@@ Line 23: / Line 23: @@
 [[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 }}
 [[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)
 {{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 ===
-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 }}]], [[#Grackle|grackle]] adds {{monzo| -44 26 0 1 }}, [[#Pontiac|pontiac]] adds {{monzo| -59 39 0 -1 }}, and [[#Schism|schism]] adds [[64/63|{{monzo| 6 -2 0 -1 }}]]. Those all have a fifth as generator.
-* [[#Garibaldi|Garibaldi]] adds [[garischisma|{{monzo| 25 -14 0 -1 }}]],
-* [[#Grackle|Grackle]] adds {{monzo| -44 26 0 1 }},
-* [[#Schism|Schism]] adds [[64/63|{{monzo| 6 -2 0 -1 }}]],
-* [[#Pontiac|Pontiac]] adds {{monzo| -59 39 0 -1 }}.
-Those all have a fifth as generator.
-* [[#Bischismic|Bischismic]] adds {{monzo| -69 40 0 2 }} and has a fifth generator with a half-octave period.
+[[#Bischismic|Bischismic]] adds {{monzo| -69 40 0 2 }} and has a fifth generator with a half-octave period. [[#Salsa|Salsa]] adds [[parahemif comma|{{monzo| 15 -13 0 2 }}]] and has a hemififth generator. [[#Hemischis|Hemischis]] adds {{monzo| -34 25 0 -2 }} and has a hemitwelfth generator. [[Gamelismic clan #Guiron|Guiron]] adds [[1029/1024|{{monzo| -10 1 0 3 }}]], with an ~8/7 generator, three of which give the fifth. [[#Term|Term]] adds {{monzo| -94 54 0 3 }} with a 1/3-octave period. [[#Squirrel|Squirrel]], [[#Tertiaschis|tertiaschis]], and [[#Countertertiaschis|countertertiaschis]] each has a generator that is 1/3 of the fourth. [[#Quadrant|Quadrant]] adds {{monzo| -119 68 0 4 }} with a 1/4-octave period. [[#Kleischismic|Kleischismic]] adds {{monzo| 49 -38 0 4 }} with a half-octave period and also a bisect generator. [[#Sesquiquartififths|Sesquiquartififths]] adds {{monzo| -35 15 0 4 }} and slices the fifth in four.
-* [[#Hemischis|Hemischis]] adds {{monzo| -34 25 0 -2 }} and has a hemififth generator.
-* [[Gamelismic clan #Guiron|Guiron]] adds [[1029/1024|{{monzo| -10 1 0 3 }}]], with an ~8/7 generator, three of which give the fifth.
+Temperaments involving larger splits include [[#Tsaharuk|tsaharuk]], [[#Quanharuk|quanharuk]], [[#Quintilipyth|quintilipyth]], [[#Quintaschis|quintaschis]], [[#Altinex|altinex]], [[Stearnsmic clan #Pogo|pogo]], [[#Sextilifourths|sextilifourths]], [[#Septant|septant]], [[#Octant|octant]], [[#Nonant|nonant]], [[#Septiquarschis|septiquarschis]], and [[#Tridecafifths|tridecafifths]]. Those split the schismic structure into five to thirteen parts.
-* [[#Term|Term]] adds {{monzo| -94 54 0 3 }} with a 1/3 octave period.
-* [[#Sesquiquartififths|Sesquiquartififths]] adds {{monzo| -35 15 0 4 }} and slices the fifth in four.
 Temperaments discussed elsewhere include:
-* ''[[Sensamagic clan #Salsa|Salsa]]'' (+245/243) → [[Sensamagic clan #Salsa|Sensamagic clan]]
+* ''[[Guiron]]'' (+1029/1024) → [[Gamelismic clan #Guiron|Gamelismic clan]]
-* ''[[Gamelismic clan #Guiron|Guiron]]'' (+1029/1024) → [[Gamelismic clan #Guiron|Gamelismic clan]]
+* ''[[Pogo]]'' (+118098/117649) → [[Stearnsmic clan #Pogo|Stearnsmic clan]]
+Considered below are garibaldi, pontiac, grackle, schism, bischismic, kleischismic, salsa, hemischis, term, altinex, squirrel, tertiaschis, countertertiaschis, quadrant, sesquiquartififths, tsaharuk, quanharuk, quintilipyth, quintaschis, sextilifourths, septant, octant, nonant, septiquarschis, and tridecafifths.
 The schismatic family boasts a variety of remarkable extensions to subgroups in high prime limits. These are listed at the bottom of this page, in [[#Subgroup extensions]].
@@ Line 57: / Line 54: @@
 {{Main| Garibaldi }}
-Garibaldi tempers out the [[garischisma]], equating the [[64/63|septimal comma]] with both the [[syntonic comma]] and the [[Pythagorean comma]]. The 7/4 is found at -14 fifths, represented by the double diminished octave (C-Cbb), or down-minor seventh (C-vBb) with the down-arrow representing the comma step. It necessitates a sharper fifth than pure. Its [[S-expression]]-based comma list is {[[5120/5103|S8/S9]], [[225/224|S15]]}.
+Garibaldi tempers out the [[garischisma]], equating the [[64/63|septimal comma]] with both the [[syntonic comma]] and the [[Pythagorean comma]]. The 7/4 is found at -14 fifths, represented by the double-diminished octave (C–C𝄫), or down-minor seventh (C-vB♭) with the down-arrow representing the comma step. It necessitates a sharper fifth than pure. Its [[S-expression]]-based comma list is {[[5120/5103|S8/S9]], [[225/224|S15]]}.
 [[Subgroup]]: 2.3.5.7
@@ Line 65: / Line 62: @@
 {{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 }}
 [[Minimax tuning]]:
@@ Line 79: / Line 80: @@
 * 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 is one of the best extensions of garibaldi to the 11- and 13-limit as well as the 2.3.5.7.11.13.19 subgroup.
+Cassandra is one of the best extensions of garibaldi to the 11- and 13-limit as well as the 2.3.5.7.11.13.19 subgroup, even though it comes with a much higher complexity.
 Subgroup: 2.3.5.7.11
@@ Line 92: / Line 93: @@
 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}}
 Minimax tuning:
@@ Line 102: / Line 105: @@
 * 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 ====
@@ Line 113: / Line 116: @@
 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}}
 Minimax tuning:
@@ Line 126: / Line 131: @@
 {{Optimal ET sequence|legend=0| 41, 53, 94, 429ccdeef, 523ccdeef }}
-Badness (Sintel): 0.020676
+Badness (Sintel): 0.854
 ===== Cassie =====
@@ Line 135: / Line 140: @@
 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}}
-{{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 ======
@@ Line 148: / Line 155: @@
 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}}
-{{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 =====
@@ Line 161: / Line 170: @@
 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}}
-{{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 ======
@@ Line 176: / Line 187: @@
 Optimal tunings:
 * 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}}
-{{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 ======
@@ Line 193: / Line 203: @@
 * WE: ~2 = 1200.2970{{c}}, ~3/2 = 702.2697{{c}}
 * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0943{{c}}
-* POTE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0960{{c}}
 {{Optimal ET sequence|legend=0| 41g, 53, 94 }}
-Badness (Smith): 0.015072
+Badness (Sintel): 1.08
 ===== Cassander =====
@@ Line 206: / Line 215: @@
 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}}
 {{Optimal ET sequence|legend=0| 41, 53g, 94 }}
-Badness (Smith): 0.022454
+Badness (Sintel): 1.14
 ====== 19-limit ======
@@ Line 219: / Line 230: @@
 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}}
 {{Optimal ET sequence|legend=0| 41, 53g, 94 }}
-Badness (Smith): 0.017576
+Badness (Sintel): 1.07
 === Andromeda ===
@@ Line 232: / Line 245: @@
 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}}
 Minimax tuning:
@@ Line 242: / Line 257: @@
 * 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 ====
@@ Line 253: / Line 268: @@
 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}}
 Minimax tuning:
@@ Line 264: / Line 281: @@
 * 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 =====
@@ Line 275: / Line 292: @@
 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}}
 {{Optimal ET sequence|legend=0| 12f, 29, 41 }}
-Badness (Smith): 0.023406
+Badness (Sintel): 1.19
 ====== 19-limit ======
@@ Line 288: / Line 307: @@
 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}}
 {{Optimal ET sequence|legend=0| 12f, 29, 41 }}
-Badness (Smith): 0.019154
+Badness (Sintel): 1.17
 ===== Schisicosiennic =====
@@ Line 301: / Line 322: @@
 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}}
-{{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 ======
@@ Line 314: / Line 337: @@
 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}}
-{{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 =====
@@ Line 327: / Line 352: @@
 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}}
-{{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 ======
@@ Line 340: / Line 367: @@
 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}}
-{{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 ===
@@ Line 353: / Line 382: @@
 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}}
 Minimax tuning:
@@ Line 359: / Line 390: @@
 : 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 ====
@@ Line 370: / Line 401: @@
 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}}
 Minimax tuning:
@@ Line 376: / Line 409: @@
 : 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 ====
@@ Line 387: / Line 420: @@
 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}}
-{{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 ====
@@ Line 400: / Line 435: @@
 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}}
+{{Optimal ET sequence|legend=0| 12f, 53, 65d }}
-{{Optimal ET sequence|legend=1| 12f, 41ef, 53, 65d, 118dg }}
+Badness (Sintel): 1.18
-Badness (Smith): 0.019411
+=== Karadeniz ===
+{{See also| Turkish maqam music temperaments #Karadeniz temperament }}
-=== Hemigari ===
 Subgroup: 2.3.5.7.11
-Comma list: 121/120, 225/224, 3125/3087
+Comma list: 225/224, 243/242, 3125/3087
-Mapping: {{mapping| 1 0 15 25 9 | 0 2 -16 -28 -7 }}
+Mapping: {{mapping| 1 1 7 11 2 | 0 2 -16 -28 5 }}
-: mapping generators: ~2, ~110/63
+: mapping generators: ~2, ~11/9
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~110/63 = 951.082{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.7351{{c}}, ~11/9 = 350.9167{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 350.9995{{c}}
-{{Optimal ET sequence|legend=0| 29, 53, 82e, 135e, 188ce }}
+{{Optimal ET sequence|legend=0| 24d, 41, 65d, 106, 147 }}
-Badness (Smith): 0.050681
+Badness (Sintel): 1.37
 ==== 13-limit ====
 Subgroup: 2.3.5.7.11.13
-Comma list: 121/120, 169/168, 225/224, 275/273
+Comma list: 225/224, 243/242, 325/324, 640/637
-Mapping: {{mapping| 1 0 15 25 9 14 | 0 2 -16 -28 -7 -13 }}
+Mapping: {{mapping| 1 1 7 11 2 -8 | 0 2 -16 -28 5 40 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~26/15 = 951.082{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.3042{{c}}, ~11/9 = 350.7533{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 350.9686{{c}}
-{{Optimal ET sequence|legend=0| 29, 53, 82e, 135ef, 188cef }}
+{{Optimal ET sequence|legend=0| 24d, 41, 65d, 106f }}
-Badness (Smith): 0.027464
+Badness (Sintel): 1.34
-=== Karadeniz ===
-{{See also| Turkish maqam music temperaments #Karadeniz temperament }}
+=== Hemigari ===
 Subgroup: 2.3.5.7.11
-Comma list: 225/224, 243/242, 3125/3087
+Comma list: 121/120, 225/224, 3125/3087
-Mapping: {{mapping| 1 1 7 11 2 | 0 2 -16 -28 5 }}
+Mapping: {{mapping| 1 0 15 25 9 | 0 2 -16 -28 -7 }}
-: mapping generators: ~2, ~11/9
+: mapping generators: ~2, ~110/63
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/9 = 350.994{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.7303{{c}}, ~110/63 = 951.6605{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~110/63 = 951.0604{{c}}
-{{Optimal ET sequence|legend=0| 41, 106, 147 }}
+{{Optimal ET sequence|legend=0| 24d, 29, 53, 82e, 135ee }}
-Badness (Smith): 0.041562
+Badness (Sintel): 1.68
 ==== 13-limit ====
 Subgroup: 2.3.5.7.11.13
-Comma list: 225/224, 243/242, 325/324, 640/637
+Comma list: 121/120, 169/168, 225/224, 275/273
-Mapping: {{mapping| 1 1 7 11 2 -8 | 0 2 -16 -28 5 40 }}
+Mapping: {{mapping| 1 0 15 25 9 14 | 0 2 -16 -28 -7 -13 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/9 = 351.014{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.8146{{c}}, ~26/15 = 951.7273{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 951.0574{{c}}
-{{Optimal ET sequence|legend=0| 41, 106, 147 }}
+{{Optimal ET sequence|legend=0| 24d, 29, 53, 82e, 135eef }}
-Badness (Smith): 0.042564
+Badness (Sintel): 1.13
 === Sanjaab ===
@@ Line 470: / Line 515: @@
 : 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}}
-{{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 ====
@@ Line 483: / Line 530: @@
 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}}
 {{Optimal ET sequence|legend=0| 29, 65d, 94 }}
-Badness (Smith): 0.033849
+Badness (Sintel): 1.40
-== Schism ==
-See [[Archytas clan #Schism]].
-Schism is a relatively low-accuracy extension as it tempers out the septimal comma. The 7/4 is found at -2 fifths, represented by the minor seventh (C-Bb). 12edo is recommendable tuning, though 29edo (29d val), 41edo (41d val), and 53edo (53d val) can be used.
 == Pontiac ==
 {{Main| Pontiac }}
-Pontiac tempers out the [[ragisma]], rendering a very accurate 7-limit microtemperament. The 7/4 is found at +39 fifths, represented by the quintuple augmented third (C-Exx#), or triple-up major sixth (C-^<sup>3</sup>A).
+Pontiac tempers out the [[ragisma]], rendering a very accurate 7-limit microtemperament. The 7/4 is found at +39 fifths, represented by the quintuple-augmented third (C-E𝄪𝄪♯), or triple-up major sixth (C-^<sup>3</sup>A).
 [[Subgroup]]: 2.3.5.7
@@ Line 505: / Line 549: @@
 {{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 }}
 [[Minimax tuning]]:
@@ Line 519: / Line 567: @@
 * 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 ===
-The helenoid temperament ({{nowrap| 53 & 118 }}) is closely related to the helenus temperament, but with the ragisma rather than the [[225/224|marvel comma]] tempered out.
+Helenoid may be described as {{nowrap| 53 & 118 }}, and is closely related to the helenus temperament, differing only by the mapping of 7.
 Subgroup: 2.3.5.7.11
@@ Line 532: / Line 580: @@
 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}}
 Minimax tuning:
@@ Line 540: / Line 590: @@
 {{Optimal ET sequence|legend=0| 53, 118, 289e, 407de }}
-Badness (Smith): 0.038863
+Badness (Sintel): 1.28
 ==== 13-limit ====
@@ Line 549: / Line 599: @@
 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}}
 Minimax tuning:
@@ Line 557: / Line 609: @@
 {{Optimal ET sequence|legend=0| 53, 118, 171e }}
-Badness (Smith): 0.033677
+Badness (Sintel): 1.39
 ===== 17-limit =====
@@ Line 566: / Line 618: @@
 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}}
 Minimax tuning:
@@ Line 572: / Line 626: @@
 : 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 ====
@@ Line 583: / Line 637: @@
 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}}
 {{Optimal ET sequence|legend=0| 53, 118f, 171ef }}
-Badness (Smith): 0.036281
+Badness (Sintel): 1.50
 ===== 17-limit =====
@@ Line 596: / Line 652: @@
 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}}
-{{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 =====
@@ Line 609: / Line 667: @@
 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}}
-{{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 ===
-The ponta temperament ({{nowrap| 53 & 171 }}) tempers out the [[540/539|swetisma]] and the ragisma.
