Xenharmonic Wiki

Dicot family: Difference between revisions

← Older editNewer edit →
VisualWikitext
Switch to Sintel's badness, WE & CWE tunings, per community consensus
Line 14: Line 14:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~5/4 = 354.664
* [[WE]]: ~2 = 1206.283{{c}}, ~6/5 = 350.420{{c}}
: [[error map]]: {{val| +6.283 +5.167 -23.328 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 351.086{{c}}
: error map: {{val| 0.000 +0.216 -35.228 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~5/4 = 354.664{{c}}
: [[error map]]: {{val| 0.000 +7.374 -31.649 }}
: [[error map]]: {{val| 0.000 +7.374 -31.649 }}
* [[POTE]]: ~2 = 1200.000, ~6/5 = 348.594
* [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 348.594{{c}}
: error map: {{val| 0.000 -4.766 -37.719 }}
: error map: {{val| 0.000 -4.766 -37.719 }} -->


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 25: Line 29:
{{Optimal ET sequence|legend=1| 3, 4, 7, 17, 24c, 31c }}
{{Optimal ET sequence|legend=1| 3, 4, 7, 17, 24c, 31c }}


[[Badness]] (Smith): 0.013028
[[Badness]] (Sintel): 0.306


=== Overview to extensions ===
=== Overview to extensions ===
Line 44: Line 48:
Comma list: 25/24, 45/44
Comma list: 25/24, 45/44


Sval mapping: {{mapping| 1 1 2 2 | 0 2 1 5 }}
Subgroup val mapping: {{mapping| 1 1 2 2 | 0 2 1 5 }}


Gencom mapping: {{mapping| 1 1 2 0 2 | 0 2 1 0 5 }}
Gencom mapping: {{mapping| 1 1 2 0 2 | 0 2 1 0 5 }}
Line 51: Line 55:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~5/4 = 352.287
* WE: ~2 = 1206.750{{c}}, ~6/5 = 348.684{{c}}
* POTE: ~2 = 1200.000, ~6/5 = 346.734
* CWE: ~2 = 1200.000{{c}}, ~6/5 = 348.954{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 352.287{{c}}
* POTE: ~2 = 1200.000{{c}}, ~6/5 = 346.734{{c}} -->


{{Optimal ET sequence|legend=0| 3e, 4e, 7, 24c, 31c, 38cc, 45cce }}
{{Optimal ET sequence|legend=0| 3e, 4e, 7, 24c, 31c }}


RMS error: 5.621 cents
Badness (Sintel): 0.370


==== 2.3.5.11.13 subgroup ====
==== 2.3.5.11.13 subgroup ====
Line 63: Line 69:
Comma list: 25/24, 40/39, 45/44
Comma list: 25/24, 40/39, 45/44


Sval mapping: {{mapping| 1 1 2 2 4 | 0 2 1 5 -1 }}
Subgroup val mapping: {{mapping| 1 1 2 2 4 | 0 2 1 5 -1 }}


Gencom mapping: {{mapping| 1 1 2 0 2 4 | 0 2 1 0 5 -1 }}
Gencom mapping: {{mapping| 1 1 2 0 2 4 | 0 2 1 0 5 -1 }}
Line 70: Line 76:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~5/4 = 352.420
* WE: ~2 = 1202.433{{c}}, ~6/5 = 351.237{{c}}
* POTE: ~2 = 1200.000, ~6/5 = 350.526
* CWE: ~2 = 1200.000{{c}}, ~6/5 = 350.978{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 352.420{{c}}
* POTE: ~2 = 1200.000{{c}}, ~6/5 = 350.526{{c}} -->


{{Optimal ET sequence|legend=0| 3e, 7, 17, 24c }}
{{Optimal ET sequence|legend=0| 3e, 7, 17 }}


