@@ Line 2: / Line 2: @@
 == Antitonic ==
-This temperament is characterized by [[9/8]] being tempering out, and has been termed a "troll temperament". It is named on account of 4/3 and 3/2 both being represented by the 600 cent half octave, which, in terms of diatonic function, serves as an antitonic. Surprisingly, it has extensions all the way up to the 11-limit, as confirmed by the data from [http://x31eq.com/cgi-bin/rt.cgi?limit=11&ets=2_4p&tuning=po x31eq].  The original 5-limit is basically the 3-limit music of [[2edo]] with the addition of harmonic 5 represented by an independent generator.
+This temperament is characterized by [[9/8]] being tempering out, and has been termed a "troll temperament". It is named on account of 4/3 and 3/2 both being represented by the 600 cent half octave, which, in terms of diatonic function, serves as an antitonic. Surprisingly, it has extensions all the way up to the 11-limit, as confirmed by the data from [http://x31eq.com/cgi-bin/rt.cgi?limit=11&ets=2_4p&tuning=po x31eq]. The original 5-limit is basically the 3-limit music of [[2edo]] with the addition of harmonic 5 represented by an independent generator.
 [[Subgroup]]: 2.3.5
@@ Line 13: / Line 13: @@
 [[Optimal tuning]]s:
+* [[CTE]]: ~3/2 = 600.000, ~5/4 = 386.314 (~6/5 = 213.686)
+: [[error map]]: {{val| 0.000 -101.955 0.000 }}
 * [[POTE]]: ~3/2 = 600.000, ~5/4 = 313.690 (~6/5 = 286.310)
+: error map: {{val| 0.000 -101.955 -72.624 }}
 {{Optimal ET sequence|legend=1| 2, 4 }}
-[[Badness]]: 0.021647
+[[Badness]] (Smith): 0.021647
 ; Music
@@ Line 30: / Line 33: @@
 Optimal tunings:
-* POTE: ~3/2 = 600.000, ~5/4 = 301.997 (~6/5 = 298.003)
+* CTE: ~3/2 = 600.000, ~5/4 = 379.210 (~6/5 = 220.890)
+* POTE: ~3/2 = 600.000, ~7/6 = 301.997 (~6/5 = 298.003)
 Optimal ET sequence: {{optimal ET sequence| 2, 4 }}
-Badness: 0.019373
+Badness (Smith): 0.019373
 ==== 11-limit ====
@@ Line 44: / Line 48: @@
 Optimal tunings:
-* POTE: ~3/2 = 600.000, ~5/4 = 340.293 (~6/5 = 259.707)
+* CTE: ~3/2 = 600.000, ~5/4 = 379.210 (~11/10 = 220.890)
+* POTE: ~3/2 = 600.000, ~5/4 = 340.293 (~8/7 = 259.707)
 Optimal ET sequence: {{optimal ET sequence| 2, 4 }}
-Badness: 0.021810
+Badness (Smith): 0.021810
 ==== Antietam ====
@@ Line 58: / Line 63: @@
 Optimal tunings:
-* POTE: ~3/2 = 600.000, ~5/4 = 322.080 (~6/5 = 277.920)
+* CTE: ~3/2 = 600.000, ~5/4 = 415.533 (~12/11 = 184.467)
+* POTE: ~3/2 = 600.000, ~7/6 = 322.080 (~6/5 = 277.920)
 Optimal ET sequence: {{optimal ET sequence| 2, 4e }}
-Badness: 0.018993
+Badness (Smith): 0.018993
 === Antaeus ===
@@ Line 72: / Line 78: @@
 Optimal tunings:
-* POTE: ~3/2 = 600.000, ~5/4 = 315.962 (~6/5 = 284.038)
+* CTE: ~3/2 = 600.000, ~5/4 = 323.296 (~7/6 = 276.704)
+* POTE: ~3/2 = 600.000, ~5/4 = 315.962 (~7/6 = 284.038)
 Optimal ET sequence: {{optimal ET sequence| 2d, 4 }}
-Badness: 0.037537
+Badness (Smith): 0.037537
 ==== 11-limit ====
@@ Line 86: / Line 93: @@
 Optimal tunings:
-* POTE: ~3/2 = 600.000, ~5/4 = 318.173 (~6/5 = 281.827)
+* CTE: ~3/2 = 600.000, ~5/4 = 323.296 (~7/6 = 276.704)
+* POTE: ~3/2 = 600.000, ~5/4 = 318.173 (~7/6 = 281.827)
 Optimal ET sequence: {{optimal ET sequence| 2d, 4 }}
-Badness: 0.033786
+Badness (Smith): 0.033786
 == Alteraugment ==
-Alteraugment is like [[augmented]], but the generator provides 5/4 instead of 3/2. [[User:VectorGraphics|Vector Graphics]] suggests the name kinsborough for this temperament.