+Ponta tempers out [[540/539]] and may be described as {{nowrap| 171 & 224 }}. [[224edo]] itself makes for an excellent tuning.
 Subgroup: 2.3.5.7.11
@@ Line 624: / Line 684: @@
 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}}
 Minimax tuning:
@@ Line 630: / Line 692: @@
 : 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 ====
@@ Line 641: / Line 703: @@
 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}}
 Minimax tuning:
@@ Line 649: / Line 713: @@
 {{Optimal ET sequence|legend=0| 53, 171, 224 }}
-Badness (Smith): 0.023616
+Badness (Sintel): 0.976
 ==== 17-limit ====
@@ Line 658: / Line 722: @@
 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}}
 Minimax tuning:
@@ Line 666: / Line 732: @@
 {{Optimal ET sequence|legend=0| 53, 171, 224, 395e, 619eg }}
-Badness (Smith): 0.022853
+Badness (Sintel): 1.16
 === Pontic ===
-The pontic temperament ({{nowrap| 118 & 171 }}) tempers out the [[441/440|werckisma]] and the ragisma.
+Pontic temperament tempers out [[441/440]] and may be described as {{nowrap| 118 & 171 }}. [[289edo]] may be recommended as a tuning.
 Subgroup: 2.3.5.7.11
@@ Line 677: / Line 743: @@
 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}}
 Minimax tuning:
@@ Line 683: / Line 751: @@
 : 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 ====
@@ Line 694: / Line 762: @@
 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}}
 Minimax tuning:
@@ Line 700: / Line 770: @@
 : 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 =====
@@ Line 711: / Line 781: @@
 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}}
 Minimax tuning:
@@ Line 717: / Line 789: @@
 : 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 ====
@@ Line 728: / Line 800: @@
 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}}
-{{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 =====
@@ Line 741: / Line 815: @@
 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}}
 {{Optimal ET sequence|legend=0| 53ef, 118f, 171, 289, 460e, 749defg }}
-Badness (Smith): 0.029383
+Badness (Sintel): 1.50
 === Bipont ===
-The bipont temperament ({{nowrap| 118 & 224 }}) has a period of half octave and tempers out the [[3025/3024|lehmerisma (3025/3024)]] and the [[9801/9800|kalisma (9801/9800)]].
+Bipont tempers out the [[3025/3024|lehmerisma (3025/3024)]] and the [[9801/9800|kalisma (9801/9800)]]. It may be described as {{nowrap| 118 & 224 }}. It has a period of half octave and a ploidacot signature of diploid monocot. [[342edo]] may be recommended as a tuning.
 Subgroup: 2.3.5.7.11
@@ Line 757: / Line 833: @@
 : 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}}
 {{Optimal ET sequence|legend=0| 106, 118, 224, 342, 1592c, 1934ce, 2276cde, 2618cde, 2960cde }}
-Badness (Smith): 0.014629
+Badness (Sintel): 0.484
 ==== 13-limit ====
@@ Line 770: / Line 848: @@
 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}}
 {{Optimal ET sequence|legend=0| 106, 118, 224, 566f, 790f }}
-Badness (Smith): 0.030172
+Badness (Sintel): 1.25
 ===== 17-limit =====
@@ Line 783: / Line 863: @@
 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}}
 {{Optimal ET sequence|legend=0| 106g, 118, 224, 342, 566f }}
-Badness (Smith): 0.027051
+Badness (Sintel): 1.38
 ==== Counterbipont ====
@@ Line 796: / Line 878: @@
 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}}
-{{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 =====
@@ Line 809: / Line 893: @@
 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}}
-{{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 =====
@@ Line 822: / Line 908: @@
 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}}
 {{Optimal ET sequence|legend=0| 106fgh, 118f, 224, 342f, 566h, 908fgh }}
-Badness (Smith): 0.022267
+Badness (Sintel): 1.35
 ==== Quadrapont ====
@@ Line 836: / Line 924: @@
 : 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}}
-{{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 tempers out {{monzo| -44 26 0 1 }}. The 7/4 is found at -26 fifths, represented by the triple diminished ninth (C-Dbbbb), or double-down minor seventh (C-vvBb), which is to say, two comma steps are required to bend the Pythagorean minor seventh to the septimal one.
+Grackle tempers out {{monzo| -44 26 0 1 }} so 7/4 is found at -26 fifths, represented by the triple-diminished ninth (C–D𝄫𝄫) or double-down minor seventh (C–vvB♭). Two comma steps are required to bend the Pythagorean minor seventh to the septimal one.
 [[Subgroup]]: 2.3.5.7
@@ Line 852: / Line 942: @@
 : 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 }}
 [[Minimax tuning]]:
@@ Line 858: / Line 952: @@
 * [[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 ===
@@ Line 869: / Line 963: @@
 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}}
-{{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 ====
@@ Line 882: / Line 978: @@
 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}}
-{{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 =====
@@ Line 895: / Line 993: @@
 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}}
-{{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 =====
@@ Line 908: / Line 1,008: @@
 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}}
-{{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 ====
@@ Line 921: / Line 1,023: @@
 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}}
-{{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 ===
@@ Line 934: / Line 1,038: @@
 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}}
-{{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 ====
@@ Line 947: / Line 1,053: @@
 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}}
 {{Optimal ET sequence|legend=0| 12f, 53dff, 65f, 77e }}
-Badness (Smith): 0.044458
+Badness (Sintel): 1.84
 ==== Catahelenic ====
@@ Line 960: / Line 1,068: @@
 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}}
-{{Optimal ET sequence|legend=0| 12f, 53df, 65 }}
+{{Optimal ET sequence|legend=0| 12f, …, 53d, 65 }}
-Badness (Smith): 0.048524
+Badness (Sintel): 2.01
+== Quasipyth ==
+Named by [[Xenllium]] in 2026, quasipyth tempers out {{monzo| 109 -67 0 -1 }}, the [[nanisma]], as well as the [[catasyc comma]], 390625/387072. The 7/4 is found at −67 fifths, represented by the nonuple-diminished thirteenth.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 32805/32768, 390625/387072
+{{Mapping|legend=1| 1 0 15 109 | 0 1 -8 -67 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.2569{{c}}, ~3/2 = 702.1149{{c}}
+: [[error map]]: {{val| +0.2569 +0.4168 -1.4342 +0.2685 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9615{{c}}
+: error map: {{val| 0.0000 +0.0065 -2.0054 -0.2437 }}
+{{Optimal ET sequence|legend=1| 53, 147d, 200, 253, 306c, 559c }}
+[[Badness]] (Sintel): 5.04
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 385/384, 19712/19683, 78125/77616
+Mapping: {{mapping| 1 0 15 109 -117 | 0 1 -8 -67 76 }}
+Optimal tunings:
+* WE: ~2 = 1200.3283{{c}}, ~3/2 = 702.1636{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.9713{{c}}
+{{Optimal ET sequence|legend=0| 53, 200, 253, 559ce }}
+Badness (Sintel): 3.83
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 325/324, 385/384, 2200/2197, 19712/19683
+Mapping: {{mapping| 1 0 15 109 -117 -28 | 0 1 -8 -67 76 20 }}
+Optimal tunings:
+* WE: ~2 = 1200.3229{{c}}, ~3/2 = 702.1603{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.9714{{c}}
+{{Optimal ET sequence|legend=0| 53, 200, 253, 559ce }}
+Badness (Sintel): 2.13
+== Schism ==
+See [[Archytas clan #Schism]].
+Schism is a relatively low-accuracy extension as it tempers out the septimal comma. The 7/4 is found at -2 fifths, represented by the minor seventh (C–B♭). 12edo is recommendable tuning, though 29edo (29d val), 41edo (41d val), and 53edo (53d val) can be used.
 == Bischismic ==
+Bischismic tempers out 3136/3125, the [[hemimean comma]], as well as 321489/320000, the [[varunisma]], and may be described as the {{nowrap| 118 & 130 }} temperament. The octave is split in halves, so the [[ploidacot]] of this temperament is diploid monocot. In schismic, -10 fifths make the interval class of 10/9. Bischismic then finds [[7/4]] by a stack of two [[10/9]]'s plus a semi-octave period, and in the [[11-limit]], it simply finds [[11/8]] by a stack of three [[10/9]]'s. [[248edo]] and [[378edo]] make for excellent tunings in both cases.
 [[Subgroup]]: 2.3.5.7
@@ Line 974: / Line 1,140: @@
 : 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 }}
 [[Minimax tuning]]:
@@ Line 980: / Line 1,150: @@
 * [[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 ===
@@ Line 991: / Line 1,161: @@
 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}}
-{{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 ====
@@ Line 1,004: / Line 1,176: @@
 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}}
-{{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 =====
@@ Line 1,017: / Line 1,191: @@
 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}}
-{{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 ====
@@ Line 1,030: / Line 1,206: @@
 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}}
 {{Optimal ET sequence|legend=0| 12f, 106deff, 118f, 130 }}
-Badness (Smith): 0.029321
+Badness (Sintel): 1.21
 ===== 17-limit =====
@@ Line 1,043: / Line 1,221: @@
 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}}
 {{Optimal ET sequence|legend=0| 12f, 106deff, 118f, 130, 248fg }}
-Badness (Smith): 0.026894
+Badness (Sintel): 1.37
 == Kleischismic ==
+Kleischismic tempers out 1500625/1492992, the [[uniwiz comma]], and may be described as the {{nowrap| 94 & 118 }} temperament. The generator is a infrafifth, two of which plus a semi-octave period make the [[3/1|3rd]] [[harmonic]]; its [[ploidacot]] is thus diploid alpha-dicot. In schismic, 10 fifths make the interval class of [[9/5]]. Kleischismic then finds [[7/4]] by that minus a [[36/35]] quartertone, which is the aforementioned generator minus a semi-octave period. The generator stands in for [[16/11]] and the quartertone stands in for [[33/32]] in the [[11-limit]]. [[212edo]] and [[330edo]] in the 330e val may be recommended as tunings.
 [[Subgroup]]: 2.3.5.7
@@ Line 1,057: / Line 1,239: @@
 : 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 }}
-{{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 ===
@@ Line 1,070: / Line 1,256: @@
 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}})
-{{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 ====
@@ Line 1,083: / Line 1,271: @@
 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}})
-{{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 =====
@@ Line 1,096: / Line 1,286: @@
 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}})
-{{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 ====
@@ Line 1,109: / Line 1,301: @@
 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}})
-{{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 =====
@@ Line 1,122: / Line 1,316: @@
 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}})
-{{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 tempers out 245/243, the [[sensamagic comma]], and may be described as the {{nowrap| 41 & 65 }} temperament. It has a neutral third as a generator; its [[ploidacot]] is dicot. In fact it is related to [[hemififths]], from which this less accurate temperament only differs by the mapping of [[5/1|5]].
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 245/243, 32805/32768
+{{Mapping|legend=1| 1 1 7 -1 | 0 2 -16 13 }}
+: mapping generators: ~2, ~128/105
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.7707{{c}}, ~128/105 = 351.2748{{c}}
+: [[error map]]: {{val| +0.771 +1.365 -1.315 -3.024 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~128/105 = 351.0471{{c}}
+: error map: {{val| 0.000 +0.139 -3.068 -5.213 }}
+{{Optimal ET sequence|legend=1| 17, 24, 41, 106d, 147d, 188cd }}
+[[Badness]] (Sintel): 2.03
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 243/242, 245/242, 385/384
+Mapping: {{mapping| 1 1 7 -1 2 | 0 2 -16 13 5 }}
+Optimal tunings:
+* WE: ~2 = 1200.3891{{c}}, ~11/9 = 351.1275{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 351.0141{{c}}
+{{Optimal ET sequence|legend=0| 17, 24, 41, 106d }}
+Badness (Sintel): 1.30
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 105/104, 144/143, 243/242, 245/242
+Mapping: {{mapping| 1 1 7 -1 2 4 | 0 2 -16 13 5 -1 }}
+Optimal tunings:
+* WE: ~2 = 1199.9362{{c}}, ~11/9 = 351.0061{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 351.0247{{c}}
+{{Optimal ET sequence|legend=0| 17, 24, 41 }}
+Badness (Sintel): 1.27
 == Hemischis ==
+Hemischis tempers out 6144/6125, the [[porwell comma]], as well as 19683/19600, the [[cataharry comma]], and may be described as the {{nowrap| 53 & 130 }} temperament. Its [[ploidacot]] is alpha-dicot.
+The [[S-expression]]-based comma list for 13-limit hemischis is {[[540/539|S12/S14]], [[676/675|S13/S15 = S26]], [[729/728|S27]], [[4096/4095|S64]], ([[4225/4224|S65]])}. Tempering out [[169/168]] ({{S|13}}), [[225/224]] ({{S|15}}) or [[625/624]] ({{S|25}}) leads to [[53edo]] while tempering out [[24192/24167]] ([[S-expression|S12/S13]]), [[10985/10976]] ([[S-expression|S13/S14]]), [[43904/43875]] ([[S-expression|S14/S15]]) or [[2401/2400]] ([[S-expression|S49]]) leads to [[130edo]] and implies S12, S13, S14, and S15 are tempered together.
 [[Subgroup]]: 2.3.5.7
@@ Line 1,136: / Line 1,386: @@
 : 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 }}
 {{Optimal ET sequence|legend=1| 24, 53, 130, 183, 313 }}
-[[Badness]] (Smith): 0.045817
+[[Badness]] (Sintel): 1.16
 === 11-limit ===
@@ Line 1,149: / Line 1,403: @@
 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}}
-{{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 ===
-Its [[S-expression]]-based comma list is {[[540/539|S12/S14]], [[676/675|S13/S15 = S26]], [[729/728|S27]], [[4096/4095|S64]](, [[4225/4224|S65]])}. Tempering out [[169/168|S13]], [[225/224|S15]] or [[625/624|S25]] leads to [[53edo]] (through [[Catakleismic]]) while tempering out [[24192/24167|S12/S13]], [[10985/10976|S13/S14]], [[43904/43875|S14/S15]] or [[2401/2400|S49]] (implying S12 = S13 = S14 = S15) leads to [[130edo]].