RMS error: 5.916 cents
Badness (Sintel): 0.536


== Septimal dicot ==
== Septimal dicot ==
Line 87: Line 95:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~6/5 = 342.257
* [[WE]]: ~2 = 1205.532{{c}}, ~6/5 = 337.931{{c}}
: [[error map]]: {{val| +5.532 -20.561 -37.319 +56.032 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~6/5 = 338.561{{c}}
: error map: {{val| 0.000 -24.834 -47.753 +46.856 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~6/5 = 342.257{{c}}
: [[error map]]: {{val| 0.000 -17.441 -44.056 +57.946 }}
: [[error map]]: {{val| 0.000 -17.441 -44.056 +57.946 }}
* [[POTE]]: ~2 = 1200.000, ~6/5 = 336.381
* [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 336.381{{c}}
: error map: {{val| 0.000 -29.193 -49.933 +40.316 }}
: error map: {{val| 0.000 -29.193 -49.933 +40.316 }} -->


{{Optimal ET sequence|legend=1| 3d, 4, 7 }}
{{Optimal ET sequence|legend=1| 3d, 4, 7 }}


[[Badness]] (Smith): 0.019935
[[Badness]] (Sintel): 0.504


=== 11-limit ===
=== 11-limit ===
Line 104: Line 116:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~6/5 = 345.596
* WE: ~2 = 1203.346{{c}}, ~6/5 = 343.078{{c}}
* POTE: ~2 = 1200.000, ~6/5 = 342.125
* CWE: ~2 = 1200.000{{c}}, ~6/5 = 343.260{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~6/5 = 345.596{{c}}
* POTE: ~2 = 1200.000{{c}}, ~6/5 = 342.125{{c}} -->


{{Optimal ET sequence|legend=0| 3de, 4e, 7 }}
{{Optimal ET sequence|legend=0| 3de, 4e, 7 }}


Badness (Smith): 0.019854
Badness (Sintel): 0.656


=== Eudicot ===
=== Eudicot ===
Line 119: Line 133:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~6/5 = 340.417
* WE: ~2 = 1205.828{{c}}, ~6/5 = 337.683{{c}}
* POTE: ~2 = 1200.000, ~6/5 = 336.051
* CWE: ~2 = 1200.000{{c}}, ~6/5 = 336.909{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~6/5 = 340.417{{c}}
* POTE: ~2 = 1200.000{{c}}, ~6/5 = 336.051{{c}} -->


{{Optimal ET sequence|legend=0| 3d, 4, 7, 18bc, 25bccd }}
{{Optimal ET sequence|legend=0| 3d, 4, 7, 18bc, 25bccd }}


Badness (Smith): 0.027114
Badness (Sintel): 0.896


==== 13-limit ====
==== 13-limit ====
Line 134: Line 150:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~6/5 = 340.835
* WE: ~2 = 1202.660{{c}}, ~6/5 = 339.597{{c}}
* POTE: ~2 = 1200.000, ~6/5 = 338.846
* CWE: ~2 = 1200.000{{c}}, ~6/5 = 339.104{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~6/5 = 340.835{{c}}
* POTE: ~2 = 1200.000{{c}}, ~6/5 = 338.846{{c}} -->


{{Optimal ET sequence|legend=0| 3d, 4, 7 }}
{{Optimal ET sequence|legend=0| 3d, 4, 7 }}


Badness (Smith): 0.023828
Badness (Sintel): 0.985


== Flattie ==
== Flattie ==
Line 151: Line 169:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~6/5 = 346.438
* [[WE]]: ~2 = 1220.466{{c}}, ~6/5 = 337.577{{c}}
: [[error map]]: {{val| +20.466 -6.335 -7.804 -45.004 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~6/5 = 335.391{{c}}
: error map: {{val| 0.000 -31.173 -50.922 -104.217 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~6/5 = 346.438{{c}}
: [[error map]]: {{val| 0.000 -9.080 -39.876 -115.264 }}
: [[error map]]: {{val| 0.000 -9.080 -39.876 -115.264 }}
* [[POTE]]: ~2 = 1200.000, ~6/5 = 331.916
* [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 331.916{{c}}
: error map: {{val| 0.000 -38.123 -54.398 -100.742 }}
: error map: {{val| 0.000 -38.123 -54.398 -100.742 }} -->


{{Optimal ET sequence|legend=1| 3, 4, 7d, 11cd, 18bcddd }}
{{Optimal ET sequence|legend=1| 3, 4, 7d, 11cd, 18bcddd }}


