiquartififths ==
== Sesquiquartififths ==
Line 1,794: Line 1,939:


{{Mapping|legend=1| 1 1 7 5 | 0 4 -32 -15 }}
{{Mapping|legend=1| 1 1 7 5 | 0 4 -32 -15 }}
: napping generators: ~2, ~448/405
: mapping generators: ~2, ~448/405


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~448/405 = 175.434{{c}}
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~448/405 = 175.434{{c}}
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