 Subgroup: 2.3.5.7.11.13
@@ Line 1,164: / Line 1,418: @@
 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}}
-{{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 ===
@@ Line 1,177: / Line 1,433: @@
 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}}
 {{Optimal ET sequence|legend=0| 53, 130, 183, 496d }}
-Badness (Smith): 0.021073
+Badness (Sintel): 1.07
 === 19-limit ===
@@ Line 1,190: / Line 1,448: @@
 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}}
 {{Optimal ET sequence|legend=0| 53, 130, 183, 313h }}
-Badness (Smith): 0.018262
+Badness (Sintel): 1.11
 === 23-limit ===
@@ Line 1,203: / Line 1,463: @@
 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}}
 {{Optimal ET sequence|legend=0| 53, 130, 183, 313h }}
-Badness (Smith): 0.014819
+Badness (Sintel): 1.06
 ; Music
 * ''HemischisMatic EP'' (2023) by [[User:Francium|Francium]] – [https://open.spotify.com/album/1Fx2shLclpNgFQJRw3ZHya Spotify] | [https://francium223.bandcamp.com/album/hemischismatic-ep Bandcamp] | [https://www.youtube.com/playlist?list=PLLZE7hMjEXRaiipPYK1InZBXTru_UtRsq YouTube] – 4-piece extended play
-== Squirrel ==
+== Term ==
-The squirrel temperament ({{nowrap| 29 & 36 }}) has a ~11/10 generator, three of which give the fourth (~4/3), and thirteen of which give 7/4 with octave reduction.
+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
-[[Comma list]]: 686/675, 32805/32768
+[[Comma list]]: 32805/32768, 250047/250000
+{{Mapping|legend=1| 3 0 45 94 | 0 1 -8 -18 }}
+: mapping generators: ~63/50, ~3
+[[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 }}
-{{Mapping|legend=1| 1 2 -1 1 | 0 -3 24 13 }}
+[[Minimax tuning]]:
+* [[7-odd-limit]] [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis)]]: 2.5/3
+* [[9-odd-limit]] unchanged-interval (eigenmonzo) basis: 2.9/7
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~160/147 = 166.140{{c}}
+{{Optimal ET sequence|legend=1| 12, …, 159, 171, 867, 1038, 1209, 1380, 1551, 1722 }}
-{{Optimal ET sequence|legend=1| 29, 36, 65 }}
+[[Badness]] (Sintel): 0.505
-[[Badness]] (Smith): 0.174705
+=== Terminal ===
+Terminal tempers out 441/440 and 4375/4356, and may be described as {{nowrap| 159 & 171 }}. In this temperament, 44/35 and 63/50 are represented as one period of 1/3 octave.
-=== 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 245/242, 686/675, 896/891
+Comma list: 441/440, 4375/4356, 32805/32768
-Mapping: {{mapping| 1 2 -1 1 0 | 0 -3 24 13 25 }}
+Mapping: {{mapping| 3 0 45 94 134 | 0 1 -8 -18 -26 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/10 = 166.097{{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}}
-{{Optimal ET sequence|legend=0| 29, 36, 65 }}
+{{Optimal ET sequence|legend=0| 12, …, 159, 330 }}
-Badness (Smith): 0.068310
+Badness (Sintel): 1.97
-=== 13-limit ===
+==== 13-limit ====
 Subgroup: 2.3.5.7.11.13
-Comma list: 91/90, 169/168, 245/242, 896/891
+Comma list: 364/363, 441/440, 625/624, 13720/13689
-Mapping: {{mapping| 1 2 -1 1 0 3 | 0 -3 24 13 25 5 }}
+Mapping: {{mapping| 3 0 45 94 134 168 | 0 1 -8 -18 -26 -33 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/10 = 166.054{{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}}
-{{Optimal ET sequence|legend=0| 29, 36, 65f, 94df, 159df }}
+{{Optimal ET sequence|legend=0| 12f, …, 159, 330 }}
-Badness (Smith): 0.043750
+Badness (Sintel): 1.53
-== Tertiaschis ==
+==== 17-limit ====
-The tertiaschis temperament ({{nowrap| 94 & 159 }}) has a ~11/10 generator, sharing the same 2.3.5.11 subgroup with [[#Squirrel]], but tempers out 1071875/1062882 for prime 7.
+Subgroup: 2.3.5.7.11.13.17
-[[Subgroup]]: 2.3.5.7
+Comma list: 364/363, 375/374, 441/440, 595/594, 8624/8619
-[[Comma list]]: 32805/32768, 1071875/1062882
+Mapping: {{mapping| 3 0 45 94 134 168 -2 | 0 1 -8 -18 -26 -33 3 }}
-{{Mapping|legend=1| 1 2 -1 10 | 0 -3 24 -52 }}
+Optimal tunings:
+* WE: ~34/27 = 400.0195{{c}}, ~3/2 = 701.8439{{c}}
+* CWE: ~34/27 = 400.0000{{c}}, ~3/2 = 701.8081{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~192/175 = 166.019{{c}}
+{{Optimal ET sequence|legend=0| 12f, 159, 171, 330 }}
-{{Optimal ET sequence|legend=1| 65, 94, 159, 253, 412cd }}
+Badness (Sintel): 1.38
-[[Badness]] (Smith): 0.211859
+=== Terminator ===
+Terminator tempers out 540/539, and may be described as {{nowrap| 171 & 183 }}.
-=== 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 385/384, 4000/3993, 19712/19683
+Comma list: 540/539, 32805/32768, 137781/137500
-Mapping: {{mapping| 1 2 -1 10 0 | 0 -3 24 -52 25 }}
+Mapping: {{mapping| 3 0 45 94 -137 | 0 1 -8 -18 31 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/10 = 166.017{{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}}
-{{Optimal ET sequence|legend=0| 65, 94, 159, 253, 412cd }}
+{{Optimal ET sequence|legend=0| 12e, 171, 183, 354, 537, 891de }}
-Badness (Smith): 0.061336
+Badness (Sintel): 2.21
-=== 13-limit ===
+==== 13-limit ====
 Subgroup: 2.3.5.7.11.13
-Comma list: 325/324, 385/384, 1575/1573, 10985/10976
+Comma list: 540/539, 729/728, 4096/4095, 31250/31213
-Mapping: {{mapping| 1 2 -1 10 0 12 | 0 -3 24 -52 25 -60 }}
+Mapping: {{mapping| 3 0 45 94 -137 -103 | 0 1 -8 -18 31 24 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/10 = 166.016{{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}}
-{{Optimal ET sequence|legend=0| 65f, 94, 159, 253, 412cdf, 665ccdef }}
+{{Optimal ET sequence|legend=0| 12e, 171, 183, 354, 891de }}
-Badness (Smith): 0.036700
+Badness (Sintel): 1.47
-=== 17-limit ===
+==== 17-limit ====
 Subgroup: 2.3.5.7.11.13.17
-Comma list: 325/324, 375/374, 385/384, 595/594, 10985/10976
+Comma list: 540/539, 729/728, 936/935, 1156/1155, 4096/4095
-Mapping: {{mapping| 1 2 -1 10 0 12 -2 | 0 -3 24 -52 25 -60 44 }}
+Mapping: {{mapping| 3 0 45 94 -137 -103 -2 | 0 1 -8 -18 31 24 3 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/10 = 166.012{{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}}
-{{Optimal ET sequence|legend=1| 65f, 94, 159, 253 }}
+{{Optimal ET sequence|legend=0| 12e, 171, 183, 354, 891de }}
-Badness (Smith): 0.026504
+Badness (Sintel): 1.04
-== Countertertiaschis ==
+=== Semiterm ===
-The countertertiaschis temperament ({{nowrap| 159 & 224 }}) has a ~11/10 generator, sharing the same 2.3.5.11 subgroup with [[#Squirrel]], but tempers out 244140625/243045684 for prime 7.
+The semiterm temperament tempers out [[9801/9800]] (kalisma) as well as [[151263/151250]] (odiheim comma), and may be described as {{nowrap| 12 & 342 }}. It has a period of 1/6 octave and its ploidacot is hexaploid monocot.
-[[Subgroup]]: 2.3.5.7
+Subgroup: 2.3.5.7.11
-[[Comma list]]: 32805/32768, 244140625/243045684
+Comma list: 9801/9800, 32805/32768, 151263/151250
-{{Mapping|legend=1| 1 2 -1 -12 | 0 -3 24 107 }}
+Mapping: {{mapping| 6 0 90 188 287 | 0 1 -8 -18 -28 }}
+: mapping generators: ~55/49, ~3
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~625/567 = 166.0621{{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}}
-{{Optimal ET sequence|legend=1| 65d, 159, 224, 383, 607 }}
+{{Optimal ET sequence|legend=0| 12, …, 330e, 342, 1380, 1722, 2064, 2406c, 5154bccdde }}
-[[Badness]] (Smith): 0.188043
+Badness (Sintel): 0.973
-=== 11-limit ===
+==== 13-limit ====
-Subgroup: 2.3.5.7.11
+Subgroup: 2.3.5.7.11.13
-Comma list: 3025/3024, 4000/3993, 32805/32768
+Comma list: 1716/1715, 2080/2079, 32805/32768, 34398/34375
-Mapping: {{mapping| 1 2 -1 -12 0 | 0 -3 24 107 25 }}
+Mapping: {{mapping| 6 0 90 188 287 355 | 0 1 -8 -18 -28 -35 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/10 = 166.0628{{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}}
-{{Optimal ET sequence|legend=0| 65d, 159, 224, 383, 607 }}
+{{Optimal ET sequence|legend=0| 12f, 330eff, 342f, 696f }} *
-Badness (Smith): 0.048943
+<nowiki>*</nowiki> optimal patent val: [[354edo|354]]
-=== 13-limit ===
+Badness (Sintel): 1.85
-Subgroup: 2.3.5.7.11.13
-Comma list: 625/624, 1575/1573, 2080/2079, 10985/10976
+=== Hemiterm ===
+The hemiterm temperament tempers out [[3025/3024]] (lehmerisma), and may be described as {{nowrap| 159 & 183 }}. Its ploidacot is triploid alpha-dicot.
-Mapping: {{mapping| 1 2 -1 -12 0 -10 | 0 -3 24 107 25 99 }}
+Subgroup: 2.3.5.7.11
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/10 = 166.0628{{c}}
+Comma list: 3025/3024, 32805/32768, 102487/102400
-{{Optimal ET sequence|legend=0| 65d, 159, 224, 383, 607 }}
+Mapping: {{mapping| 3 0 45 94 8 | 0 2 -16 -36 1 }}
+: mapping generators: ~63/50, ~693/400
-Badness (Smith): 0.024506
+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}})
-== Pogo ==
+{{Optimal ET sequence|legend=0| 24d, 159, 183, 342, 1209, 1551, 1893e, 2235ce }}
-{{See also| Stearnsmic clan #Pogo }}
-The pogo temperament ({{nowrap| 94 & 130 }}) splits the period in two to address the difference between [[#Tertiaschis]] and [[#Countertertiaschis]]. The schismic tempering of the fifth is just about right for tempering out the stearnsma.
+Badness (Sintel): 0.684
-[[Subgroup]]: 2.3.5.7
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
-[[Comma list]]: 32805/32768, 118098/117649
+Comma list: 676/675, 1001/1000, 3025/3024, 19773/19712
-{{Mapping|legend=1| 2 1 22 2 | 0 3 -24 5 }}
+Mapping: {{mapping| 3 0 45 94 8 42 | 0 2 -16 -36 1 -13 }}
-: mapping generators: ~343/243, ~9/7
-[[Optimal tuning]] ([[POTE]]): ~343/243 = 600.000{{c}}, ~9/7 = 433.901{{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}})
-{{Optimal ET sequence|legend=1| 36, 94, 130, 224, 354 }}
+{{Optimal ET sequence|legend=0| 24d, 159, 183, 342f }}
-[[Badness]] (Smith): 0.079635
+Badness (Sintel): 1.30
-=== 11-limit ===
+==== 17-limit ====
-Subgroup: 2.3.5.7.11
+Subgroup: 2.3.5.7.11.13.17
-Comma list: 540/539, 4000/3993, 32805/32768
+Comma list: 676/675, 715/714, 936/935, 1001/1000, 11271/11264
-Mapping: {{mapping| 2 1 22 2 25 | 0 3 -24 5 -25 }}
+Mapping: {{mapping| 3 0 45 94 8 42 -2 | 0 2 -16 -36 1 -13 6 }}
-Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~9/7 = 433.911{{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}})
-{{Optimal ET sequence|legend=0| 36, 94, 130, 224, 354, 578 }}
+{{Optimal ET sequence|legend=0| 24d, 159, 183, 342f, 525f }}
-Badness (Smith): 0.031857
+Badness (Sintel): 1.14
-=== 13-limit ===
+== Altinex ==
-Subgroup: 2.3.5.7.11.13
+Named by [[Aura]] in 2021, altinex is an alternative to [[#Hemiterm|hemiterm]] and may be described as {{nowrap| 24 & 159 }}. [[159edo]] itself makes for a recommendable tuning.
-Comma list: 540/539, 729/728, 1575/1573, 4096/4095
+[[Subgroup]]: 2.3.5.7
-Mapping: {{mapping| 2 1 22 2 25 -2 | 0 3 -24 5 -25 13 }}
+[[Comma list]]: 32805/32768, 367653125/362797056
-Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~9/7 = 433.911{{c}}
+{{Mapping|legend=1| 3 0 45 -32 | 0 2 -16 17 }}
+: mapping generators: ~1536/1225, ~34300/19683
-{{Optimal ET sequence|legend=0| 36, 94, 130, 224, 354, 578 }}
+[[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 }}
-Badness (Smith): 0.017514
+{{Optimal ET sequence|legend=1| 24, 135, 159, 612ccdd }}
-== Term ==
+[[Badness]] (Sintel): 10.7
-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
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
-[[Comma list]]: 32805/32768, 250047/250000
+Comma list: 385/384, 14700/14641, 19712/19683
-{{Mapping|legend=1| 3 0 45 94 | 0 1 -8 -18 }}
+Mapping: {{mapping| 3 0 45 -32 8 | 0 2 -16 17 1 }}
-: mapping generators: ~63/50, ~3
-[[Optimal tuning]] ([[POTE]]): ~63/50 = 400.000{{c}}, ~3/2 = 701.742{{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}}
-[[Minimax tuning]]:
+{{Optimal ET sequence|legend=0| 24, 135, 159 }}
-* [[7-odd-limit]] [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis)]]: 2.5/3
-* [[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 }}
+Badness (Sintel): 3.35
-[[Badness]] (Smith): 0.019950
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
-=== Terminal ===
+Comma list: 364/363, 385/384, 676/675, 19712/19683
-The terminal temperament ({{nowrap| 12 & 159 }}) tempers out 441/440 and 4375/4356. In this temperament, 44/35 and 63/50 are represented as one period of 1/3 octave.
-Subgroup: 2.3.5.7.11
+Mapping: {{mapping| 3 0 45 -32 8 42 | 0 2 -16 17 1 -13 }}
-Comma list: 441/440, 4375/4356, 32805/32768
+Optimal tunings:
+* WE: ~44/35 = 400.1396{{c}}, ~26/15 = 951.2799{{c}}
+* CWE: ~44/35 = 400.0000{{c}}, ~26/15 = 950.9462{{c}}
-Mapping: {{mapping| 3 0 45 94 134 | 0 1 -8 -18 -26 }}
+{{Optimal ET sequence|legend=0| 24, 135f, 159 }}
-Optimal tuning (POTE): ~44/35 = 400.000{{c}}, ~3/2 = 701.824{{c}}
+Badness (Sintel): 2.27
-{{Optimal ET sequence|legend=0| 12, 147de, 159, 330 }}
+== Squirrel ==
+Squirrel tempers out 686/675, the [[sengic comma]], and may be described as {{nowrap| 29 & 36 }}. It has a [[~]][[11/10]] generator, three of which give the fourth ([[4/3]]), and thirteen of which give [[7/4]] with octave reduction. Its [[ploidacot]] is omega-tricot.
