@@ Line 1: / Line 1: @@
 {{Technical data page}}
-The 5-limit parent comma for the '''diaschismic family''' is 2048/2025, the [[diaschisma]]. The period is half an octave, and the generator is a fifth. Three periods gives 1800 cents, and decreasing this by two fifths gives the major third. [[34edo]] is a good tuning choice, with [[46edo]], [[56edo]], [[58edo]], or [[80edo]] being other possibilities. Both [[12edo]] and [[22edo]] support it, and retuning them to a MOS of diaschismic gives two scale possibilities.
+The '''diaschismic family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the diaschisma, [[2048/2025]].
 == Diaschismic ==
 {{Main| Diaschismic }}
-This temperament is also known as '''srutal''' in the 5-limit, but that name more strictly speaking refers to the [[Diaschismic family#Srutal|34d&46 extension]] to the [[7-limit]] that adds [[4375/4374]] to the comma list.
+The [[period]] of diaschismic is half an [[2/1|octave]], and the [[generator]] is a fifth; the [[ploidacot]] is diploid monocot. Three periods gives 1800 cents, and decreasing this by two fifths gives the major third. [[34edo]] is a good tuning choice, with [[46edo]], [[56edo]], [[58edo]], or [[80edo]] being other possibilities. Both [[12edo]] and [[22edo]] support it, and retuning them to a [[mos]] of diaschismic gives two scale possibilities.
+This temperament is also known as '''srutal''' in the 5-limit, but that name more strictly speaking refers to the [[#Srutal|34d & 46 extension]] to the [[7-limit]] that adds [[4375/4374]] to the comma list.
 [[Subgroup]]: 2.3.5
@@ Line 12: / Line 14: @@
 {{Mapping|legend=1| 2 0 11 | 0 1 -2 }}
 : mapping generators: ~45/32, ~3
-[[Optimal tuning]] ([[POTE]]): ~45/32 = 1\2, ~3/2 = 704.898
+[[Optimal tuning]]s:
+* [[WE]]: ~45/32 = 599.4107{{c}}, ~3/2 = 704.2059{{c}}
+: [[error map]]: {{val| -1.179 +1.072 +1.150 }}
+* [[CWE]]: ~45/32 = 600.0000{{c}}, ~3/2 = 704.9585{{c}}
+: error map: {{val| 0.000 +3.003 +3.769 }}
 [[Tuning ranges]]:
-* 5-odd-limit [[diamond monotone]]: ~3/2 = [600.000 to 720.000] (1\2 to 6\10)
+* [[5-odd-limit]] [[diamond monotone]]: ~3/2 = [600.000 to 720.000] (1\2 to 6\10)
 * 5-odd-limit [[diamond tradeoff]]: ~3/2 = [701.955, 706.843]
-* 5-odd-limit diamond monotone and tradeoff: ~3/2 = [701.955, 706.843]
 {{Optimal ET sequence|legend=1| 10, 12, 22, 34, 46, 80, 206c, 286bc }}
-[[Badness]]: 0.019915
+[[Badness]] (Sintel): 0.467
-=== Srutal archagall ===
+=== Overview to extensions ===
-{{See also | Fiventeen }}
+==== 7-limit extensions ====
+To get the 7-limit extensions, we add another comma:
-Since the diaschisma factors into ([[256/255]])<sup>2</sup>([[289/288]]) in the 17-limit, it extends naturally to the 2.3.5.17 subgroup, resulting in ''srutal archagall''. The [[S-expression]]-based comma list of this temperament is {[[256/255|S16]], [[289/288|S17]]}.
+* Septimal diaschismic adds [[126/125]], the starling comma, to obtain 7-limit harmony by more complex methods than pajara, but with greater accuracy.
+* Pajara adds [[50/49]] or [[64/63]] and is a popular and well-known choice.
+* Srutal adds [[4375/4374]], the ragisma, which is about as accurate as septimal diaschismic but has a much more complex mapping of 7.
+* Keen adds [[875/864]].
-Subgroup: 2.3.5.17
+Those all keep the same half-octave period and fifth generator.
