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Dicot family: Difference between revisions

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Review, +CTE tunings and error maps
m Spell out 1\1 in decimal, note the badness metric being used, and misc. cleanup
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~5/4 = 354.664
* [[CTE]]: ~2 = 1200.000, ~5/4 = 354.664
: [[error map]]: {{val| 0.000 +7.374 -31.649 }}
: [[error map]]: {{val| 0.000 +7.374 -31.649 }}
* [[POTE]]: ~2 = 1\1, ~6/5 = 348.594
* [[POTE]]: ~2 = 1200.000, ~6/5 = 348.594
: error map: {{val| 0.000 -4.766 -37.719 }}
: error map: {{val| 0.000 -4.766 -37.719 }}


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{{Optimal ET sequence|legend=1| 3, 4, 7, 17, 24c, 31c }}
{{Optimal ET sequence|legend=1| 3, 4, 7, 17, 24c, 31c }}


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


=== Overview to extensions ===
=== Overview to extensions ===
Line 45: Line 45:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 352.287
* CTE: ~2 = 1200.000, ~5/4 = 352.287
* POTE: ~2 = 1\1, ~6/5 = 346.734
* POTE: ~2 = 1200.000, ~6/5 = 346.734


{{Optimal ET sequence|legend=0| 3e, 4e, 7, 24c, 31c, 38cc, 45cce }}
{{Optimal ET sequence|legend=0| 3e, 4e, 7, 24c, 31c, 38cc, 45cce }}
Line 57: Line 57:
Comma list: 25/24, 40/39, 45/44
Comma list: 25/24, 40/39, 45/44


Gencom mapping]]: {{mapping| 1 1 2 0 2 4 | 0 2 1 0 5 -1 }}
Sval 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: [2 5/4; 25/24 40/39 45/44]
: gencom: [2 5/4; 25/24 40/39 45/44]
Sval mapping: {{mapping| 1 1 2 2 4 | 0 2 1 5 -1 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 352.420
* CTE: ~2 = 1200.000, ~5/4 = 352.420
* POTE: ~2 = 1\1, ~6/5 = 350.526
* POTE: ~2 = 1200.000, ~6/5 = 350.526


{{Optimal ET sequence|legend=0| 3e, 7, 17, 24c }}
{{Optimal ET sequence|legend=0| 3e, 7, 17, 24c }}
Line 81: Line 81:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~6/5 = 342.257
* [[CTE]]: ~2 = 1200.000, ~6/5 = 342.257
: [[error map]]: {{val| 0.000 -17.441 -44.056 +57.946 }}
: [[error map]]: {{val| 0.000 -17.441 -44.056 +57.946 }}
* [[POTE]]: ~2 = 1\1, ~6/5 = 336.381
* [[POTE]]: ~2 = 1200.000, ~6/5 = 336.381
: 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]]: 0.019935
[[Badness]] (Smith): 0.019935


=== 11-limit ===
=== 11-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~6/5 = 345.596
* CTE: ~2 = 1200.000, ~6/5 = 345.596
* POTE: ~2 = 1\1, ~6/5 = 342.125
* POTE: ~2 = 1200.000, ~6/5 = 342.125


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


Badness: 0.019854
Badness (Smith): 0.019854


=== Eudicot ===
=== Eudicot ===
Line 113: Line 113:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~6/5 = 340.417
* CTE: ~2 = 1200.000, ~6/5 = 340.417
* POTE: ~2 = 1\1, ~6/5 = 336.051
* POTE: ~2 = 1200.000, ~6/5 = 336.051


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


Badness: 0.027114
Badness (Smith): 0.027114


==== 13-limit ====
==== 13-limit ====
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~6/5 = 340.835
* CTE: ~2 = 1200.000, ~6/5 = 340.835
* POTE: ~2 = 1\1, ~6/5 = 338.846
* POTE: ~2 = 1200.000, ~6/5 = 338.846


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


Badness: 0.023828
Badness (Smith): 0.023828


== Flat ==
== Flat ==
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~6/5 = 346.438
* [[CTE]]: ~2 = 1200.000, ~6/5 = 346.438
: [[error map]]: {{val| 0.000 -9.080 -39.876 -115.264 }}
: [[error map]]: {{val| 0.000 -9.080 -39.876 -115.264 }}
* [[POTE]]: ~2 = 1\1, ~6/5 = 331.916
* [[POTE]]: ~2 = 1200.000, ~6/5 = 331.916
: 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]]: 0.025381
[[Badness]] (Smith): 0.025381