-Badness (Smith): 0.059502
+[[Subgroup]]: 2.3.5.7
-==== 13-limit ====
+[[Comma list]]: 686/675, 32805/32768
-Subgroup: 2.3.5.7.11.13
-Comma list: 364/363, 441/440, 625/624, 13720/13689
+{{Mapping|legend=1| 1 2 -1 1 | 0 -3 24 13 }}
-Mapping: {{mapping| 3 0 45 94 134 168 | 0 1 -8 -18 -26 -33 }}
+[[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 }}
-Optimal tuning (POTE): ~44/35 = 400.000{{c}}, ~3/2 = 701.821{{c}}
+{{Optimal ET sequence|legend=1| 29, 36, 65 }}
-{{Optimal ET sequence|legend=0| 12f, 147def, 159, 330 }}
+[[Badness]] (Sintel): 4.42
-Badness (Smith): 0.037082
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
-==== 17-limit ====
+Comma list: 245/242, 686/675, 896/891
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 364/363, 375/374, 441/440, 595/594, 8624/8619
+Mapping: {{mapping| 1 2 -1 1 0 | 0 -3 24 13 25 }}
-Mapping: {{mapping| 3 0 45 94 134 168 -2 | 0 1 -8 -18 -26 -33 3 }}
+Optimal tunings:
+* WE: ~2 = 1200.6379{{c}}, ~11/10 = 166.1853{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 166.1157{{c}}
-Optimal tuning (POTE): ~34/27 = 400.000{{c}}, ~3/2 = 701.810{{c}}
+{{Optimal ET sequence|legend=0| 29, 36, 65 }}
-{{Optimal ET sequence|legend=0| 12f, 147def, 159, 171, 330 }}
+Badness (Sintel): 2.26
-Badness (Smith): 0.027073
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
-=== Terminator ===
+Comma list: 91/90, 169/168, 245/242, 896/891
-Subgroup: 2.3.5.7.11
-Comma list: 540/539, 32805/32768, 137781/137500
+Mapping: {{mapping| 1 2 -1 1 0 3 | 0 -3 24 13 25 5 }}
-Mapping: {{mapping| 3 0 45 94 -137 | 0 1 -8 -18 31 }}
+Optimal tunings:
+* WE: ~2 = 1201.1361{{c}}, ~11/10 = 166.2110{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 166.0833{{c}}
-Optimal tuning (POTE): ~63/50 = 400.000{{c}}, ~3/2 = 701.685{{c}}
+{{Optimal ET sequence|legend=0| 29, 65f, 94df }}
-{{Optimal ET sequence|legend=0| 12e, 159e, 171, 183, 354, 537, 891de }}
+Badness (Sintel): 1.81
-Badness (Smith): 0.066968
+== Tertiaschis ==
+Named by [[Xenllium]] in 2021, tertiaschis may be described as {{nowrap| 94 & 159 }}. It has a [[~]][[11/10]] generator, sharing the same 2.3.5.11 subgroup with [[#Squirrel|squirrel]], but tempers out 1071875/1062882 for prime 7.
-==== 13-limit ====
+[[Subgroup]]: 2.3.5.7
-Subgroup: 2.3.5.7.11.13
-Comma list: 540/539, 729/728, 4096/4095, 31250/31213
+[[Comma list]]: 32805/32768, 1071875/1062882
-Mapping: {{mapping| 3 0 45 94 -137 -103 | 0 1 -8 -18 31 24 }}
+{{Mapping|legend=1| 1 2 -1 10 | 0 -3 24 -52 }}
-Optimal tuning (POTE): ~63/50 = 400.000{{c}}, ~3/2 = 701.689{{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 }}
-{{Optimal ET sequence|legend=0| 171, 183, 354, 891de, 1245dee, 1599ddee }}
+{{Optimal ET sequence|legend=1| 65, 94, 159, 253, 412cd }}
-Badness (Smith): 0.035487
+[[Badness]] (Sintel): 5.36
-==== 17-limit ====
+=== 11-limit ===
-Subgroup: 2.3.5.7.11.13.17
+Subgroup: 2.3.5.7.11
-Comma list: 540/539, 729/728, 936/935, 1156/1155, 4096/4095
+Comma list: 385/384, 4000/3993, 19712/19683
-Mapping: {{mapping| 3 0 45 94 -137 -103 -2 | 0 1 -8 -18 31 24 3 }}
+Mapping: {{mapping| 1 2 -1 10 0 | 0 -3 24 -52 25 }}
-Optimal tuning (POTE): ~63/50 = 400.000{{c}}, ~3/2 = 701.688{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.3379{{c}}, ~11/10 = 166.0638{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 166.0167{{c}}
-{{Optimal ET sequence|legend=0| 171, 183, 354, 891de, 1245dee, 1599ddee }}
+{{Optimal ET sequence|legend=0| 65, 94, 159, 253, 412cd, 665ccde }}
-Badness (Smith): 0.020434
+Badness (Sintel): 2.07
-=== Semiterm ===
+=== 13-limit ===
-The semiterm temperament ({{nowrap| 12 & 342 }}) has a period of 1/6 octave and tempers out [[9801/9800]] (kalisma) and 151263/151250 (odiheim comma).
+Subgroup: 2.3.5.7.11.13
-Subgroup: 2.3.5.7.11
+Comma list: 325/324, 385/384, 1575/1573, 10985/10976
-Comma list: 9801/9800, 32805/32768, 151263/151250
+Mapping: {{mapping| 1 2 -1 10 0 12 | 0 -3 24 -52 25 -60 }}
-Mapping: {{mapping| 6 0 90 188 287 | 0 1 -8 -18 -28 }}
+Optimal tunings:
-: mapping generators: ~55/49, ~3
+* WE: ~2 = 1200.3467{{c}}, ~11/10 = 166.0635{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 166.0142{{c}}
-Optimal tuning (POTE): ~55/49 = 200.0000{{c}}, ~3/2 = 701.7460{{c}}
+{{Optimal ET sequence|legend=0| 65f, 94, 159, 253, 412cdf, 665ccdef }}
-{{Optimal ET sequence|legend=0| 12, 330e, 342, 1380, 1722, 2064, 2406c }}
+Badness (Sintel): 1.52
-Badness (Smith): 0.029438
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
-==== 13-limit ====
+Comma list: 325/324, 375/374, 385/384, 595/594, 10985/10976
-Subgroup: 2.3.5.7.11.13
-Comma list: 1716/1715, 2080/2079, 32805/32768, 34398/34375
+Mapping: {{mapping| 1 2 -1 10 0 12 -2 | 0 -3 24 -52 25 -60 44 }}
-Mapping: {{mapping| 6 0 90 188 287 355 | 0 1 -8 -18 -28 -35 }}
+Optimal tunings:
+* WE: ~2 = 1200.3019{{c}}, ~11/10 = 166.0535{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 166.0114{{c}}
-Optimal tuning (POTE): ~55/49 = 200.0000{{c}}, ~3/2 = 701.7256{{c}}
+{{Optimal ET sequence|legend=1| 65f, 94, 159, 253 }}
-{{Optimal ET sequence|legend=0| 12f, 330eff, 342f, 696f }} *
+Badness (Sintel): 1.35
-<nowiki>*</nowiki> optimal patent val: [[354edo|354]]
+== Countertertiaschis ==
+Named by [[Flora Canou]] in 2021, Countertertiaschis may be described as {{nowrap| 159 & 224 }}. It has a [[~]][[11/10]] generator, sharing the same 2.3.5.11 subgroup with [[#Squirrel|squirrel]], but tempers out 244140625/243045684 for prime 7.
-Badness (Smith): 0.044657
+[[Subgroup]]: 2.3.5.7
-=== Hemiterm ===
+[[Comma list]]: 32805/32768, 244140625/243045684
-Subgroup: 2.3.5.7.11
-Comma list: 3025/3024, 32805/32768, 102487/102400
+{{Mapping|legend=1| 1 2 -1 -12 | 0 -3 24 107 }}
-Mapping: {{mapping| 3 0 45 94 8 | 0 2 -16 -36 1 }}
+[[Optimal tuning]]s:
-: mapping generators: ~63/50, ~693/400
+* [[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 }}
-Optimal tuning (POTE): ~63/50 = 400.000{{c}}, ~693/400 = 950.872{{c}} (~12/11 = 150.872{{c}})
+{{Optimal ET sequence|legend=1| 65d, 159, 224, 383, 607 }}
-{{Optimal ET sequence|legend=0| 24d, 159, 183, 342, 1209, 1551, 1893e, 2235ce }}
+[[Badness]] (Sintel): 4.76
-Badness (Smith): 0.020687
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
-==== 13-limit ====
+Comma list: 3025/3024, 4000/3993, 32805/32768
-Subgroup: 2.3.5.7.11.13
-Comma list: 676/675, 1001/1000, 3025/3024, 19773/19712
+Mapping: {{mapping| 1 2 -1 -12 0 | 0 -3 24 107 25 }}
-Mapping: {{mapping| 3 0 45 94 8 42 | 0 2 -16 -36 1 -13 }}
+Optimal tunings:
+* WE: ~2 = 1200.0804{{c}}, ~11/10 = 166.0739{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 166.0634{{c}}
-Optimal tuning (POTE): ~63/50 = 400.000{{c}}, ~26/15 = 950.873{{c}} (~12/11 = 150.873{{c}})
+{{Optimal ET sequence|legend=0| 65d, 159, 224, 383, 607 }}
-{{Optimal ET sequence|legend=0| 24d, 159, 183, 342f }}
+Badness (Sintel): 1.62
-Badness (Smith): 0.031362
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
-==== 17-limit ====
+Comma list: 625/624, 1575/1573, 2080/2079, 10985/10976
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 676/675, 715/714, 936/935, 1001/1000, 11271/11264
+Mapping: {{mapping| 1 2 -1 -12 0 -10 | 0 -3 24 107 25 99 }}
-Mapping: {{mapping| 3 0 45 94 8 42 -2 | 0 2 -16 -36 1 -13 6 }}
+Optimal tunings:
+* WE: ~2 = 1200.0805{{c}}, ~11/10 = 166.0740{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~11/10 = 166.0635{{c}}
-Optimal tuning (POTE): ~34/27 = 400.000{{c}}, ~26/15 = 950.867{{c}} (~12/11 = 150.867{{c}})
+{{Optimal ET sequence|legend=0| 65d, 159, 224, 383, 607 }}
-{{Optimal ET sequence|legend=0| 24d, 159, 183, 342f, 525f, 867ff }}
+Badness (Sintel): 1.01
-Badness (Smith): 0.022316
+== Quadrant ==
+Named by [[Xenllium]] in 2021, quadrant tempers out 390625/388962, the [[dimcomp comma]], and maps [[25/21]] to the 1/4-octave period. It may be described as the {{nowrap| 12 & 212 }} temperament; its ploidacot is tetraploid monocot. Just as [[#Term|term]] equates the syntonic~Pythagorean comma with three [[marvel comma]]s, quadrant equates the syntonic~Pythagorean comma with four. A [[septimal comma]] is then found as a stack of five marvel commas.
-== Altinex ==
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: 32805/32768, 367653125/362797056
+[[Comma list]]: 32805/32768, 390625/388962
-{{Mapping|legend=1| 3 0 45 -32 | 0 2 -16 17 }}
+{{Mapping|legend=1| 4 0 60 119 | 0 1 -8 -17 }}
-: mapping generators: ~1536/1225, ~34300/19683
+: mapping generators: ~25/21, ~3
-[[Optimal tuning]] ([[CTE]]): ~1536/1225 = 400.000{{c}}, ~34300/19683 = 950.9654{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 300.0255{{c}}, ~3/2 = 701.8831{{c}}
+: [[error map]]: {{val| +0.102 +0.030 -0.664 +0.462 }}
+* [[CWE]]: ~2 = 300.0000{{c}}, ~3/2 = 701.8180{{c}}
+: error map: {{val| 0.000 -0.137 -0.858 +0.268 }}
-{{Optimal ET sequence|legend=1| 24, …, 111c, 135, 159, 612ccdd, 771ccdd }}
+{{Optimal ET sequence|legend=1| 12, …, 200, 212, 224, 436, 660 }}
-[[Badness]] (Smith): 0.422026
+[[Badness]] (Sintel): 2.79
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 385/384, 14700/14641, 19712/19683
+Comma list: 1375/1372, 6250/6237, 32805/32768
-Mapping: {{mapping| 3 0 45 -32 8 | 0 2 -16 17 1 }}
+Mapping: {{mapping| 4 0 60 119 185 | 0 1 -8 -17 -27 }}
-Optimal tuning (CTE): ~44/35 = 400.000{{c}}, ~121/70 = 950.9658{{c}}
+Optimal tunings:
+* WE: ~25/21 = 300.0244{{c}}, ~3/2 = 701.8759{{c}}
+* CWE: ~25/21 = 300.0000{{c}}, ~3/2 = 701.8145{{c}}
-{{Optimal ET sequence|legend=0| 24, …, 111c, 135, 159, 612ccdd, 771ccdd }}
+{{Optimal ET sequence|legend=0| 12, …, 212, 224, 436, 660 }}
-Badness (Smith): 0.101224
+Badness (Sintel): 1.51
 === 13-limit ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 364/363, 385/384, 676/675, 19712/19683
+Comma list: 625/624, 1375/1372, 2080/2079, 10648/10647
-Mapping: {{mapping| 3 0 45 -32 8 42 | 0 2 -16 17 1 -13 }}
+Mapping: {{mapping| 4 0 60 119 185 224 | 0 1 -8 -17 -27 -33 }}
-Optimal tuning (CTE): ~44/35 = 400.000{{c}}, ~26/15 = 950.9360{{c}}
+Optimal tunings:
+* WE: ~25/21 = 300.0234{{c}}, ~3/2 = 701.8707{{c}}
+* CWE: ~25/21 = 300.0000{{c}}, ~3/2 = 701.8123{{c}}
-{{Optimal ET sequence|legend=0| 24, …, 111cf, 135f, 159 }}
+{{Optimal ET sequence|legend=0| 12f, …, 212, 224, 436, 660 }}
-Badness (Smith): 0.054894
+Badness (Sintel): 1.13
 == Sesquiquartififths ==
+Sesquiquartififths tempers out 2401/2400, the [[breedsma]], and may be described as the {{nowrap| 41 & 171 }} temperament. It splits the fifth into four; its [[ploidacot]] is thus tetracot.
 [[Subgroup]]: 2.3.5.7
@@ Line 1,609: / Line 1,945: @@
 {{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]]s:
+* [[WE]]: ~2 = 1200.0846{{c}}, ~448/405 = 175.4460{{c}}
+: [[error map]]: {{val| +0.085 -0.086 +0.007 -0.093 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~448/405 = 175.4320{{c}}
+: error map: {{val| 0.000 -0.227 -0.137 -0.306 }}
 [[Minimax tuning]]:
@@ Line 1,619: / Line 1,959: @@
 {{Optimal ET sequence|legend=1| 41, 89, 130, 171, 814, 985, 1156, 1327, 1498, 2825bd }}
-[[Badness]] (Smith): 0.011244
+[[Badness]] (Sintel): 0.285
 === Sesquart ===
+Sesquart is the main [[11-limit|11-]] and [[13-limit]] extension of sesquiquartififths of practical interest, as it identifies the neutral third with [[11/9]], which is realized in [[41edo]], [[89edo]], [[130edo]], and [[171edo]] also makes for a possible tuning.