-Comma list: 136/135, 256/255
+Bidia adds [[3136/3125]], the hemimean comma, with a 1/4-octave period. Shrutar adds [[245/243]] and shru adds [[392/375]], with a quartertone generator. Sruti adds [[19683/19600]] and anguirus adds [[49/48]], with a neutral third or hemitwelfth generator. Those split the original generator in two. Echidna adds [[1728/1715]], the orwellisma, with a ~9/7 generator. Echidnic adds [[686/675]], the senga, with a ~8/7 generator. Those split the original generator in three. Finally, quadrasruta adds [[2401/2400]] and splits the original  generator in four.
-Sval mapping: {{mapping| 2 0 11 5 | 0 1 -2 1 }}
+==== Subgroup extensions ====
+Since the diaschisma factors into ([[256/255]])<sup>2</sup>([[289/288]]) in the 17-limit, it extends naturally to the 2.3.5.17 subgroup as ''srutal archagall'', considered in [[#Subgroup extensions]]. The [[S-expression]]-based comma list of this temperament is {[[256/255|S16]], [[289/288|S17]]}.
-: mapping generators: ~17/12, ~3
+== Septimal diaschismic ==
+{{Main| Diaschismic }}
+{{See also| Srutal vs diaschismic }}
-Optimal tuning (CTE): ~17/12 = 1\2, ~3/2 = 705.1272
+A simpler characterization than the one given by the normal comma list is that septimal diaschismic adds [[126/125]] or [[5120/5103]] to the set of commas, and it can also be called {{nowrap| 46 & 58 }}. However described, septimal diaschismic has a 1/2-octave period and a sharp fifth generator like the 5-limit version, but not so sharp, giving a more accurate but more complex temperament. [[104edo]] with the 104c [[val]] provides an excellent tuning, which is close to tuning [[7/4]] just by making the fifth 703.897 cents.
-Optimal ET sequence: {{Optimal ET sequence| 10, 12, 22, 34, 80, 114, 194bc }}
+Diaschismic extends naturally to the 17-limit, for which the same tunings may be used, making it one of the most important of the higher-limit rank-2 temperaments. Adding the 11-limit adds the commas 176/175, 896/891 and 441/440. The 13-limit yields 196/195, 351/350, and 364/363; the 17-limit adds 136/135, 221/220, and 442/441. This mapping can also be rationalized by [[parapyth]], which makes sense due to the sharp fifth, and prime 17 is found as in srutal archagall. If you want to explore higher-limit harmonies, diaschismic is certainly one excellent way to do it; [[mos]] scales of 34 notes and even more the 46-note mos will encompass very great deal of it. Of course 46 or 58 equal provide alternatives which in many ways are similar, particularly in the case of 58.
-Badness: 0.00575
-=== Overview to extensions ===
-To get the 7-limit extensions, we add another comma:
-* Pajara derives from [[64/63]] and is a popular and well-known choice.
-* Diaschismic adds [[126/125]], the starling comma, to obtain 7-limit harmony by more complex methods, but with greater accuracy.
-* Srutal adds [[4375/4374]], the ragisma. It does no significant tuning damage, so we keep the 5-limit label srutal.
-* Keen adds [[875/864]].
-* Bidia adds [[3136/3125]], the hemimean comma.
-* Echidna adds [[1728/1715]], the orwellisma.
-* Shrutar adds [[245/243]], the sensamagic comma.
-Pajara, diaschismic, srutal and keen keep the same half-octave period and fifth generator, but shrutar has a generator of a quarter-tone (which can be taken as [[36/35]], the septimal quarter-tone) and echidna has a generator of 9/7. Bidia has a quarter-octave period and a fifth generator.