+Alteraugment is like [[augmented]], but the generator provides 5/4 instead of 3/2. [[User:VectorGraphics|Vector Graphics]] suggests the name ''kinsborough'' for this temperament.
 [[Subgroup]]: 2.3.5
@@ Line 104: / Line 112: @@
 [[Optimal tuning]]s:
+* [[CTE]]: ~4/3 = 400.000, ~5/4 = 386.314 (~16/15 = 13.686)
+: [[error map]]: {{val| 0.000 +98.045 0.000 }}
 * [[POTE]]: ~4/3 = 400.000, ~5/4 = 459.935 (~10/9 = 59.935)
+: error map: {{val| 0.000 +98.045 +73.621 }}
-{{Optimal ET sequence|legend=1| 3, 12bcc, 15bbcc, 18bbcc }}
+{{Optimal ET sequence|legend=1| 3, 12bcc, 15bbcc }}
-[[Badness]]: 0.078042
+[[Badness]] (Smith): 0.078042
 == Yo (2c &amp; 3)  ==
@@ Line 120: / Line 131: @@
 [[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000, ~3/2 = 761.310
+: [[error map]]: {{val| 0.000 +74.015 -34.374 }}
 * [[POTE]]: ~2 = 1200.000, ~3/2 = 775.970
+: error map: {{val| 0.000 +65.763 -50.878 }}
 {{Optimal ET sequence|legend=1| 3, 11bc, 14bc, 17bb }}
-[[Badness]]: 0.016712
+[[Badness]] (Smith): 0.016712
 === Brutus ===
@@ Line 134: / Line 148: @@
 Optimal tunings:
+* CTE: ~2 = 1200.000, ~3/2 = 813.116
 * POTE: ~2 = 1200.000, ~3/2 = 848.221
-Optimal ET sequence: {{optimal ET sequence| 3, 7bc, 10bc }}
+Optimal ET sequence: {{optimal ET sequence| 3, 7bc }}
-Badness: 0.053389
+Badness (Smith): 0.053389
 === Phlegyas ===
@@ Line 148: / Line 163: @@
 Optimal tunings:
+* CTE: ~2 = 1200.000, ~3/2 = 747.225
 * POTE: ~2 = 1200.000, ~3/2 = 743.135
-Optimal ET sequence: {{optimal ET sequence| 3, 5c, 8c, 13bcc }}
+Optimal ET sequence: {{optimal ET sequence| 3, 5c, 8c }}
-Badness: 0.051293
+Badness (Smith): 0.051293
 === Charon ===
@@ Line 162: / Line 178: @@
 Optimal tunings:
-* POTE: ~2 = 1200.000, ~3/2 = 782.604 (~15/14 = 182.604)
+* CTE: ~7/5 = 600.000, ~3/2 = 768.427 (~15/14 = 168.427)
+* POTE: ~7/5 = 600.000, ~3/2 = 782.604 (~15/14 = 182.604)
-Optimal ET sequence: {{optimal ET sequence| 6, 14bc, 20bb }}
+Optimal ET sequence: {{optimal ET sequence| 4bcd, 6 }}
-Badness: 0.056404
+Badness (Smith): 0.056404
 === Nessus ===
@@ Line 176: / Line 193: @@
 Mapping: {{mapping| 1 0 -1 2 | 0 2 4 1 }}
+: mapping generators: ~2, ~7/4
 Optimal tunings:
-* POTE: ~2 = 1200.000, ~7/6 = 213.117
+* CTE: ~2 = 1200.000, ~7/4 = 980.335
+* POTE: ~2 = 1200.000, ~7/4 = 986.883
-Optimal ET sequence: {{optimal ET sequence| 5c, 6, 11bc, 17bb }}
+Optimal ET sequence: {{optimal ET sequence| 5c, 6 }}
-Badness: 0.059070
+Badness (Smith): 0.059070
 == Geryon ==
@@ Line 194: / Line 214: @@
 [[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000, ~5/4 = 354.664
+: [[error map]]: {{val| 0.000 +7.373 -31.649 +231.174 }}
 * [[POTE]]: ~2 = 1200.000, ~5/4 = 385.440
+: error map: {{val| 0.000 +68.926 -0.873 +231.174 }}
-{{Optimal ET sequence|legend=1| 3d }}, {{val| 16 26 37 48 }}, {{val| 19 31 44 57 }}, {{val| 22 36 51 66 }}
+{{Optimal ET sequence|legend=1| 1b, 2b, 3d }}
-[[Badness]]: 0.051009