[[Badness]] (Smith): 0.025381
[[Badness]] (Sintel): 0.642


=== 11-limit ===
=== 11-limit ===
Line 168: Line 190:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~6/5 = 343.139
* WE: ~2 = 1216.069{{c}}, ~6/5 = 342.052{{c}}
* POTE: ~2 = 1200.000, ~6/5 = 337.532
* CWE: ~2 = 1200.000{{c}}, ~6/5 = 338.467{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~6/5 = 343.139{{c}}
* POTE: ~2 = 1200.000{{c}}, ~6/5 = 337.532{{c}} -->


{{Optimal ET sequence|legend=0| 3, 4, 7d }}
{{Optimal ET sequence|legend=0| 3, 4, 7d }}


Badness (Smith): 0.024988
Badness (Sintel): 0.826


=== 13-limit ===
=== 13-limit ===
Line 183: Line 207:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~6/5 = 343.655
* WE: ~2 = 1211.546{{c}}, ~6/5 = 344.304{{c}}
* POTE: ~2 = 1200.000, ~6/5 = 341.023
* CWE: ~2 = 1200.000{{c}}, ~6/5 = 341.373{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~6/5 = 343.655{{c}}
* POTE: ~2 = 1200.000{{c}}, ~6/5 = 341.023{{c}} -->


{{Optimal ET sequence|legend=0| 3, 4, 7d }}
{{Optimal ET sequence|legend=0| 3, 4, 7d }}


Badness (Smith): 0.023420
Badness (Sintel): 0.968


== Sharpie ==
== Sharpie ==
Line 200: Line 226:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~5/4 = 359.564
* [[WE]]: ~2 = 1202.488{{c}}, ~5/4 = 358.680{{c}}
: [[error map]]: {{val| +2.488 +17.893 -22.658 -14.258 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 358.495{{c}}
: error map: {{val| 0.000 +15.035 -27.818 -17.854 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~5/4 = 359.564{{c}}
: [[error map]]: {{val| 0.000 +17.173 -26.750 -11.442 }}
: [[error map]]: {{val| 0.000 +17.173 -26.750 -11.442 }}
* [[POTE]]: ~2 = 1200.000, ~5/4 = 357.938
* [[POTE]]: ~2 = 1200.000{{c}}, ~5/4 = 357.938{{c}}
: error map: {{val| 0.000 +13.921 -28.376 -21.198 }}
: error map: {{val| 0.000 +13.921 -28.376 -21.198 }} -->


{{Optimal ET sequence|legend=1| 3d, 7d, 10 }}
{{Optimal ET sequence|legend=1| 3d, 7d, 10 }}


[[Badness]] (Smith): 0.028942
[[Badness]] (Sintel): 0.732


=== 11-limit ===
=== 11-limit ===
Line 217: Line 247:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~5/4 = 357.261
* WE: ~2 = 1201.518{{c}}, ~5/4 = 356.557{{c}}
* POTE: ~2 = 1200.000, ~5/4 = 356.106
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 356.457{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 357.261{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 356.106{{c}} -->


{{Optimal ET sequence|legend=0| 3de, 7d, 10, 17d }}
{{Optimal ET sequence|legend=0| 3de, 7d, 10, 17d }}


Badness (Smith): 0.022366
Badness (Sintel): 0.739


== Dichotic ==
== Dichotic ==
Line 234: Line 266:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~5/4 = 356.333
* [[WE]]: ~2 = 1200.802{{c}}, ~5/4 = 356.502{{c}}
: [[error map]]: {{val| +0.802 +11.851 -28.208 +8.374 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 356.275{{c}}
: error map: {{val| 0.000 +10.595 -30.039 +6.074 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~5/4 = 356.333{{c}}
: [[error map]]: {{val| 0.000 +10.710 -29.981 +5.844 }}
: [[error map]]: {{val| 0.000 +10.710 -29.981 +5.844 }}
* [[POTE]]: ~2 = 1200.000, ~5/4 = 356.264
* [[POTE]]: ~2 = 1200.000{{c}}, ~5/4 = 356.264{{c}}
: error map: {{val| 0.000 +10.573 -30.050 +6.119 }}
: error map: {{val| 0.000 +10.573 -30.050 +6.119 }} -->