-== Srutal ==
-{{See also| Srutal vs diaschismic }}
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: 2048/2025, 4375/4374
+[[Comma list]]: 126/125, 2048/2025
-{{Mapping|legend=1| 2 0 11 -42 | 0 1 -2 15 }}
+{{Mapping|legend=1| 2 0 11 31 | 0 1 -2 -8 }}
-{{Multival|legend=1| 2 -4 30 -11 42 81 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~45/32 = 599.4449{{c}}, ~3/2 = 703.0299{{c}}
-[[Optimal tuning]] ([[POTE]]): ~45/32 = 1\2, ~3/2 = 704.814
+: [[error map]]: {{val| -1.110 -0.035 +3.740 -1.391 }}
+* [[CWE]]: ~45/32 = 600.0000{{c}}, ~3/2 = 703.7739{{c}}
+: error map: {{val| 0.000 +1.819 +6.138 +0.983 }}
 [[Tuning ranges]]:
-* 7- and 9-odd-limit [[diamond monotone]]: ~3/2 = [703.448, 705.882] (34\58 to 20\34)
+* 7- and 9-odd-limit [[diamond monotone]]: ~3/2 = [700.000, 705.882] (7\12 to 20\34)
 * 7- and 9-odd-limit [[diamond tradeoff]]: ~3/2 = [701.955, 706.843]
-* 7- and 9-odd-limit diamond monotone and tradeoff: ~3/2 = [703.448, 705.882]
-{{Optimal ET sequence|legend=1| 34d, 46, 80, 126, 206cd, 332bcd }}
+{{Optimal ET sequence|legend=1| 12, 34, 46, 58, 104c, 162c }}
-[[Badness]]: 0.091504
+[[Badness]] (Sintel): 0.959
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 176/175, 896/891, 1331/1323
+Comma list: 126/125, 176/175, 896/891
-Mapping: {{mapping| 2 0 11 -42 -28 | 0 1 -2 15 11 }}
+Mapping: {{mapping| 2 0 11 31 45 | 0 1 -2 -8 -12 }}
-Optimal tuning (POTE): ~45/32 = 1\2, ~3/2 = 704.856
+Optimal tunings:
+* WE: ~45/32 = 599.4471{{c}}, ~3/2 = 703.0657{{c}}
+* CWE: ~45/32 = 600.0000{{c}}, ~3/2 = 703.7996{{c}}
 Tuning ranges:
-* 11-odd-limit diamond monotone: ~3/2 = [704.348, 705.882] (27\46 to 20\34)
+* 11-odd-limit diamond monotone: ~3/2 = [700.000, 704.348] (7\12 to 27\46)
 * 11-odd-limit diamond tradeoff: ~3/2 = [701.955, 706.843]
-* 11-odd-limit diamond monotone and tradeoff: ~3/2 = [704.348, 705.882]
-{{Optimal ET sequence|legend=1| 34d, 46, 80, 126, 206cd }}
+{{Optimal ET sequence|legend=0| 12, 34e, 46, 58, 104c, 162ce }}
-Badness: 0.035315
+Badness (Sintel): 0.828
 === 13-limit ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 169/168, 176/175, 325/324, 364/363
+Comma list: 126/125, 176/175, 196/195, 364/363
-Mapping: {{mapping| 2 0 11 -42 -28 -18 | 0 1 -2 15 11 8 }}
+Mapping: {{mapping| 2 0 11 31 45 55 | 0 1 -2 -8 -12 -15 }}
-Optimal tuning (POTE): ~45/32 = 1\2, ~3/2 = 704.881
+Optimal tunings:
+* WE: ~45/32 = 599.4451{{c}}, ~3/2 = 703.0528{{c}}
+* CWE: ~45/32 = 600.0000{{c}}, ~3/2 = 703.7813{{c}}
 Tuning ranges:
-* 13- and 15-odd-limit diamond monotone: ~3/2 = [704.348, 705.882] (27\46 to 20\34)
+* 13- and 15-odd-limit diamond monotone: ~3/2 = [703.448, 704.348] (34\58 to 27\46)
 * 13-odd-limit diamond tradeoff: ~3/2 = [701.955, 706.843]
 * 15-odd-limit diamond tradeoff: ~3/2 = [701.955, 711.731]
-* 13- and 15-odd-limit diamond monotone and tradeoff: ~3/2 = [704.348, 705.882]
-{{Optimal ET sequence|legend=1| 34d, 46, 80, 206cd, 286bcde }}
+{{Optimal ET sequence|legend=0| 12f, 34ef, 46, 58, 104c, 162cef }}
-Badness: 0.025286
+Badness (Sintel): 0.782
 === 17-limit ===
 Subgroup: 2.3.5.7.11.13.17
-Comma list: 136/135, 169/168, 176/175, 221/220, 256/255
+Comma list: 126/125, 136/135, 176/175, 196/195, 256/255
-Mapping: {{mapping| 2 0 11 -42 -28 -18 5 | 0 1 -2 15 11 8 1 }}
+Mapping: {{mapping| 2 0 11 31 45 55 5 | 0 1 -2 -8 -12 -15 1 }}
-Optimal tuning (POTE): ~17/12 = 1\2, ~3/2 = 704.840