+[[Badness]] (Smith): 0.051009
 == Malacoda ==
+{{See also| Semaphoresmic clan }}
 [[Subgroup]]: 2.3.5.7
@@ Line 206: / Line 231: @@
 {{Mapping|legend=1| 1 0 3 2 | 0 2 -1 1 }}
+: mapping generators: ~2, ~7/4
 [[Optimal tuning]]s:
-* [[POTE]]: ~2 = 1200.000, ~7/6 = 276.283
+* [[CTE]]: ~2 = 1200.000, ~7/4 = 938.796
+: [[error map]]: {{val| 0.000 -24.362 -125.110 -30.029 }}
+* [[POTE]]: ~2 = 1200.000, ~7/4 = 923.717
+: error map: {{val| 0.000 -54.521 -110.031 -45.109 }}
-{{Optimal ET sequence|legend=1| 1, 4, 9c, 13bcc }}
+{{Optimal ET sequence|legend=1| 1, 3b, 4, 9c, 13bcc }}
-[[Badness]]: 0.037207
+[[Badness]] (Smith): 0.037207
 == Ugolino ==
@@ Line 224: / Line 254: @@
 [[Optimal tuning]]s:
-* [[POTE]]: ~2 = 1200.000, ~6/5 = 278.360
+* [[CTE]]: ~2 = 1200.000, ~5/3 = 926.868
+: [[error map]]: {{val| 0.000 -48.218 -5.708 +65.517 }}
+* [[POTE]]: ~2 = 1200.000, ~5/3 = 921.640
+: error map: {{val| 0.000 -58.675 -21.394 +39.374 }}
-{{Optimal ET sequence|legend=1| 4, 9d, 13bd }}
+{{Optimal ET sequence|legend=1| 1cdd, 3bcdd, 4, 9d }}
-[[Badness]]: 0.043758
+[[Badness]] (Smith): 0.043758
 == Uncle ==
@@ Line 242: / Line 275: @@
 [[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000, ~3/2 = 733.721
+: [[error map]]: {{val| 0.000 +31.766 +11.362 }}
 * [[CWE]]: ~2 = 1200.000, ~3/2 = 731.732
+: error map: {{val| 0.000 +29.777 +23.296 }}
 {{Optimal ET sequence|legend=1| 5, 13, 18, 23bc }}
-[[Badness]] (Sintel): 6.332
+[[Badness]]:
+* Smith: 0.270
+* Dirichlet: 6.33
 == Medusa ==
-{{See also| Pelogic family }}
+{{See also| Archytas clan | Pelogic family }}
 [[Subgroup]]: 2.3.5.7
@@ Line 258: / Line 296: @@
 [[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000, ~3/2 = 684.722
+: [[error map]]: {{val| 0.000 -17.233 -40.480 +61.730 }}
 * [[POTE]]: ~2 = 1200.000, ~3/2 = 685.632
+: error map: {{val| 0.000 -16.323 -43.209 +59.911 }}
 {{Optimal ET sequence|legend=1| 2, 5c, 7 }}
-[[Badness]]: 0.042712
+[[Badness]] (Smith): 0.042712
 === 11-limit ===
@@ Line 272: / Line 313: @@
 Optimal tunings:
+* CTE: ~2 = 1200.000, ~3/2 = 683.589
 * POTE: ~2 = 1200.000, ~3/2 = 685.809
 Optimal ET sequence: {{optimal ET sequence| 2, 5c, 7 }}
-Badness: 0.026828
+Badness (Smith): 0.026828
 == Plutus ==
@@ Line 288: / Line 330: @@
 [[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000, ~3/2 = 685.837
+: [[error map]]: {{val| 0.000 -16.118 -42.965 +60.359 }}
 * [[POTE]]: ~2 = 1200.000, ~3/2 = 682.895
+: error map: {{val| 0.000 -19.060 -54.734 +45.649 }}
 {{Optimal ET sequence|legend=1| 2cd, 5d, 7 }}
-[[Badness]]: 0.045275
+[[Badness]] (Smith): 0.045275
 === 11-limit ===
@@ Line 302: / Line 347: @@
 Optimal tunings:
+* CTE: ~2 = 1200.000, ~3/2 = 687.743
 * POTE: ~2 = 1200.000, ~3/2 = 685.234
 Optimal ET sequence: {{optimal ET sequence| 2cde, 5de, 7 }}
-Badness: 0.032521
+Badness (Smith): 0.032521
 == Involution ==
+Involution was named by [[User:CompactStar|CompactStar]] in 2023.