{{Optimal ET sequence|legend=1| 3, 7, 10, 17, 27c }}
{{Optimal ET sequence|legend=1| 3, 7, 10, 17, 27c }}


[[Badness]] (Smith): 0.037565
[[Badness]] (Sintel): 0.951


=== 11-limit ===
=== 11-limit ===
Line 251: Line 287:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~5/4 = 354.183
* WE: ~2 = 1199.504{{c}}, ~5/4 = 354.115{{c}}
* POTE: ~2 = 1200.000, ~5/4 = 354.262
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 354.236{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 354.183{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 354.262{{c}} -->


{{Optimal ET sequence|legend=0| 7, 10, 17 }}
{{Optimal ET sequence|legend=0| 7, 10, 17 }}


Badness (Smith): 0.030680
Badness (Sintel): 1.01


==== 13-limit ====
==== 13-limit ====
Line 266: Line 304:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~5/4 = 354.247
* WE: ~2 = 1199.289{{c}}, ~5/4 = 354.156{{c}}
* POTE: ~2 = 1200.000, ~5/4 = 354.365
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 354.340{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 354.247{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 354.365{{c}} -->


{{Optimal ET sequence|legend=0| 7, 10, 17, 27ce, 44cce }}
{{Optimal ET sequence|legend=0| 7, 10, 17, 27ce, 44cce }}


Badness (Smith): 0.021674
Badness (Sintel): 0.896


=== Dichotomic ===
=== Dichotomic ===
Line 281: Line 321:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~5/4 = 353.751
* WE: ~2 = 1203.949{{c}}, ~5/4 = 355.239{{c}}
* POTE: ~2 = 1200.000, ~5/4 = 354.073
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 354.024{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 353.751{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 354.073{{c}} -->


{{Optimal ET sequence|legend=0| 3, 7, 10e }}
{{Optimal ET sequence|legend=0| 3, 7, 10e }}


Badness (Smith): 0.031719
Badness (Sintel): 1.05


==== 13-limit ====
==== 13-limit ====
Line 296: Line 338:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~5/4 = 353.850
* WE: ~2 = 1202.979{{c}}, ~5/4 = 355.193{{c}}
* POTE: ~2 = 1200.000, ~5/4 = 354.313
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 354.254{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 353.850{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 354.313{{c}} -->


{{Optimal ET sequence|legend=0| 3, 7, 10e }}
{{Optimal ET sequence|legend=0| 3, 7, 10e }}


Badness (Smith): 0.022741
Badness (Sintel): 0.940


=== Dichosis ===
=== Dichosis ===
Line 311: Line 355:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~5/4 = 361.081
* WE: ~2 = 1197.526{{c}}, ~5/4 = 359.915{{c}}
* POTE: ~2 = 1200.000, ~5/4 = 360.659
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 360.745{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 361.081{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 360.659{{c}} -->


{{Optimal ET sequence|legend=0| 3, 7e, 10 }}
{{Optimal ET sequence|legend=0| 3, 7e, 10 }}


Badness (Smith): 0.041361
Badness (Sintel): 1.37


==== 13-limit ====
==== 13-limit ====
Line 326: Line 372:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~5/4 = 361.061
* WE: ~2 = 1197.922{{c}}, ~5/4 = 360.021{{c}}
* POTE: ~2 = 1200.000, ~5/4 = 360.646
* CWE: ~2 = 1200.000{{c}}, ~5/4 = 360.722{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/4 = 361.061{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/4 = 360.646{{c}} -->


{{Optimal ET sequence|legend=0| 3, 7e, 10 }}
{{Optimal ET sequence|legend=0| 3, 7e, 10 }}