+Optimal tunings:
+* WE: ~17/12 = 599.6253{{c}}, ~3/2 = 703.3726{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~3/2 = 703.8520{{c}}
 Tuning ranges:
-* 17-odd-limit diamond monotone: ~3/2 = [704.348, 705.882] (27\46 to 20\34)
+* 17-odd-limit diamond monotone: ~3/2 = [703.448, 704.348] (34\58 to 27\46)
 * 17-odd-limit diamond tradeoff: ~3/2 = [698.955, 711.731]
-* 17-odd-limit diamond monotone and tradeoff: ~3/2 = [704.348, 705.882]
-{{Optimal ET sequence|legend=1| 34d, 46, 80, 126, 206cd }}
+{{Optimal ET sequence|legend=0| 12f, 34ef, 46, 58, 104c }}
-Badness: 0.018594
+Badness (Sintel): 0.837
-=== 19-limit ===
+=== 2.3.5.7.11.13.17.23 subgroup (Na"Naa') ===
-Srutal, shrutar and bidia have similar 19-limit properties, tempering 190/189, related rank-3 [[julius]].
+<b>Na"Naa'</b> is a remarkable subgroup temperament of {{nowrap| 46 & 58 }} with a prime harmonic of 23. It is yet to be found why it got this strange name.
-Subgroup: 2.3.5.7.11.13.17.19
+Subgroup: 2.3.5.7.11.13.17.23
-Comma list: 136/135, 169/168, 176/175, 190/189, 221/220, 256/255
+Comma list: 126/125, 136/135, 176/175, 196/195, 231/230, 256/255
-Mapping: {{mapping| 2 0 11 -42 -28 -18 5 -55 | 0 1 -2 15 11 8 1 20 }}
-Optimal tuning (POTE): ~17/12 = 1\2, ~3/2 = 704.905
-{{Optimal ET sequence|legend=1| 34dh, 46, 80, 206cd }}
-Badness: 0.017063
-==== Srutaloo ====
-Srutaloo adds 576/575, 736/729 or 208/207, rhymes with [[Skidoo]].
-Subgroup: 2.3.5.7.11.13.17.19.23
-Comma list: 136/135, 169/168, 176/175, 190/189, 208/207, 221/220, 256/255
-Mapping: {{mapping| 2 0 11 -42 -28 -18 5 -55 -10 | 0 1 -2 15 11 8 1 20 6 }}
-Optimal tuning (POTE): ~17/12 = 1\2, ~3/2 = 704.899
-{{Optimal ET sequence|legend=1| 34dh, 46, 80, 206cd }}
-Badness: 0.013555
-===== 29-limit =====
-Subgroup: 2.3.5.7.11.13.17.19.23.29
-Comma list: 136/135, 169/168, 176/175, 190/189, 208/207, 221/220, 232/231, 256/255
-Mapping: {{mapping| 2 0 11 -42 -28 -18 5 -55 -10 -76 | 0 1 -2 15 11 8 1 20 6 27 }}
-Optimal tuning (POTE): ~17/12 = 1\2, ~3/2 = 704.906
-{{Optimal ET sequence|legend=1| 34dhj, 46, 80, 206cd }}
-Badness: 0.013203
+Subgroup-val mapping: {{mapping| 2 0 11 31 45 55 5 63 | 0 1 -2 -8 -12 -15 1 -17 }}
-===== 31-limit =====
+Optimal tunings:
+* WE: ~17/12 = 599.6272{{c}}, ~3/2 = 703.4326{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~3/2 = 703.9093{{c}}
-Subgroup: 2.3.5.7.11.13.17.19.23.29.31
+{{Optimal ET sequence|legend=0| 12i, 34efi, 46, 58i, 104ci }}
-Comma list: 136/135, 169/168, 176/175, 190/189, 208/207, 217/216, 221/220, 232/231, 256/255
+Badness (Sintel): 0.882
-Mapping: {{mapping| 2 0 11 -42 -28 -18 5 -55 -10 -76 48 | 0 1 -2 15 11 8 1 20 6 27 -12 }}
-Optimal tuning (POTE): ~17/12 = 1\2, ~3/2 = 704.817
-{{Optimal ET sequence|legend=1| 46, 80, 126 }}
-Badness: 0.015073
 == Pajara ==
 {{Main| Pajara }}
-Pajara is closely associated with 22edo (not to mention [[Paul Erlich]]) but other tunings are possible. The 1/2-octave period serves as both a [[10/7]] and a [[7/5]]. Aside from 22edo, 34 with the val {{val| 34 54 79 96 }} and 56 with the val {{val| 56 89 130 158 }} are are interesting alternatives, with more accpetable fifths, and a tetrad which is more clearly a dominant seventh. As such, they are closer to the tuning of 12edo and of common practice Western music in general, while retaining the distictiveness of a sharp fifth.