 Subgroup: 2.3.5.7.11
@@ Line 1,628: / Line 1,970: @@
 Mapping: {{mapping| 1 1 7 5 2 | 0 4 -32 -15 10 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~256/231 = 175.406{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.8171{{c}}, ~256/231 = 175.3793{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~256/231 = 175.4081{{c}}
 {{Optimal ET sequence|legend=0| 41, 89, 130, 301e, 431e }}
-Badness (Smith): 0.029306
+Badness (Sintel): 0.969
 ==== 13-limit ====
@@ Line 1,641: / Line 1,985: @@
 Mapping: {{mapping| 1 1 7 5 2 -2 | 0 4 -32 -15 10 39 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~72/65 = 175.409{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.8352{{c}}, ~72/65 = 175.3852{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~72/65 = 175.4095{{c}}
 {{Optimal ET sequence|legend=0| 41, 89, 130, 301e, 431e }}
-Badness (Smith): 0.022396
+Badness (Sintel): 0.925
-===== Sesquartia =====
+===== Heartia =====
 Subgroup: 2.3.5.7.11.13.17
-Comma list: 243/242, 364/363, 441/440, 595/594, 3584/3575
+Comma list: 243/242, 256/255, 273/272, 364/363, 441/440
+Mapping: {{mapping| 1 1 7 5 2 -2 0 | 0 4 -32 -15 10 39 28 }}
+Optimal tunings:
+* WE: ~2 = 1199.6422{{c}}, ~72/65 = 175.3338{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~72/65 = 175.3857{{c}}
+{{Optimal ET sequence|legend=0| 41, 89, 130g }}
+Badness (Sintel): 1.45
+====== 19-limit ======
+Subgroup: 2.3.5.7.11.13.17.19
+Comma list: 171/170, 243/242, 256/255, 273/272, 324/323, 441/440
+Mapping: {{mapping| 1 1 7 5 2 -2 0 6 | 0 4 -32 -15 10 39 28 -12 }}
+Optimal tunings:
+* WE: ~2 = 1199.7499{{c}}, ~21/19 = 175.3432{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~21/19 = 175.3797{{c}}
+{{Optimal ET sequence|legend=0| 41, 89, 130g }}
+Badness (Sintel): 1.40
+===== Sesquartia =====
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 243/242, 364/363, 441/440, 595/594, 3584/3575
 Mapping: {{mapping| 1 1 7 5 2 -2 -6 | 0 4 -32 -15 10 39 69 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~72/65 = 175.424{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.8902{{c}}, ~72/65 = 175.4077{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~72/65 = 175.4234{{c}}
-{{Optimal ET sequence|legend=0| 41, 89g, 130, 171, 301e }}
+{{Optimal ET sequence|legend=0| 41, 130, 171 }}
-Badness (Smith): 0.023126
+Badness (Sintel): 1.18
 ====== 19-limit ======
@@ Line 1,667: / Line 2,045: @@
 Mapping: {{mapping| 1 1 7 5 2 -2 -6 6 | 0 4 -32 -15 10 39 69 -12 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/19 = 175.419{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.9864{{c}}, ~21/19 = 175.4169{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~21/19 = 175.4189{{c}}
-{{Optimal ET sequence|legend=0| 41, 89g, 130, 171, 301eh }}
+{{Optimal ET sequence|legend=0| 41, 130, 171 }}
-Badness (Smith): 0.020466
+Badness (Sintel): 1.24
 ====== 23-limit ======
@@ Line 1,680: / Line 2,060: @@
 Mapping: {{mapping| 1 1 7 5 2 -2 -6 6 -6 | 0 4 -32 -15 10 39 69 -12 72 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/19 = 175.412{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.9606{{c}}, ~21/19 = 175.4067{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~21/19 = 175.4123{{c}}
-{{Optimal ET sequence|legend=0| 41i, 89gi, 130, 171, 301eh }}
+{{Optimal ET sequence|legend=0| 41i, 130, 171 }}
-Badness (Smith): 0.019043
+Badness (Sintel): 1.36
-===== Heartia =====
+===== Hearty =====
 Subgroup: 2.3.5.7.11.13.17
-Comma list: 243/242, 256/255, 273/272, 364/363, 441/440
+Comma list: 221/220, 243/242, 364/363, 441/440, 1632/1625
-Mapping: {{mapping| 1 1 7 5 2 -2 0 | 0 4 -32 -15 10 39 28 }}
+Mapping: {{mapping| 1 1 7 5 2 -2 13 | 0 4 -32 -15 10 39 -61 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~72/65 = 175.386{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.9458{{c}}, ~72/65 = 175.3689{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~72/65 = 175.3770{{c}}
-{{Optimal ET sequence|legend=0| 41, 89, 130g }}
+{{Optimal ET sequence|legend=0| 41g, 89, 130 }}
-Badness (Smith): 0.028443
+Badness (Sintel): 1.56
 ====== 19-limit ======
 Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 171/170, 243/242, 256/255, 273/272, 324/323, 441/440
+Comma list: 221/220, 243/242, 361/360, 364/363, 441/440, 456/455
-Mapping: {{mapping| 1 1 7 5 2 -2 0 6 | 0 4 -32 -15 10 39 28 -12 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/19 = 175.380{{c}}
-{{Optimal ET sequence|legend=0| 41, 89, 130g }}
-Badness (Smith): 0.023059
-===== Hearty =====
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 221/220, 243/242, 364/363, 441/440, 1632/1625
-Mapping: {{mapping| 1 1 7 5 2 -2 13 | 0 4 -32 -15 10 39 -61 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~72/65 = 175.377{{c}}
-{{Optimal ET sequence|legend=0| 41g, 89, 130, 609ceefgg }}
-Badness (Smith): 0.030680
-====== 19-limit ======
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 221/220, 243/242, 361/360, 364/363, 441/440, 456/455
 Mapping: {{mapping| 1 1 7 5 2 -2 13 6 | 0 4 -32 -15 10 39 -61 -12 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/19 = 175.377{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.0114{{c}}, ~72/65 = 175.3783{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~72/65 = 175.3765{{c}}
-{{Optimal ET sequence|legend=0| 41g, 89, 130, 609ceefggh }}
+{{Optimal ET sequence|legend=0| 41g, 89, 130 }}
-Badness (Smith): 0.022816
+Badness (Sintel): 1.39
 ====== 23-limit ======
@@ Line 1,745: / Line 2,105: @@
 Mapping: {{mapping| 1 1 7 5 2 -2 13 6 13 | 0 4 -32 -15 10 39 -61 -12 -58 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/19 = 175.376{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.0122{{c}}, ~72/65 = 175.3782{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~72/65 = 175.3763{{c}}
-{{Optimal ET sequence|legend=0| 41g, 89, 130, 609ceefggh }}
+{{Optimal ET sequence|legend=0| 41g, 89, 130 }}
-Badness (Smith): 0.019121
+Badness (Sintel): 1.37
 === Bisesqui ===
@@ Line 1,759: / Line 2,121: @@
 : mapping generators: ~99/70, ~448/405
-Optimal tuning (POTE): ~99/70 = 600.000{{c}}, ~448/405 = 175.435{{c}}
+Optimal tunings:
+* WE: ~99/70 = 600.0429{{c}}, ~448/405 = 175.4474{{c}}
+* CWE: ~99/70 = 600.0000{{c}}, ~448/405 = 175.4334{{c}}
-{{Optimal ET sequence|legend=1| 82e, 130, 212, 342, 1156, 1498, 1840d }}
+{{Optimal ET sequence|legend=1| 82e, 130, 212, 342, 1156, 1498, 1840d, 5862bbccdddee }}
-Badness (Smith): 0.016968
+Badness (Sintel): 0.561
-== Quintilipyth ==
+== Tsaharuk ==
-The quintilipyth temperament ({{nowrap| 12 & 253 }}, formerly ''quintilischis'') slices the pythagorean fourth ([[4/3]]) into five semitones and tempers out the compass comma (9765625/9680832) in the 7-limit.
+{{Main| Tsaharuk }}
+Tsaharuk tempers out 420175/419904, the [[wizma]], and may be described as the {{nowrap| 77 & 94 }} temperament. It is generated by a slightly flat neutral second of [[~]][[13/12]], five of which make the [[3/2|perfect fifth]], so its [[ploidacot]] is pentacot.
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: 32805/32768, 9765625/9680832
+[[Comma list]]: 32805/32768, 420175/419904
-{{Mapping|legend=1| 1 2 -1 -4 | 0 -5 40 82 }}
+{{Mapping|legend=1| 1 1 7 0 | 0 5 -40 24 }}
+: mapping generators: ~2, ~243/224
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~625/588 = 99.625{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.1039{{c}}, ~243/224 = 140.3620{{c}}
+: [[error map]]: {{val| +0.104 -0.041 -0.067 -0.137 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~243/224 = 140.3496{{c}}
+: error map: {{val| 0.000 -0.207 -0.296 -0.436 }}
-{{Optimal ET sequence|legend=1| 12, 253, 265 }}
+{{Optimal ET sequence|legend=1| 17, 77, 94, 171 }}
-[[Badness]] (Smith): 0.253966
+[[Badness]] (Sintel): 0.777
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 1375/1372, 4375/4356, 32805/32768
+Comma list: 385/384, 1331/1323, 19712/19683
-Mapping: {{mapping| 1 2 -1 -4 -7 | 0 -5 40 82 126 }}
+Mapping: {{mapping| 1 1 7 0 1 | 0 5 -40 24 21 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~35/33 = 99.616{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.3103{{c}}, ~88/81 = 140.4011{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~88/81 = 140.3649{{c}}
-{{Optimal ET sequence|legend=0| 12, 253, 265, 518c, 783cc }}
+{{Optimal ET sequence|legend=0| 17, 77, 94, 171e, 265e }}
-Badness (Smith): 0.113044
+Badness (Sintel): 2.10
 === 13-limit ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 1375/1372, 2080/2079, 4375/4356, 10648/10647
+Comma list: 352/351, 385/384, 729/728, 1331/1323
-Mapping: {{mapping| 1 2 -1 -4 -7 -9 | 0 -5 40 82 126 153 }}
+Mapping: {{mapping| 1 1 7 0 1 3 | 0 5 -40 24 21 6 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~35/33 = 99.612{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.1840{{c}}, ~13/12 = 140.3840{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 140.3627{{c}}
-{{Optimal ET sequence|legend=0| 12f, 253, 518c, 771cc }}
+{{Optimal ET sequence|legend=0| 17, 77, 94, 171e }}
-Badness (Smith): 0.069127
+Badness (Sintel): 1.57
-=== 17-limit ===
+== Quanharuk ==
-Subgroup: 2.3.5.7.11.13.17
+Quanharuk tempers out 16875/16807, the [[mirkwai]] comma, and may be described as the {{nowrap| 41 & 183 }} temperament. The generator is a slightly flat major third of [[~]][[56/45]], five of which make the [[3/1|3rd]] [[harmonic]], so the [[ploidacot]] of this temperament is alpha-pentacot. [[224edo]] makes for a recommendable tuning.
-Comma list: 375/374, 595/594, 833/832, 1375/1372, 8624/8619
+[[Subgroup]]: 2.3.5.7
-Mapping: {{mapping| 1 2 -1 -4 -7 -9 5 | 0 -5 40 82 126 153 -11 }}
+[[Comma list]]: 16875/16807, 32805/32768
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~18/17 = 99.612{{c}}
+{{Mapping|legend=1| 1 0 15 12 | 0 5 -40 -29 }}
+: mapping generators: ~2, ~56/45
-{{Optimal ET sequence|legend=0| 12f, 253, 518c, 771cc }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0032{{c}}, ~56/45 = 380.3557{{c}}
+: [[error map]]: {{val| +0.003 -0.177 -0.493 +0.898 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~56/45 = 380.3546{{c}}
+: error map: {{val| 0.000 -0.182 -0.498 +0.890 }}
-Badness (Smith): 0.045992
+{{Optimal ET sequence|legend=1| 41, 142, 183, 224 }}
-=== 19-limit ===
+[[Badness]] (Sintel): 1.82
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 375/374, 400/399, 495/494, 595/594, 1375/1372, 3978/3971
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
-Mapping: {{mapping| 1 2 -1 -4 -7 -9 5 4 | 0 -5 40 82 126 153 -11 3 }}
+Comma list: 540/539, 1375/1372, 32805/32768
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~18/17 = 99.615{{c}}
+Mapping: {{mapping| 1 0 15 12 -7 | 0 5 -40 -29 33 }}
-{{Optimal ET sequence|legend=0| 12f, 253, 265, 518ch }}
+Optimal tunings:
+* WE: ~2 = 1199.9709{{c}}, ~56/45 = 380.3423{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~56/45 = 380.3517{{c}}
-Badness (Smith): 0.038155
+{{Optimal ET sequence|legend=0| 41, 142, 183, 224, 631d, 855d }}
-== Quintaschis ==
+Badness (Sintel): 1.04
-The quintaschis temperament ({{nowrap| 12 & 289 }}) slices the fourth (4/3) into five semitones and tempers out 49009212/48828125 in the 7-limit.