Badness (Smith): 0.027938
Badness (Sintel): 1.15


== Decimal ==
== Decimal ==
Line 346: Line 394:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~7/5 = 600.000, ~7/4 = 955.608 (~8/7 = 244.392)
* [[WE]]: ~7/5 = 603.286{{c}}, ~7/4 = 953.637{{c}} (~7/6 = 252.935{{c}})
: [[error map]]: {{val| +6.571 +5.318 -22.821 -2.047 }}
* [[CWE]]: ~7/5 = 600.000{{c}}, ~7/4 = 950.957{{c}} (~7/6 = 249.043{{c}})
: error map: {{val| 0.000 -0.041 -35.357 -17.869 }}
<!-- * [[CTE]]: ~7/5 = 600.000{{c}}, ~7/4 = 955.608{{c}} (~8/7 = 244.392{{c}})
: [[error map]]: {{val| 0.000 +9.260 -30.706 -13.218 }}
: [[error map]]: {{val| 0.000 +9.260 -30.706 -13.218 }}
* [[POTE]]: ~7/5 = 600.000, ~7/4 = 948.443 (~7/6 = 251.557)
* [[POTE]]: ~7/5 = 600.000{{c}}, ~7/4 = 948.443{{c}} (~7/6 = 251.557{{c}})
: error map: {{val| 0.000 -5.069 -37.871 -20.383 }}
: error map: {{val| 0.000 -5.069 -37.871 -20.383 }} -->


{{Optimal ET sequence|legend=1| 4, 10, 14c, 24c, 38ccd }}
{{Optimal ET sequence|legend=1| 4, 10, 14c, 24c, 38ccd }}


[[Badness]] (Smith): 0.028334
[[Badness]] (Sintel): 0.717


=== 11-limit ===
=== 11-limit ===
Line 363: Line 415:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~7/4 = 952.812 (~8/7 = 247.188)
* WE: ~7/5 = 603.558{{c}}, ~7/4 = 952.121{{c}} (~7/6 = 254.996{{c}})
* POTE: ~7/5 = 600.000, ~7/4 = 946.507 (~7/6 = 253.493)
* CWE: ~7/5 = 600.000{{c}}, ~7/4 = 948.610{{c}} (~7/6 = 251.390{{c}})
<!-- * CTE: ~7/5 = 600.000{{c}}, ~7/4 = 952.812{{c}} (~8/7 = 247.188{{c}})
* POTE: ~7/5 = 600.000{{c}}, ~7/4 = 946.507{{c}} (~7/6 = 253.493{{c}}) -->


{{Optimal ET sequence|legend=0| 4e, 10, 14c, 24c }}
{{Optimal ET sequence|legend=0| 4e, 10, 14c, 24c }}


Badness (Smith): 0.026712
Badness (Sintel): 0.883


==== 13-limit ====
==== 13-limit ====
Line 378: Line 432:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~7/4 = 954.469 (~8/7 = 245.531)
* WE: ~7/5 = 603.612{{c}}, ~7/4 = 953.663{{c}} (~7/6 = 253.562{{c}})
* POTE: ~7/5 = 600.000, ~7/4 = 947.955 (~7/6 = 252.045)
* CWE: ~7/5 = 600.000{{c}}, ~7/4 = 950.116{{c}} (~7/6 = 249.884{{c}})
<!-- * CTE: ~7/5 = 600.000{{c}}, ~7/4 = 954.469{{c}} (~8/7 = 245.531{{c}})
* POTE: ~7/5 = 600.000{{c}}, ~7/4 = 947.955{{c}} (~7/6 = 252.045{{c}}) -->


{{Optimal ET sequence|legend=0| 4ef, 10, 14cf, 24cf }}
{{Optimal ET sequence|legend=0| 4ef, 10, 14cf, 24cf }}


Badness (Smith): 0.021326
Badness (Sintel): 0.881


=== Decimated ===
=== Decimated ===
Line 393: Line 449:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~7/4 = 950.940 (~7/6 = 249.060)
* WE: ~7/5 = 604.535{{c}}, ~7/4 = 952.076{{c}} (~7/6 = 256.994{{c}})
* POTE: ~7/5 = 600.000, ~7/4 = 944.934 (~7/6 = 255.066)
* CWE: ~7/5 = 600.000{{c}}, ~7/4 = 946.108{{c}} (~7/6 = 253.892{{c}})
<!-- * CTE: ~7/5 = 600.000{{c}}, ~7/4 = 950.940{{c}} (~7/6 = 249.060{{c}})
* POTE: ~7/5 = 600.000{{c}}, ~7/4 = 944.934{{c}} (~7/6 = 255.066{{c}}) -->