+Pajara is closely associated with 22edo (not to mention [[Paul Erlich]]) but other tunings are possible. The 1/2-octave period serves as both a [[10/7]] and a [[7/5]]. Aside from 22edo, 34 with the val {{val| 34 54 79 96 }} (34d) and 56 with the val {{val| 56 89 130 158 }} (56d) are interesting alternatives, with more acceptable fifths, and a tetrad which is more clearly a dominant seventh. As such, they are closer to the tuning of 12edo and of common practice Western music in general, while retaining the distictiveness of a sharp fifth.
-Pajara extends nicely to an 11-limit version, for which the 56 tuning can be used, but a good alternative is to make the major thirds pure by setting the fifth to be 706.843 cents. Now 99/98, 100/99, 176/175 and 896/891 are being tempered out.
+Pajara extends nicely to an 11-limit version, for which the 56edo tuning can be used, but a good alternative is to make the major thirds pure by setting the fifth to be 706.843 cents. Now 99/98, 100/99, 176/175 and 896/891 are being tempered out.
 [[Subgroup]]: 2.3.5.7
@@ Line 205: / Line 161: @@
 {{Mapping|legend=1| 2 0 11 12 | 0 1 -2 -2 }}
-{{Multival|legend=1| 2 -4 -4 -11 -12 2 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~7/5 = 598.8483{{c}}, ~3/2 = 705.6906{{c}}
-[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~3/2 = 707.048
+: [[error map]]: {{val| -2.303 +1.432 -5.756 +10.580 }}
+* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 707.3438{{c}}
+: error map: {{val| 0.000 +5.389 -1.001 +16.487 }}
 [[Tuning ranges]]:
 * 7- and 9-odd-limit [[diamond monotone]]: ~3/2 = [700.000, 720.000] (7\12 to 6\10)
 * 7- and 9-odd-limit [[diamond tradeoff]]: ~3/2 = [701.955, 715.587]
-* 7- and 9-odd-limit diamond monotone and tradeoff: ~3/2 = [701.955, 715.587]
 {{Optimal ET sequence|legend=1| 10, 12, 22, 34d, 56d }}
-[[Badness]]: 0.020033
+[[Badness]] (Sintel): 0.507
+=== 2.3.5.7.17 subgroup ===
+Subgroup: 2.3.5.7.17
+Comma list: 50/49, 64/63, 85/84
+Mapping: {{mapping| 2 0 11 12 5 | 0 1 -2 -2 1 }}
+Optimal tunings:
+* WE: ~7/5 = 599.053{{c}}, ~3/2 = 706.355{{c}}
+* CWE: ~7/5 = 600.000{{c}}, ~3/2 = 707.607{{c}}
+{{Optimal ET sequence|legend=0| 10, 12, 22, 56d }}
+Badness (Sintel): 0.438
 === 11-limit ===
@@ Line 225: / Line 197: @@
 Mapping: {{mapping| 2 0 11 12 26 | 0 1 -2 -2 -6 }}
-{{Multival|legend=1| 2 -4 -4 -12 -11 -12 -26 2 -14 -20 }}
+Optimal tunings:
+* WE: ~7/5 = 598.8485{{c}}, ~3/2 = 705.5285{{c}}
-Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 706.885
+* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 707.1826{{c}}
 Tuning ranges:
 * 11-odd-limit diamond monotone: ~3/2 = [700.000, 709.091] (7\12 to 13\22)