=== 11-limit ===
=== 11-limit ===
Line 162: Line 162:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~6/5 = 343.139
* CTE: ~2 = 1200.000, ~6/5 = 343.139
* POTE: ~2 = 1\1, ~6/5 = 337.532
* POTE: ~2 = 1200.000, ~6/5 = 337.532


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


Badness: 0.024988
Badness (Smith): 0.024988


=== 13-limit ===
=== 13-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~6/5 = 343.655
* CTE: ~2 = 1200.000, ~6/5 = 343.655
* POTE: ~2 = 1\1, ~6/5 = 341.023
* POTE: ~2 = 1200.000, ~6/5 = 341.023


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


Badness: 0.023420
Badness (Smith): 0.023420


== Sharp ==
== Sharp ==
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~5/4 = 359.564
* [[CTE]]: ~2 = 1200.000, ~5/4 = 359.564
: [[error map]]: {{val| 0.000 +17.173 -26.750 -11.442 }}
: [[error map]]: {{val| 0.000 +17.173 -26.750 -11.442 }}
* [[POTE]]: ~2 = 1\1, ~5/4 = 357.938
* [[POTE]]: ~2 = 1200.000, ~5/4 = 357.938
: error map: {{val| 0.000 +13.921 -28.376 -21.198 }}
: error map: {{val| 0.000 +13.921 -28.376 -21.198 }}


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


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


=== 11-limit ===
=== 11-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 357.261
* CTE: ~2 = 1200.000, ~5/4 = 357.261
* POTE: ~2 = 1\1, ~5/4 = 356.106
* POTE: ~2 = 1200.000, ~5/4 = 356.106


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


Badness: 0.022366
Badness (Smith): 0.022366


== Dichotic ==
== Dichotic ==
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~5/4 = 356.333
* [[CTE]]: ~2 = 1200.000, ~5/4 = 356.333
: [[error map]]: {{val| 0.000 +10.710 -29.981 +5.844 }}
: [[error map]]: {{val| 0.000 +10.710 -29.981 +5.844 }}
* [[POTE]]: ~2 = 1\1, ~5/4 = 356.264
* [[POTE]]: ~2 = 1200.000, ~5/4 = 356.264
: 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]]: 0.037565
[[Badness]] (Smith): 0.037565


=== 11-limit ===
=== 11-limit ===
Line 245: Line 245:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 354.183
* CTE: ~2 = 1200.000, ~5/4 = 354.183
* POTE: ~2 = 1\1, ~5/4 = 354.262
* POTE: ~2 = 1200.000, ~5/4 = 354.262


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


Badness: 0.030680
Badness (Smith): 0.030680


==== 13-limit ====
==== 13-limit ====
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 354.247
* CTE: ~2 = 1200.000, ~5/4 = 354.247
* POTE: ~2 = 1\1, ~5/4 = 354.365
* POTE: ~2 = 1200.000, ~5/4 = 354.365


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


Badness: 0.021674
Badness (Smith): 0.021674


=== Dichotomic ===
=== Dichotomic ===
Line 275: Line 275:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 353.751
* CTE: ~2 = 1200.000, ~5/4 = 353.751
* POTE: ~2 = 1\1, ~5/4 = 354.073
* POTE: ~2 = 1200.000, ~5/4 = 354.073


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


Badness: 0.031719
Badness (Smith): 0.031719


==== 13-limit ====
==== 13-limit ====
Line 290: Line 290:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 353.850
* CTE: ~2 = 1200.000, ~5/4 = 353.850
* POTE: ~2 = 1\1, ~5/4 = 354.313
* POTE: ~2 = 1200.000, ~5/4 = 354.313


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


Badness: 0.022741
Badness (Smith): 0.022741


=== Dichosis ===
=== Dichosis ===
Line 305: Line 305:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 361.081
* CTE: ~2 = 1200.000, ~5/4 = 361.081
* POTE: ~2 = 1\1, ~5/4 = 360.659
* POTE: ~2 = 1200.000, ~5/4 = 360.659