-[[Subgroup]]: 2.3.5.7
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
-[[Comma list]]: 32805/32768, 49009212/48828125
+Comma list: 540/539, 729/728, 1375/1372, 4096/4095
+Mapping: {{mapping| 1 0 15 12 -7 -15 | 0 5 -40 -29 33 59 }}
+Optimal tunings:
+* WE: ~2 = 1199.9663{{c}}, ~56/45 = 380.3403{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~56/45 = 380.3509{{c}}
+{{Optimal ET sequence|legend=0| 41, 142, 183, 224, 631d, 855d }}
+Badness (Sintel): 0.884
+== Quintilipyth ==
+Named by [[Xenllium]] in 2021, quintilipyth (formerly ''quintilischis'') slices the [[4/3|perfect fourth]] into five semitones and tempers out the [[compass comma]] (9765625/9680832) in the [[7-limit]]. It may be described as the {{nowrap| 12 & 253 }} temperament, and its [[ploidacot]] is omega-pentacot.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 32805/32768, 9765625/9680832
-{{Mapping|legend=1| 1 2 -1 -5 | 0 -5 40 94 }}
+{{Mapping|legend=1| 1 2 -1 -4 | 0 -5 40 82 }}
+: mapping generators: ~2, ~625/588
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~200/189 = 99.664{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.1138{{c}}, ~625/588 = 99.6347{{c}}
+: [[error map]]: {{val| +0.114 +0.099 -1.041 +0.761 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~625/588 = 99.6265{{c}}
+: error map: {{val| 0.000 -0.087 -1.255 +0.544 }}
-{{Optimal ET sequence|legend=1| 12, …, 289, 301, 590, 891, 1192 }}
+{{Optimal ET sequence|legend=1| 12, …, 253, 265 }}
-[[Badness]] (Smith): 0.132890
+[[Badness]] (Sintel): 6.43
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 441/440, 32805/32768, 1953125/1951488
+Comma list: 1375/1372, 4375/4356, 32805/32768
-Mapping: {{mapping| 1 2 -1 -5 -8 | 0 -5 40 94 138 }}
+Mapping: {{mapping| 1 2 -1 -4 -7 | 0 -5 40 82 126 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~35/33 = 99.653{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.1503{{c}}, ~35/33 = 99.6287{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~35/33 = 99.6176{{c}}
-{{Optimal ET sequence|legend=0| 12, …, 277d, 289 }}
+{{Optimal ET sequence|legend=0| 12, …, 253, 265, 518c }}
-Badness (Smith): 0.111477
+Badness (Sintel): 3.74
-==== 13-limit ====
+=== 13-limit ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 364/363, 441/440, 32805/32768, 109512/109375
+Comma list: 1375/1372, 2080/2079, 4375/4356, 10648/10647
-Mapping: {{mapping| 1 2 -1 -5 -8 -11 | 0 -5 40 94 138 177 }}
+Mapping: {{mapping| 1 2 -1 -4 -7 -9 | 0 -5 40 82 126 153 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~35/33 = 99.658{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.1774{{c}}, ~35/33 = 99.6267{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~35/33 = 99.6134{{c}}
-{{Optimal ET sequence|legend=0| 12f, …, 277dff, 289 }}
+{{Optimal ET sequence|legend=0| 12f, …, 241cdef, 253 }}
-Badness (Smith): 0.074218
+Badness (Sintel): 2.86
-==== 17-limit ====
+=== 17-limit ===
 Subgroup: 2.3.5.7.11.13.17
-Comma list: 364/363, 441/440, 595/594, 3757/3750, 32805/32768
+Comma list: 375/374, 595/594, 833/832, 1375/1372, 8624/8619
-Mapping: {{mapping| 1 2 -1 -5 -8 -11 5 | 0 -5 40 94 138 177 -11 }}
+Mapping: {{mapping| 1 2 -1 -4 -7 -9 5 | 0 -5 40 82 126 153 -11 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~18/17 = 99.656{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.1745{{c}}, ~18/17 = 99.6265{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~18/17 = 99.6131{{c}}
-{{Optimal ET sequence|legend=0| 12f, 277dff, 289 }}
+{{Optimal ET sequence|legend=0| 12f, 241cdef, 253 }}
-Badness (Smith): 0.050571
+Badness (Sintel): 2.34
-==== 19-limit ====
+=== 19-limit ===
 Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 364/363, 441/440, 476/475, 595/594, 3757/3750, 6885/6859
+Comma list: 375/374, 400/399, 495/494, 595/594, 1375/1372, 3978/3971
-Mapping: {{mapping| 1 2 -1 -5 -8 -11 5 4 | 0 -5 40 94 138 177 -11 3 }}
+Mapping: {{mapping| 1 2 -1 -4 -7 -9 5 4 | 0 -5 40 82 126 153 -11 3 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~18/17 = 99.659{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.0713{{c}}, ~18/17 = 99.6208{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~18/17 = 99.6152{{c}}
-{{Optimal ET sequence|legend=0| 12f, 289 }}
+{{Optimal ET sequence|legend=0| 12f, 253, 265 }}
-Badness (Smith): 0.042120
+Badness (Sintel): 2.32
-=== Quintahelenic ===
+== Quintaschis ==
-Subgroup: 2.3.5.7.11
+Named by [[Xenllium]] in 2021, quintaschis slices the [[4/3|perfect fourth]] into five semitones and tempers out 49009212/48828125 in the [[7-limit]]. It may be described as the {{nowrap| 12 & 289 }} temperament, and its [[ploidacot]] is omega-pentacot.
-Comma list: 5632/5625, 8019/8000, 151263/151250
+[[Subgroup]]: 2.3.5.7
-Mapping: {{mapping| 1 2 -1 -5 -9 | 0 -5 40 94 150 }}
+[[Comma list]]: 32805/32768, 49009212/48828125
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~200/189 = 99.671{{c}}
+{{Mapping|legend=1| 1 2 -1 -5 | 0 -5 40 94 }}
-{{Optimal ET sequence|legend=0| 12, …, 289e, 301, 915 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0536{{c}}, ~200/189 = 99.6684{{c}}
+: [[error map]]: {{val| +0.054 -0.190 +0.370 -0.262 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~200/189 = 99.6645{{c}}
+: error map: {{val| 0.000 -0.277 +0.266 -0.363 }}
-Badness (Smith): 0.082225
+{{Optimal ET sequence|legend=1| 12, …, 289, 301, 590, 891, 1192 }}
-==== 13-limit ====
+[[Badness]] (Sintel): 3.36
-Subgroup: 2.3.5.7.11.13
-Comma list: 847/845, 1716/1715, 5632/5625, 8019/8000
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
-Mapping: {{mapping| 1 2 -1 -5 -9 -11 | 0 -5 40 94 150 177 }}
+Comma list: 441/440, 32805/32768, 1953125/1951488
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~200/189 = 99.661{{c}}
+Mapping: {{mapping| 1 2 -1 -5 -8 | 0 -5 40 94 138 }}
-{{Optimal ET sequence|legend=0| 12f, …, 289e, 301 }}
+Optimal tunings:
+* WE: ~2 = 1200.0988{{c}}, ~35/33 = 99.6613{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~35/33 = 99.6540{{c}}
-Badness (Smith): 0.055570
+{{Optimal ET sequence|legend=0| 12, …, 277d, 289 }}
-===== 17-limit =====
+Badness (Sintel): 3.69
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 561/560, 833/832, 847/845, 1701/1700, 3757/3750
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
-Mapping: {{mapping| 1 2 -1 -5 -9 -11 5 | 0 -5 40 94 150 177 -11 }}
+Comma list: 364/363, 441/440, 32805/32768, 109512/109375
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~18/17 = 99.665{{c}}
+Mapping: {{mapping| 1 2 -1 -5 -8 -11 | 0 -5 40 94 138 177 }}
-{{Optimal ET sequence|legend=1| 12f, 289e, 301 }}
+Optimal tunings:
+* WE: ~2 = 1200.0625{{c}}, ~35/33 = 99.6630{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~35/33 = 99.6583{{c}}
-Badness (Smith): 0.040412
+{{Optimal ET sequence|legend=0| 12f, …, 277dff, 289 }}
-===== 19-limit =====
+Badness (Sintel): 3.07
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 476/475, 495/494, 561/560, 833/832, 847/845, 1701/1700
+==== 17-limit ====
+Subgroup: 2.3.5.7.11.13.17
-Mapping: {{mapping| 1 2 -1 -5 -9 -11 5 4 | 0 -5 40 94 150 177 -11 3 }}
+Comma list: 364/363, 441/440, 595/594, 3757/3750, 32805/32768
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~18/17 = 99.668{{c}}
+Mapping: {{mapping| 1 2 -1 -5 -8 -11 5 | 0 -5 40 94 138 177 -11 }}
-{{Optimal ET sequence|legend=0| 12f, 301 }}
+Optimal tunings:
+* WE: ~2 = 1200.1286{{c}}, ~18/17 = 99.6668{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~18/17 = 99.6568{{c}}
-Badness (Smith): 0.036840
+{{Optimal ET sequence|legend=0| 12f, 277dff, 289 }}
-==== Quintahelenoid ====
+Badness (Sintel): 2.58
-Subgroup: 2.3.5.7.11.13
-Comma list: 729/728, 1001/1000, 4096/4095, 86515/86436
+==== 19-limit ====
+Subgroup: 2.3.5.7.11.13.17.19
-Mapping: {{mapping| 1 2 -1 -5 -9 14 | 0 -5 40 94 150 -124 }}
+Comma list: 364/363, 441/440, 476/475, 595/594, 3757/3750, 6885/6859
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~200/189 = 99.672{{c}}
+Mapping: {{mapping| 1 2 -1 -5 -8 -11 5 4 | 0 -5 40 94 138 177 -11 3 }}
-{{Optimal ET sequence|legend=0| 12, 301, 614, 915 }}
+Optimal tunings:
+* WE: ~2 = 1200.0289{{c}}, ~18/17 = 99.6609{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~18/17 = 99.6586{{c}}
-Badness (Smith): 0.066108
+{{Optimal ET sequence|legend=0| 12f, 289 }}
-===== 17-limit =====
+Badness (Sintel): 2.56
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 561/560, 729/728, 1001/1000, 4096/4095, 14161/14157
+=== Quintahelenic ===
+Subgroup: 2.3.5.7.11
-Mapping: {{mapping| 1 2 -1 -5 -9 14 5 | 0 -5 40 94 150 -124 -11 }}
+Comma list: 5632/5625, 8019/8000, 151263/151250
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~18/17 = 99.671{{c}}
+Mapping: {{mapping| 1 2 -1 -5 -9 | 0 -5 40 94 150 }}
-{{Optimal ET sequence|legend=0| 12, 301 }}
+Optimal tunings:
+* WE: ~2 = 1200.0195{{c}}, ~200/189 = 99.6723{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~200/189 = 99.6709{{c}}
-Badness (Smith): 0.047908
+{{Optimal ET sequence|legend=0| 12, …, 289e, 301, 915 }}
-===== 19-limit =====
+Badness (Sintel): 2.72
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 476/475, 561/560, 729/728, 1001/1000, 4096/4095, 6144/6137
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
-Mapping: {{mapping| 1 2 -1 -5 -9 14 5 4 | 0 -5 40 94 150 -124 -11 3 }}
+Comma list: 847/845, 1716/1715, 5632/5625, 8019/8000
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~18/17 = 99.672{{c}}
+Mapping: {{mapping| 1 2 -1 -5 -9 -11 | 0 -5 40 94 150 177 }}
-{{Optimal ET sequence|legend=0| 12, 301 }}
+Optimal tunings:
+* WE: ~2 = 1200.0442{{c}}, ~200/189 = 99.6709{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~200/189 = 99.6675{{c}}
-Badness (Smith): 0.039542
+{{Optimal ET sequence|legend=0| 12f, …, 289e, 301 }}
-== Sextilifourths ==
+Badness (Sintel): 2.30
-The sextilifourths ({{nowrap| 130 & 159 }}, also known as ''sextilischis'', formerly ''sextilififths'') temperament slices the fourth (4/3) into six small semitones, which serves as both 21/20 and 22/21.
-[[Subgroup]]: 2.3.5.7
+===== 17-limit =====
+Subgroup: 2.3.5.7.11.13.17
-[[Comma list]]: 32805/32768, 235298/234375
+Comma list: 561/560, 833/832, 847/845, 1701/1700, 3757/3750
-{{Mapping|legend=1| 1 2 -1 -1 | 0 -6 48 55 }}
+Mapping: {{mapping| 1 2 -1 -5 -9 -11 5 | 0 -5 40 94 150 177 -11 }}
-: mapping generators: ~2, ~21/2
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~21/20 = 83.053{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.1227{{c}}, ~200/189 = 99.6753{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~200/189 = 99.6658{{c}}
-{{Optimal ET sequence|legend=1| 29, 72cd, 101, 130, 289, 419 }}
+{{Optimal ET sequence|legend=1| 12f, 289e, 301 }}
-[[Badness]] (Smith): 0.108794
+Badness (Sintel): 2.06
-=== 11-limit ===
+===== 19-limit =====
-Subgroup: 2.3.5.7.11
+Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 441/440, 4000/3993, 235298/234375
+Comma list: 476/475, 495/494, 561/560, 833/832, 847/845, 1701/1700
-Mapping: {{mapping| 1 2 -1 -1 0 | 0 -6 48 55 50 }}
+Mapping: {{mapping| 1 2 -1 -5 -9 -11 5 4 | 0 -5 40 94 150 177 -11 3 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/20 = 83.049{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.0230{{c}}, ~200/189 = 99.6694{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~200/189 = 99.6676{{c}}
-{{Optimal ET sequence|legend=0| 29, 72cde, 101e, 130, 289 }}
+{{Optimal ET sequence|legend=0| 12f, 301 }}
-Badness (Smith): 0.045457
+Badness (Sintel): 2.24
-=== 13-limit ===
+==== Quintahelenoid ====
 Subgroup: 2.3.5.7.11.13
-Comma list: 364/363, 441/440, 676/675, 10985/10976
+Comma list: 729/728, 1001/1000, 4096/4095, 86515/86436
-Mapping: {{mapping| 1 2 -1 -1 0 1 | 0 -6 48 55 50 39 }}
+Mapping: {{mapping| 1 2 -1 -5 -9 14 | 0 -5 40 94 150 -124 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~21/20 = 83.049{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.9919{{c}}, ~200/189 = 99.6712{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~200/189 = 99.6718{{c}}
-{{Optimal ET sequence|legend=0| 29, 72cdef, 101e, 130, 289 }}
+{{Optimal ET sequence|legend=0| 12, 301, 614, 915 }}
-Badness (Smith): 0.025276
+Badness (Sintel): 2.73
-== Septiquarschis ==
+===== 17-limit =====
-The septiquarschis temperament ({{nowrap| 89 & 94 }}) splits septimal minor seventh ([[7/4]]) into four generators and tempers out 829440/823543 (mynaslender comma) and 67108864/66706983 (septiness comma).
+Subgroup: 2.3.5.7.11.13.17
-[[Subgroup]]: 2.3.5.7
+Comma list: 561/560, 729/728, 1001/1000, 4096/4095, 14161/14157
-[[Comma list]]: 32805/32768, 829440/823543
+Mapping: {{mapping| 1 2 -1 -5 -9 14 5 | 0 -5 40 94 150 -124 -11 }}
-{{Mapping|legend=1| 1 3 -9 2 | 0 -7 -56 4 }}
+Optimal tunings:
+* WE: ~2 = 1200.0469{{c}}, ~18/17 = 99.6749{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~18/17 = 99.6710{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~147/128 = 242.614{{c}}
+{{Optimal ET sequence|legend=0| 12, 301 }}
-{{Optimal ET sequence|legend=1| 89, 94, 183, 460d, 643d, 1103dd }}
+Badness (Sintel): 2.44
-[[Badness]] (Smith): 0.187047
+===== 19-limit =====
+Subgroup: 2.3.5.7.11.13.17.19
-=== 11-limit ===
+Comma list: 476/475, 561/560, 729/728, 1001/1000, 4096/4095, 6144/6137
-Subgroup: 2.3.5.7.11
-Comma list: 540/539, 15488/15435, 32805/32768
+Mapping: {{mapping| 1 2 -1 -5 -9 14 5 4 | 0 -5 40 94 150 -124 -11 3 }}
-Mapping: {{mapping| 1 3 -9 2 -2 | 0 -7 -56 4 27 }}
+Optimal tunings:
+* WE: ~2 = 1199.9925{{c}}, ~18/17 = 99.6710{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~18/17 = 99.6716{{c}}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~147/128 = 242.616{{c}}
+{{Optimal ET sequence|legend=0| 12, 301 }}
-{{Optimal ET sequence|legend=0| 89, 94, 183, 460d, 643d, 826dd }}
+Badness (Sintel): 2.41
-Badness (Smith): 0.052002
+== Sextilifourths ==
+Named by [[Xenllium]] in 2021, sextilifourths (also known as ''sextilischis'', formerly ''sextilififths'') slices the [[4/3|perfect fourth]] into six small semitones, which serves as both [[21/20]] and [[22/21]]. It may be described as {{nowrap| 130 & 159 }}, and its [[ploidacot]] is omega-hexacot. [[289edo]] gives a highly recommendable tuning.