{{Optimal ET sequence|legend=0| 4, 10e, 14c }}
{{Optimal ET sequence|legend=0| 4, 10e, 14c }}


Badness (Smith): 0.031456
Badness (Sintel): 1.04


=== Decibel ===
=== Decibel ===
Line 408: Line 466:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 600.000, ~7/4 = 955.608 (~8/7 = 244.392)
* WE: ~7/5 = 599.404{{c}}, ~7/4 = 955.557{{c}} (~8/7 = 243.251{{c}})
* POTE: ~7/5 = 600.000, ~7/4 = 956.507 (~8/7 = 243.493)
* CWE: ~7/5 = 600.000{{c}}, ~7/4 = 956.169{{c}} (~8/7 = 243.831{{c}})
<!-- * CTE: ~7/5 = 600.000{{c}}, ~7/4 = 955.608{{c}} (~8/7 = 244.392{{c}})
* POTE: ~7/5 = 600.000{{c}}, ~7/4 = 956.507{{c}} (~8/7 = 243.493{{c}}) -->


{{Optimal ET sequence|legend=0| 4, 6, 10 }}
{{Optimal ET sequence|legend=0| 4, 6, 10 }}


Badness (Smith): 0.032385
Badness (Sintel): 1.07


== Sidi ==
== Sidi ==
Line 420: Line 480:
[[Comma list]]: 25/24, 245/243
[[Comma list]]: 25/24, 245/243


{{Mapping|legend=1| 1 3 3 6 | 0 -4 -2 -9 }}
{{Mapping|legend=1| 1 -1 1 -3 | 0 4 2 9 }}


: mapping generators: ~2, ~9/7
: mapping generators: ~2, ~14/9


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~9/7 = 424.452
* [[WE]]: ~2 = 1207.178{{c}}, ~14/9 = 777.414{{c}}
: [[error map]]: {{val| +7.178 +0.523 -24.308 +6.367 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~14/9 = 773.872{{c}}
: error map: {{val| 0.000 -6.464 -38.569 -3.973 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~14/9 = 775.548{{c}}
: [[error map]]: {{val| 0.000 +0.238 -35.217 +11.108 }}
: [[error map]]: {{val| 0.000 +0.238 -35.217 +11.108 }}
* [[POTE]]: ~2 = 1200.000, ~9/7 = 427.208
* [[POTE]]: ~2 = 1200.000{{c}}, ~14/9 = 772.792{{c}}
: error map: {{val| 0.000 -10.789 -40.731 -13.702 }}
: error map: {{val| 0.000 -10.789 -40.731 -13.702 }} -->


{{Optimal ET sequence|legend=1| 3d, …, 11cd, 14c }}
{{Optimal ET sequence|legend=1| 3d, …, 11cd, 14c }}


[[Badness]] (Smith): 0.056586
[[Badness]] (Sintel): 1.43


=== 11-limit ===
=== 11-limit ===
Line 439: Line 503:
Comma list: 25/24, 45/44, 99/98
Comma list: 25/24, 45/44, 99/98


Mapping: {{mapping| 1 3 3 6 7 | 0 -4 -2 -9 -10 }}
Mapping: {{mapping| 1 -1 1 -3 -3 | 0 4 2 9 10 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~9/7 = 424.587
* WE: ~2 = 1207.200{{c}}, ~11/7 = 777.363{{c}}
* POTE: ~2 = 1200.000, ~9/7 = 427.273
* CWE: ~2 = 1200.000{{c}}, ~11/7 = 773.777{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~11/7 = 775.413{{c}}
* POTE: ~2 = 1200.000{{c}}, ~11/7 = 772.727{{c}} -->


{{Optimal ET sequence|legend=0| 3de, …, 11cdee, 14c }}
{{Optimal ET sequence|legend=0| 3de, …, 11cdee, 14c }}


Badness (Smith): 0.032957
Badness (Sintel): 1.09


[[Category:Temperament families]]
[[Category:Temperament families]]
Retrieved from "https://en.xen.wiki/w/Dicot_family"