 [[Subgroup]]: 2.3.5
@@ Line 319: / Line 367: @@
 [[Optimal tuning]]s:
 * [[CTE]]: ~2 = 1200.000, ~3/2 = 509.892
+: [[error map]]: {{val| 0.000 -192.063 -206.097 }}
+* [[CWE]]: ~2 = 1200.000, ~3/2 = 520.625
+: error map: {{val| 0.000 -181.330 -227.565 }}
 {{Optimal ET sequence|legend=1| 2c, 5bc, 7bbcc }}
-[[Badness]]: 0.133021
+[[Badness]] (Smith): 0.133021
 === 7-limit ===
@@ Line 333: / Line 384: @@
 Optimal tunings:
 * CTE: ~2 = 1200.000, ~3/2 = 509.892
+* CWE: ~2 = 1200.000, ~3/2 = 515.099
 Optimal ET sequence: none
-Badness: 0.118764
+Badness (Smith): 0.118764
 == Devolution ==
+Devolution was named by [[User:Akselai|Akselai]] in 2024.
 [[Subgroup]]: 3.5.7
@@ Line 349: / Line 403: @@
 [[Optimal tuning]]s:
 * [[CTE]]: ~3 = 1901.955, ~5/3 = 701.863
+: [[error map]]: {{val| 0.000 -182.496 -266.779 }}
+* [[CWE]]: ~3 = 1901.995, ~5/3 = 691.468
+: error map: {{val| 0.000 -192.891 -256.384 }}
-[[Optimal ET sequence]]: [[3edt|b3]], [[8edt|b8cdd]]
+[[Optimal ET sequence]]: [[1edt|b1]], [[2edt|b2d]], [[3edt|b3]], [[8edt|b8cdd]]
-[[Badness]] (Sintel): 0.751
+[[Badness]]:
+* Smith: 0.00406
+* Dirichlet: 0.751
 == Codex ==
 {{See also| Bug family }}
-This temperament is named as an abbreviation of "co-decimal", as it resembles [[decimal]] in many ways, but exchanges the roles of 5s and 7s. While decimal equates [[8/7]] and [[7/6]], as well as [[6/5]] and [[5/4]], this equates [[10/9]] and [[6/5]], as well as [[7/6]] and [[9/7]]. It is an extension of [[bug]] in the same way decimal is of [[semaphore]].
+This temperament was named by [[User:Jerdle|Jerdle]] as an abbreviation of "co-decimal", as it resembles [[decimal]] in many ways, but exchanges the roles of 5's and 7's. While decimal equates [[8/7]] and [[7/6]], as well as [[6/5]] and [[5/4]], this equates [[10/9]] and [[6/5]], as well as [[7/6]] and [[9/7]]. It is an extension of [[bug]] in the same way decimal is of [[semaphore]].
 [[Subgroup]]: 2.3.5.7
@@ Line 367: / Line 426: @@
 [[Optimal tuning]]s:
 * [[CTE]]: ~7/5 = 600.000, ~5/3 = 935.289
+: [[error map]]: {{val| 0.000 -31.377 +19.554 +37.041 }}
+* [[CWE]]: ~7/5 = 600.000, ~5/3 = 936.030
+: error map: {{val| 0.000 -29.895 +21.776 +39.264 }}
-{{Optimal ET sequence|legend=1| 10cd, 14d }}
+{{Optimal ET sequence|legend=1| 4, 10cd, 14d }}
-[[Badness]]: 0.077065
+[[Badness]] (Smith): 0.077065
 [[Category:Temperament collections]]

Very low accuracy temperaments: Difference between revisions