-=== 13-limit ===
+[[Subgroup]]: 2.3.5.7
-Subgroup: 2.3.5.7.11.13
-Comma list: 540/539, 729/728, 1573/1568, 4096/4095
+[[Comma list]]: 32805/32768, 235298/234375
-Mapping: {{mapping| 1 3 -9 2 -2 13 | 0 -7 -56 4 27 -46 }}
+{{Mapping|legend=1| 1 2 -1 -1 | 0 -6 48 55 }}
+: mapping generators: ~2, ~21/20
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~147/128 = 242.610{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0987{{c}}, ~21/20 = 83.0599{{c}}
+: [[error map]]: {{val| +0.099 -0.117 +0.462 -0.630 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~21/20 = 83.0543{{c}}
+: error map: {{val| 0.000 -0.281 +0.295 -0.837 }}
-{{Optimal ET sequence|legend=0| 89, 94, 183, 277, 460d }}
+{{Optimal ET sequence|legend=1| 29, 72cd, 101, 130, 289, 419 }}
-Badness (Smith): 0.035315
+[[Badness]] (Sintel): 2.75
-== Tsaharuk ==
+=== 11-limit ===
-{{Main| Tsaharuk }}
+Subgroup: 2.3.5.7.11
-[[Subgroup]]: 2.3.5.7
+Comma list: 441/440, 4000/3993, 235298/234375
-[[Comma list]]: 32805/32768, 420175/419904
+Mapping: {{mapping| 1 2 -1 -1 0 | 0 -6 48 55 50 }}
-{{Mapping|legend=1| 1 1 7 0 | 0 5 -40 24 }}
+Optimal tunings:
-: mapping generators: ~2, ~243/224
+* WE: ~2 = 1200.0424{{c}}, ~21/20 = 83.0520{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.0497{{c}}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~243/224 = 140.350{{c}}
+{{Optimal ET sequence|legend=0| 29, 72cde, 101e, 130, 289 }}
-{{Optimal ET sequence|legend=1| 17, 60c, 77, 94, 171 }}
+Badness (Sintel): 1.50
-[[Badness]] (Smith): 0.030697
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
-=== 11-limit ===
+Comma list: 364/363, 441/440, 676/675, 10985/10976
-Subgroup: 2.3.5.7.11
-Comma list: 385/384, 1331/1323, 19712/19683
+Mapping: {{mapping| 1 2 -1 -1 0 1 | 0 -6 48 55 50 39 }}
-Mapping: {{mapping| 1 1 7 0 1 | 0 5 -40 24 21 }}
+Optimal tunings:
+* WE: ~2 = 1200.1056{{c}}, ~21/20 = 83.0566{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.0508{{c}}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~88/81 = 140.365{{c}}
+{{Optimal ET sequence|legend=0| 29, 72cdef, 101e, 130, 289 }}
-{{Optimal ET sequence|legend=0| 17, 60ce, 77, 94, 171e, 265e, 436ee }}
+Badness (Sintel): 1.04
-Badness (Smith): 0.063499
+== Septant ==
+Named by [[Xenllium]] in 2021, septant notably tempers out the [[akjaysma]] ({{monzo| 47 -7 -7 -7 }}) and may be described as the {{nowrap| 224 & 301 }} temperament. It has a period of 1/7 octave, and its [[ploidacot]] is heptaploid monocot.
-=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 352/351, 385/384, 729/728, 1331/1323
-Mapping: {{mapping| 1 1 7 0 1 3 | 0 5 -40 24 21 6 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~13/12 = 140.363{{c}}
-{{Optimal ET sequence|legend=0| 17, 60ce, 77, 94, 171e, 436ee }}
-Badness (Smith): 0.037886
-== Quanharuk ==
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: 16875/16807, 32805/32768
+[[Comma list]]: 32805/32768, 516560652/514714375
-{{Mapping|legend=1| 1 0 15 12 | 0 5 -40 -29 }}
+{{Mapping|legend=1| 7 0 105 -56 | 0 1 -8 7 }}
-: mapping generators: ~2, ~56/45
+: mapping generators: ~8575/7776, ~3
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~56/45 = 380.355{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~8575/7776 = 171.4303{{c}}, ~3/2 = 701.7091{{c}}
+: [[error map]]: {{val| +0.012 -0.234 +0.096 +0.265 }}
+* [[CWE]]: ~8575/7776 = 171.4286{{c}}, ~3/2 = 701.7022{{c}}
+: error map: {{val| 0.000 -0.253 +0.069 +0.232 }}
-{{Optimal ET sequence|legend=1| 41, 142, 183, 224, 1303d, 1527cd, 1751cd, 1975cd }}
+{{Optimal ET sequence|legend=1| 77, 147, 224, 301, 525, 826, 1351 }}
-[[Badness]] (Smith): 0.071950
+[[Badness]] (Sintel): 2.81
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 540/539, 1375/1372, 32805/32768
+Comma list: 3025/3024, 24057/24010, 32805/32768
-Mapping: {{mapping| 1 0 15 12 -7 | 0 5 -40 -29 33 }}
+Mapping: {{mapping| 7 0 105 -56 -120 | 0 1 -8 7 13 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~56/45 = 380.352{{c}}
+Optimal tunings:
+* WE: ~495/448 = 171.4334{{c}}, ~3/2 = 701.7387{{c}}
+* CWE: ~495/448 = 171.4286{{c}}, ~3/2 = 701.7198{{c}}
-{{Optimal ET sequence|legend=0| 41, 142, 183, 224, 631d, 855d, 1079d }}
+{{Optimal ET sequence|legend=0| 77, 147, 224, 301, 525 }}
-Badness (Smith): 0.031549
+Badness (Sintel): 1.46
 === 13-limit ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 540/539, 729/728, 1375/1372, 4096/4095
+Comma list: 729/728, 1716/1715, 2200/2197, 3025/3024
-Mapping: {{mapping| 1 0 15 12 -7 -15 | 0 5 -40 -29 33 59 }}
+Mapping: {{mapping| 7 0 105 -56 -120 37 | 0 1 -8 7 13 -1 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~56/45 = 380.351{{c}}
+Optimal tunings:
+* WE: ~495/448 = 171.4282{{c}}, ~3/2 = 701.7229{{c}}
+* CWE: ~495/448 = 171.4286{{c}}, ~3/2 = 701.7242{{c}}
-{{Optimal ET sequence|legend=0| 41, 142, 183, 224, 631d, 855d }}
+{{Optimal ET sequence|legend=0| 77, 147, 224, 525, 1274f }}
-Badness (Smith): 0.021392
+Badness (Sintel): 1.02
-== Quadrant ==
+== Octant ==
-The ''quadrant'' temperament ({{nowrap| 12 & 224 }}) has a period of quarter octave and tempers out the [[dimcomp comma]], 390625/388962. In this temperament, 25/21 is mapped into quarter octave.
+Octant may be described as the {{nowrap| 224 & 248 }} temperament. It has a period of 1/8 octave, and its [[ploidacot]] is octaploid monocot. In this temperament, [[12/11]], [[35/27]], and [[99/70]] are mapped to 1\8, 3\8, and 4\8 respectively.
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: 32805/32768, 390625/388962
+[[Comma list]]: 32805/32768, 2259436291848/2251875390625
-{{Mapping|legend=1| 4 0 60 119 | 0 1 -8 -17 }}
+{{Mapping|legend=1| 8 0 120 -117 | 0 1 -8 11 }}
-: mapping generators: ~25/21, ~3
+: mapping generators: ~42875/39366, ~3
-[[Optimal tuning]] ([[POTE]]): ~25/21 = 300.0000{{c}}, ~3/2 = 701.8234{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~42875/39366 = 150.0048{{c}}, ~3/2 = 701.7356{{c}}
+: [[error map]]: {{val| +0.039 -0.181 +0.071 +0.127 }}
+* [[CWE]]: ~42875/39366 = 150.0000{{c}}, ~3/2 = 701.7134{{c}}
+: error map: {{val| 0.000 -0.242 -0.021 +0.022 }}
-{{Optimal ET sequence|legend=1| 212, 224, 436, 660, 1096c }}
+{{Optimal ET sequence|legend=1| 24, …, 224, 472, 696, 1168 }}
-[[Badness]] (Smith): 0.110242
+[[Badness]] (Sintel): 3.98
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 1375/1372, 6250/6237, 32805/32768
+Comma list: 9801/9800, 32805/32768, 46656/46585
-Mapping: {{mapping| 4 0 60 119 185 | 0 1 -8 -17 -27 }}
+Mapping: {{mapping| 8 0 120 -117 15 | 0 1 -8 11 1 }}
-Optimal tuning (POTE): ~25/21 = 300.0000{{c}}, ~3/2 = 701.8176{{c}}
+Optimal tunings:
+* WE: ~12/11 = 150.0010{{c}}, ~3/2 = 701.7177{{c}}
+* CWE: ~12/11 = 150.0000{{c}}, ~3/2 = 701.7131{{c}}
-{{Optimal ET sequence|legend=0| 212, 224, 436, 660 }}
+{{Optimal ET sequence|legend=0| 24, …, 224, 472, 696, 1168 }}
-Badness (Smith): 0.045738
+Badness (Sintel): 1.48
 === 13-limit ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 625/624, 1375/1372, 2080/2079, 10648/10647
+Comma list: 729/728, 1575/1573, 2200/2197, 6656/6655
-Mapping: {{mapping| 4 0 60 119 185 224 | 0 1 -8 -17 -27 -33 }}
+Mapping: {{mapping| 8 0 120 -117 15 93 | 0 1 -8 11 1 -5 }}
-Optimal tuning (POTE): ~25/21 = 300.0000{{c}}, ~3/2 = 701.8158{{c}}
+Optimal tunings:
+* WE: ~12/11 = 149.9957{{c}}, ~3/2 = 701.7046{{c}}
+* CWE: ~12/11 = 150.0000{{c}}, ~3/2 = 701.7247{{c}}
-{{Optimal ET sequence|legend=0| 212, 224, 436, 660 }}
+{{Optimal ET sequence|legend=0| 24, 224, 472, 696 }}
-Badness (Smith): 0.027243
+Badness (Sintel): 1.26
-== Septant ==
+== Nonant ==
-The septant temperament ({{nowrap| 224 & 301 }}) has a period of 1/7 octave and tempers out the [[akjaysma]], {{monzo| 47 -7 -7 -7 }}.
+Named by [[Xenllium]] in 2023, nonant tempers out the [[septimal ennealimma]] ({{monzo| -11 -9 0 9 }}) and may be described as the {{nowrap| 36 & 171 }} temperament. It has a period of 1/9 octave, and its [[ploidacot]] is enneaploid monocot.
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: 32805/32768, 516560652/514714375
+[[Comma list]]: 32805/32768, 40353607/40310784
-{{Mapping|legend=1| 7 0 105 -56 | 0 1 -8 7 }}
+{{Mapping|legend=1| 9 0 135 11 | 0 1 -8 1 }}
-: mapping generators: ~8575/7776, ~3
+: mapping generators: ~2592/2401, ~3
-[[Optimal tuning]] ([[POTE]]): ~8575/7776 = 171.429{{c}}, ~3/2 = 701.702{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2592/2401 = 133.3442{{c}}, ~3/2 = 701.8000{{c}}
+: [[error map]]: {{val| +0.098 -0.057 -0.027 -0.141 }}
+* [[CWE]]: ~2592/2401 = 133.3333{{c}}, ~3/2 = 701.7384{{c}}
+: error map: {{val| 0.000 -0.217 -0.221 -0.421 }}
-{{Optimal ET sequence|legend=1| 77, 147, 224, 301, 525, 826, 1351 }}
+{{Optimal ET sequence|legend=1| 36, 99c, 135, 171, 2772bd, 2943bdd, …, 5166bccddd, 5337bccddd }}
-[[Badness]] (Smith): 0.111142
+[[Badness]] (Sintel): 1.77
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 3025/3024, 24057/24010, 32805/32768
+Comma list: 540/539, 32805/32768, 42875/42592
-Mapping: {{mapping| 7 0 105 -56 -120 | 0 1 -8 7 13 }}
+Mapping: {{mapping| 9 0 135 11 131 | 0 1 -8 1 -7 }}
-Optimal tuning (POTE): ~495/448 = 171.429{{c}}, ~3/2 = 701.719{{c}}
+Optimal tunings:
+* WE: ~242/225 = 133.3308{{c}}, ~3/2 = 701.8205{{c}}
+* CWE: ~242/225 = 133.3333{{c}}, ~3/2 = 701.8351{{c}}
-{{Optimal ET sequence|legend=0| 77, 147, 224, 301, 525 }}
+{{Optimal ET sequence|legend=0| 36, 135, 171 }}
-Badness (Smith): 0.044122
+Badness (Sintel): 4.20
 === 13-limit ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 729/728, 1716/1715, 2200/2197, 3025/3024
+Comma list: 540/539, 729/728, 4096/4095, 16807/16731
-Mapping: {{mapping| 7 0 105 -56 -120 37 | 0 1 -8 7 13 -1 }}
+Mapping: {{mapping| 9 0 135 11 131 -38 | 0 1 -8 1 -7 5 }}
-Optimal tuning (POTE): ~495/448 = 171.429{{c}}, ~3/2 = 701.724{{c}}
+Optimal tunings:
+* WE: ~242/225 = 133.3180{{c}}, ~3/2 = 701.6956{{c}}
+* CWE: ~242/225 = 133.3333{{c}}, ~3/2 = 701.7800{{c}}
-{{Optimal ET sequence|legend=0| 77, 147, 224, 525 }}
+{{Optimal ET sequence|legend=0| 36, 99cf, 135, 171 }}
-Badness (Smith): 0.024706
+Badness (Sintel): 3.15
-== Octant ==
+== Septiquarschis ==
-The octant temperament ({{nowrap| 224 & 472 }}) has a period of 1/8 octave. In this temperament, 12/11, 35/27, and 99/70 are mapped into 1\8, 3\8, and 4\8 respectively.
+Named by [[Xenllium]] in 2021, septiquarschis tempers out [[829440/823543]] (mynaslender comma) and [[67108864/66706983]] (septiness comma), and may be described as the {{nowrap| 89 & 94 }} temperament. It splits septimal minor seventh ([[7/4]]) into four generators. Note that in the data below, the generator is the [[octave complement]] so that seven of them minus five octaves make a [[3/2|perfect fifth]]; its [[ploidacot]] is thus epsilon-heptacot.