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


Badness: 0.041361
Badness (Smith): 0.041361


==== 13-limit ====
==== 13-limit ====
Line 320: Line 320:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~5/4 = 361.061
* CTE: ~2 = 1200.000, ~5/4 = 361.061
* POTE: ~2 = 1\1, ~5/4 = 360.646
* POTE: ~2 = 1200.000, ~5/4 = 360.646


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


Badness: 0.027938
Badness (Smith): 0.027938


== Decimal ==
== Decimal ==
Line 341: Line 341:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~7/5 = 1\2, ~7/4 = 955.608 (~8/7 = 244.392)
* [[CTE]]: ~7/5 = 600.000, ~7/4 = 955.608 (~8/7 = 244.392)
: [[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 = 1\2, ~7/4 = 948.443 (~7/6 = 251.557)
* [[POTE]]: ~7/5 = 600.000, ~7/4 = 948.443 (~7/6 = 251.557)
: 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]]: 0.028334
[[Badness]] (Smith): 0.028334


=== 11-limit ===
=== 11-limit ===
Line 358: Line 358:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 1\2, ~7/4 = 952.812 (~8/7 = 247.188)
* CTE: ~7/5 = 600.000, ~7/4 = 952.812 (~8/7 = 247.188)
* POTE: ~7/5 = 1\2, ~7/4 = 946.507 (~7/6 = 253.493)
* POTE: ~7/5 = 600.000, ~7/4 = 946.507 (~7/6 = 253.493)


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


Badness: 0.026712
Badness (Smith): 0.026712


==== 13-limit ====
==== 13-limit ====
Line 373: Line 373:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 1\2, ~7/4 = 954.469 (~8/7 = 245.531)
* CTE: ~7/5 = 600.000, ~7/4 = 954.469 (~8/7 = 245.531)
* POTE: ~7/5 = 1\2, ~7/4 = 947.955 (~7/6 = 252.045)
* POTE: ~7/5 = 600.000, ~7/4 = 947.955 (~7/6 = 252.045)


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


Badness: 0.021326
Badness (Smith): 0.021326


=== Decimated ===
=== Decimated ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 1\2, ~7/4 = 950.940 (~7/6 = 249.060)
* CTE: ~7/5 = 600.000, ~7/4 = 950.940 (~7/6 = 249.060)
* POTE: ~7/5 = 1\2, ~7/4 = 944.934 (~7/6 = 255.066)
* POTE: ~7/5 = 600.000, ~7/4 = 944.934 (~7/6 = 255.066)


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


Badness: 0.031456
Badness (Smith): 0.031456


=== Decibel ===
=== Decibel ===
Line 403: Line 403:


Optimal tunings:  
Optimal tunings:  
* CTE: ~7/5 = 1\2, ~7/4 = 955.608 (~8/7 = 244.392)
* CTE: ~7/5 = 600.000, ~7/4 = 955.608 (~8/7 = 244.392)
* POTE: ~7/5 = 1\2, ~7/4 = 956.507 (~8/7 = 243.493)
* POTE: ~7/5 = 600.000, ~7/4 = 956.507 (~8/7 = 243.493)


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


Badness: 0.032385
Badness (Smith): 0.032385


== Sidi ==
== Sidi ==
Line 422: Line 422:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1\1, ~9/7 = 424.452
* [[CTE]]: ~2 = 1200.000, ~9/7 = 424.452
: [[error map]]: {{val| 0.000 +0.238 -35.217 +11.108 }}
: [[error map]]: {{val| 0.000 +0.238 -35.217 +11.108 }}
* [[POTE]]: ~2 = 1\1, ~9/7 = 427.208
* [[POTE]]: ~2 = 1200.000, ~9/7 = 427.208
: 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]]: 0.056586
[[Badness]] (Smith): 0.056586


=== 11-limit ===
=== 11-limit ===
Line 439: Line 439:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1\1, ~9/7 = 424.587
* CTE: ~2 = 1200.000, ~9/7 = 424.587
* POTE: ~2 = 1\1, ~9/7 = 427.273
* POTE: ~2 = 1200.000, ~9/7 = 427.273


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


Badness: 0.032957
Badness (Smith): 0.032957


[[Category:Temperament families]]
[[Category:Temperament families]]
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