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: 32805/32768, 2259436291848/2251875390625
+[[Comma list]]: 32805/32768, 829440/823543
-{{Mapping|legend=1| 8 0 120 -117 | 0 1 -8 11 }}
+{{Mapping|legend=1| 1 -4 47 6 | 0 7 56 -4 }}
-: mapping generators: ~42875/39366, ~3
+: mapping generators: ~2, ~256/147
-[[Optimal tuning]] ([[POTE]]): ~42875/39366 = 150.000{{c}}, ~3/2 = 701.713{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.8855{{c}}, ~256/147 = 957.2944{{c}}
+: [[error map]]: {{val| -0.114 -0.436 -0.182 +1.310 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~256/147 = 957.3867{{c}}
+: error map: {{val| 0.000 -0.248 +0.032 +1.627 }}
-{{Optimal ET sequence|legend=1| 24, 224, 472, 696, 1168 }}
+{{Optimal ET sequence|legend=1| 89, 94, 183, 460d, 643d }}
-[[Badness]] (Smith): 0.157186
+[[Badness]] (Sintel): 4.73
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 9801/9800, 32805/32768, 46656/46585
+Comma list: 540/539, 15488/15435, 32805/32768
-Mapping: {{mapping| 8 0 120 -117 15 | 0 1 -8 11 1 }}
+Mapping: {{mapping| 1 -4 47 6 25 | 0 7 56 -4 -27 }}
-Optimal tuning (POTE): ~12/11 = 150.000{{c}}, ~3/2 = 701.713{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.9430{{c}}, ~256/147 = 957.3390{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~256/147 = 957.3849{{c}}
-{{Optimal ET sequence|legend=0| 24, 224, 472, 696, 1168 }}
+{{Optimal ET sequence|legend=0| 89, 94, 183, 460d }}
-Badness (Smith): 0.044778
+Badness (Sintel): 1.72
 === 13-limit ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 729/728, 1575/1573, 2200/2197, 6656/6655
+Comma list: 540/539, 729/728, 1573/1568, 4096/4095
-Mapping: {{mapping| 8 0 120 -117 15 93 | 0 1 -8 11 1 -5 }}
+Mapping: {{mapping| 1 -4 47 6 25 -33 | 0 7 56 -4 -27 46 }}
-Optimal tuning (POTE): ~12/11 = 150.000{{c}}, ~3/2 = 701.725{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.0058{{c}}, ~256/147 = 957.3946{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~256/147 = 957.3900{{c}}
-{{Optimal ET sequence|legend=0| 24, 224, 472, 696 }}
+{{Optimal ET sequence|legend=0| 89, 94, 183, 277, 460d }}
-Badness (Smith): 0.030425
+Badness (Sintel): 1.46
-== Nonant ==
+== Tridecafifths ==
-The ''nonant'' temperament ({{nowrap| 36 & 135 }}) has a period of 1/9 octave and tempers out the [[septimal ennealimma]], {{monzo| -11 -9 0 9 }}.
+Named by [[Eliora]] in 2023, tridecafifths may be described as the {{nowrap| 89 & 200 }} temperament. It divides the [[3/2|perfect fifth]] into thirteen quartertones, so its [[ploidacot]] is 13-cot. [[289edo]] gives a highly recommendable tuning.
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: 32805/32768, 40353607/40310784
+[[Comma list]]: 32805/32768, {{monzo| -14 -1 -9 13 }}
-{{Mapping|legend=1| 9 0 135 11 | 0 1 -8 1 }}
+{{Mapping|legend=1| 1 1 7 6 | 0 13 -104 -71 }}
-: mapping generators: ~2592/2401, ~3
+: mapping generators: ~2, ~1323/1280
-[[Optimal tuning]] ([[CTE]]): ~2592/2401 = 133.3333{{c}}, ~3/2 = 701.7232{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.1431{{c}}, ~1323/1280 = 53.9838{{c}}
+: [[error map]]: {{val| +0.143 -0.023 +0.375 -0.816 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~1323/1280 = 53.9764{{c}}
+: error map: {{val| 0.000 -0.261 -0.221 -0.421 }}
-{{Optimal ET sequence|legend=1| 36, 99c, 135, 171 }}
+{{Optimal ET sequence|legend=1| 89, 200, 289 }}
-[[Badness]] (Smith): 0.069896
+[[Badness]] (Sintel): 10.9
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 540/539, 32805/32768, 42875/42592
+Comma list: 441/440, 32805/32768, 55296000/55240493
+Mapping: {{mapping| 1 1 7 6 4 | 0 13 -104 -71 -12 }}
+Optimal tunings:
+* WE: ~2 = 1200.0311{{c}}, ~33/32 = 53.9766{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~33/32 = 53.9750{{c}}
+{{Optimal ET sequence|legend=0| 89, 200, 289 }}
+Badness (Sintel): 4.23
+== Subgroup extensions ==
+=== Maqamschismic (2.3.5.11) ===
+Proposed by [[Eufalesio]] in 2026, maqamschismic is equivalent to the no-7 [[cassandra]]. The 2.3.5.11.13 subgroup adds [[352/351]] to the comma list and tempers 11/9~39/32 together (and 16/13~27/22), providing a very simple framework for tuning [[maqam]]at (especially the Turkish version), as outlined by [[Ozan Yarman]]. 41edo and 53edo are simplest, but 94edo is more optimized. It is only slightly worse than the no-7 [[helenus]].
+Subgroup: 2.3.5.11
+Comma list: 2200/2187, 4125/4096
-Mapping: {{mapping| 9 0 135 11 131 | 0 1 -8 1 -7 }}
+Subgroup-val mapping: {{mapping| 1 0 15 -33 | 0 1 -8 23 }}
-Optimal tuning (CTE): ~242/225 = 133.3333{{c}}, ~3/2 = 701.8398{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.5458{{c}} ~3/2 = 702.4021{{c}}
+* CWE: 2 = 1200.0000{{c}}, ~3/2 = 702.0906{{c}}
-{{Optimal ET sequence|legend=0| 36, 99c, 135, 171, 477ce, 648cee }}
+{{Optimal ET sequence|legend=0| 12e, …, 41, 53, 94, 147e, 241ce, 335ce }}
-Badness (Smith): 0.126910
+Badness (Sintel): 1.34
-=== 13-limit ===
+==== 2.3.5.11.13 subgroup ====
-Subgroup: 2.3.5.7.11.13
+Subgroup: 2.3.5.11.13
-Comma list: 540/539, 729/728, 4096/4095, 16807/16731
+Comma list: 325/324, 352/351, 4125/4096
-Mapping: {{mapping| 9 0 135 11 131 -38 | 0 1 -8 1 -7 5 }}
+Subgroup-val mapping: {{mapping| 1 0 15 -33 -28 | 0 1 -8 23 20 }}
-Optimal tuning (CTE): ~242/225 = 133.3333{{c}}, ~3/2 = 701.7998{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.4565{{c}} ~3/2 = 702.3057{{c}}
+* CWE: 2 = 1200.0000{{c}}, ~3/2 = 702.0485{{c}}
-{{Optimal ET sequence|legend=0| 36, 99cf, 135, 171 }}
+{{Optimal ET sequence|legend=0| 12e, …, 41, 53, 94, 147e }}
-Badness (Smith): 0.076195
+Badness (Sintel): 0.862
-== Tridecafifths ==
+=== Tridecaschismic (2.3.5.13) ===
-Tridecafifths divides the perfect 3/2 into 13 quartertones.
+Proposed by [[Eufalesio]] in 2026, tridecaschismic adds the [[325/324|marveltwin comma]] to the comma list, or equivalently, the [[tridecapyth comma]]. It benefits from a fifth that is just, or practically indistinguishable from just, like in 53edo. It is one of the lowest badness schismic extensions. It is also equivalent to the 2.3.5.13 [[restriction]] of 13-limit [[cassandra]].
-[[Subgroup]]: 2.3.5.7
+Subgroup: 2.3.5.13
-[[Comma list]]: 32805/32768, {{monzo| -14 -1 -9 13 }}
+Comma list: 325/324, 32805/32768
-{{Mapping|legend=1| 1 1 7 6 | 0 13 -104 -71 }}
+Subgroup-val mapping: {{mapping| 1 0 15 -28 | 0 1 -8 20 }}
-: mapping generators: ~2, ~1323/1280
-[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~1323/1280 = 53.9741{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.3326{{c}} ~3/2 = 702.1092{{c}}
+* CWE: 2 = 1200.0000{{c}}, ~3/2 = 701.9189{{c}}
-{{Optimal ET sequence|legend=1| 89, 200, 289 }}
+{{Optimal ET sequence|legend=0| 12, …, 41, 53, 412cf, 465cf, …, 783ccff, 836ccfff }}
-[[Badness]] (Smith): 0.432580
+Badness (Sintel): 0.582
-=== 11-limit ===
+==== 2.3.5.13.19 subgroup ====
-Subgroup: 2.3.5.7.11
+Subgroup: 2.3.5.13.19
-Comma list: 441/440, 32805/32768, 55296000/55240493
+Comma list: 325/324, 361/360, 513/512
-Mapping: {{mapping| 1 1 7 6 4 | 0 13 -104 -71 -12 }}
+Subgroup-val mapping: {{mapping| 1 0 15 -28 9 | 0 1 -8 20 -3 }}
-Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~33/32 = 53.9744{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.4236{{c}}, ~3/2 = 702.1510{{c}}
+* CWE: 2 = 1200.0000{{c}}, ~3/2 = 701.9064{{c}}
-{{Optimal ET sequence|legend=0| 89, 200, 289 }}
+{{Optimal ET sequence|legend=0| 12, …, 41, 53 }}
-Badness (Smith): 0.127820
+Badness (Sintel): 0.354
-== Subgroup extensions ==
 === Photia (2.3.5.17) ===
 {{See also| No-elevens subgroup temperaments #Garibaldia }}
@@ Line 2,365: / Line 2,857: @@
 : mapping generators: ~2, ~3
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~3/2 = 701.491{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.5471{{c}}, ~3/2 = 701.2262{{c}}
+: [[error map]]: {{val| -0.453 -1.182 +0.706 +3.628 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.4976{{c}}
+: error map: {{val| 0.000 -0.457 +1.705 +5.528 }}
-{{Optimal ET sequence|legend=1| 12, 41, 53, 65 }}
+{{Optimal ET sequence|legend=1| 12, 41, 53, 65, 207g, 272gg }}
-[[Tp tuning #T2 tuning|RMS error]]: 0.4842 cents
+[[Badness]] (Sintel): 0.479
 ==== 2.3.5.17.19 subgroup ====
@@ Line 2,380: / Line 2,876: @@
 Gencom mapping: {{mapping| 1 0 15 0 0 0 -7 9 | 0 1 -8 0 0 0 7 -3 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 701.470{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.7225{{c}}, ~3/2 = 701.3077{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.4754{{c}}
-{{Optimal ET sequence|legend=0| 12, 41, 53, 65 }}
+{{Optimal ET sequence|legend=0| 12, 41, 53, 65, 142g }}
-RMS error: 0.5374 cents
+Badness (Sintel): 0.332
 === Nestoria (2.3.5.19) ===
 : ''See also: [[No-elevens subgroup temperaments #Garibaldia]] and [[No-elevens subgroup temperaments #Pontia|#Pontia]]''
-The [[S-expression]]-based comma list of this temperament is {[[1216/1215|S16/S18]], [[361/360|S19]] (, ''[[513/512|S15/S20]]'')}. Strangely, despite prime 19 being optimized by a flatter fifth, the fifth in optimal tunings of nestoria is actually sharper than the fifth in optimal schismic. This is likely due to its optimization considering intervals like 19/10 and 19/15.
+Nestoria is notable for having one of the lowest-badness subgroup extensions of schismic. Note that despite prime [[19/1|19]] being optimized by a flatter fifth, the fifth in optimal tunings of nestoria is generally not flatter than the fifth in optimal schismic due to its optimization considering intervals like [[19/10]] and [[19/15]].
 [[Subgroup]]: 2.3.5.19
@@ Line 2,400: / Line 2,898: @@
 : mapping generators: ~2, ~3
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~3/2 = 701.746{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.2250{{c}}, ~3/2 = 701.8776{{c}}
+: [[error map]]: {{val| +0.225 +0.148 +0.240 -1.796 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7307{{c}}
+: error map: {{val| 0.000 -0.224 -0.159 -2.705 }}
-{{Optimal ET sequence|legend=1| 12, 29, 41, 53, 118, 171 }}
+{{Optimal ET sequence|legend=1| 12, 29, 41, 53, 118, 171, 460hh, 631hh }}
-[[Tp tuning #T2 tuning|RMS error]]: 0.1763 cents
+[[Badness]] (Sintel): 0.126
 === Taylor (2.3.5.13) ===
@@ Line 2,418: / Line 2,920: @@
 : mapping generators: ~2, ~26/15
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~26/15 = 950.855{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.1497{{c}}, ~26/15 = 950.9740{{c}}
+: [[error map]]: {{val| +0.150 -0.007 +0.348 -1.094 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~26/15 = 950.8493{{c}}
+: error map: {{val| 0.000 -0.256 +0.098 -1.568 }}
-{{Optimal ET sequence|legend=1| 24, 53, 130, 183, 236 }}
+{{Optimal ET sequence|legend=1| 24, 53, 130, 183, 236, 525f, 761ff }}
-[[Tp tuning #T2 tuning|RMS error]]: 0.1485 cents
+[[Badness]] (Sintel): 0.334
 ==== Dakota (2.3.5.13.19) ====
@@ Line 2,431: / Line 2,937: @@
 Subgroup-val mapping: {{mapping| 1 0 15 14 9 | 0 2 -16 -13 -6 }}
-Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~26/15 = 950.8199{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.2611{{c}}, ~26/15 = 951.0703{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 950.8532{{c}}
 {{Optimal ET sequence|legend=0| 24, 29, 53, 130, 183, 236h, 289h }}
-Badness (Smith): 0.00575
+Badness (Sintel): 0.262
 ===== 2.3.5.13.19.37 subgroup =====
@@ Line 2,444: / Line 2,952: @@
 Subgroup-val mapping: {{mapping| 1 0 15 14 9 6 | 0 2 -16 -13 -6 -1 }}
-Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~26/15 = 950.8187{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.2987{{c}}, ~26/15 = 951.1060{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 950.8595{{c}}
 {{Optimal ET sequence|legend=0| 24, 29, 53, 183, 236h, 289hl, 631fhhll }}
-Badness (Smith): 0.00357
+Badness (Sintel): 0.223
 === Quintilischis (2.3.5.17) ===
@@ Line 2,462: / Line 2,972: @@
 : mapping generators: ~2, ~18/17
-[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~18/17 = 99.649{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.1370{{c}}, ~18/17 = 99.6602{{c}}
+: [[error map]]: {{val| +0.137 +0.018 -0.042 -0.533 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~18/17 = 99.6499{{c}}
+: error map: {{val| 0.000 -0.205 -0.317 -1.104 }}
-{{Optimal ET sequence|legend=1| 12, 253, 265, 277, 289 }}
+{{Optimal ET sequence|legend=1| 12, …, 253, 265, 277, 289, 566g, 855g }}
-[[Tp tuning #T2 tuning|RMS error]]: 0.0719 cents
+[[Badness]] (Sintel): 1.34
 ==== 2.3.5.17.19 subgroup ====
@@ Line 2,477: / Line 2,991: @@
 Gencom mapping: {{mapping| 1 2 -1 0 0 0 5 4 | 0 -5 40 0 0 0 -11 3 }}
-Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~18/17 = 99.652{{c}}
+Optimal tunings:
+* WE: ~2 = 1200.0350{{c}}, ~18/17 = 99.6550{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~18/17 = 99.6520{{c}}
-{{Optimal ET sequence|legend=0| 12, 253, 265, 277, 289 }}
+{{Optimal ET sequence|legend=0| 12, …, 253, 265, 277, 289 }}
-RMS error: 0.1636 cents
+Badness (Sintel): 1.17
 [[Category:Temperament families]]
 [[Category:Schismatic family| ]] <!-- main article -->
 [[Category:Rank 2]]

Schismatic family: Difference between revisions