 * 11-odd-limit diamond tradeoff: ~3/2 = [701.955, 715.587]
-* 11-odd-limit diamond monotone and tradeoff: ~3/2 = [701.955, 709.091]
-{{Optimal ET sequence|legend=1| 10e, 12, 22, 34d, 56d }}
+{{Optimal ET sequence|legend=0| 10e, 12, 22, 34d, 56d }}
-Badness: 0.020343
+Badness (Sintel): 0.673
+==== 2.3.5.7.11.17 subgroup ====
+Subgroup: 2.3.5.7.11.17
+Comma list: 50/49, 64/63, 85/84, 99/98
+Mapping: {{mapping| 2 0 11 12 26 5 | 0 1 -2 -2 -6 1 }}
+Optimal tunings:
+* WE: ~7/5 = 599.062{{c}}, ~3/2 = 706.095{{c}}
+* CWE: ~7/5 = 600.000{{c}}, ~3/2 = 707.370{{c}}
+{{Optimal ET sequence|legend=0| 10e, 12, 22, 34d, 56d }}
+Badness (Sintel): 0.645
 ==== 13-limit ====
@@ Line 245: / Line 231: @@
 Mapping: {{mapping| 2 0 11 12 26 1 | 0 1 -2 -2 -6 2 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 708.919
+Optimal tunings:
+* WE: ~7/5 = 599.9732{{c}}, ~3/2 = 708.8873{{c}}
+* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 708.9227{{c}}
-{{Optimal ET sequence|legend=1| 10e, 12, 22 }}
+{{Optimal ET sequence|legend=0| 10e, 12, 22 }}
-Badness: 0.027642
+Badness (Sintel): 1.14
 ===== 17-limit =====
@@ Line 258: / Line 246: @@
 Mapping: {{mapping| 2 0 11 12 26 1 5 | 0 1 -2 -2 -6 2 1 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 708.806
+Optimal tunings:
+* WE: ~7/5 = 599.8871{{c}}, ~3/2 = 708.6725{{c}}
+* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 708.8176{{c}}
-{{Optimal ET sequence|legend=1| 10e, 12, 22 }}
+{{Optimal ET sequence|legend=0| 10e, 12, 22 }}
-Badness: 0.020899
+Badness (Sintel): 1.06
 ==== Pajarina ====
@@ Line 271: / Line 261: @@
 Mapping: {{mapping| 2 0 11 12 26 36 | 0 1 -2 -2 -6 -9 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 706.133
+Optimal tunings:
+* WE: ~7/5 = 598.7732{{c}}, ~3/2 = 704.6889{{c}}
+* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 706.3950{{c}}
-{{Optimal ET sequence|legend=1| 12f, 22, 34d }}
+{{Optimal ET sequence|legend=0| 12f, 22, 34d }}
-Badness: 0.022327
+Badness (Sintel): 0.923
 ===== 17-limit =====
@@ Line 284: / Line 276: @@
 Mapping: {{mapping| 2 0 11 12 26 36 5 | 0 1 -2 -2 -6 -9 1 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 706.410
+Optimal tunings:
+* WE: ~7/5 = 599.0204{{c}}, ~3/2 = 705.2572{{c}}
+* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 706.5660{{c}}
-{{Optimal ET sequence|legend=1| 12f, 22, 34d }}
+{{Optimal ET sequence|legend=0| 12f, 22, 34d }}
-Badness: 0.018375
+Badness (Sintel): 0.936
 ==== Pajarita ====
@@ Line 297: / Line 291: @@
 Mapping: {{mapping| 2 0 11 12 26 17 | 0 1 -2 -2 -6 -3 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 707.450
+Optimal tunings:
+* WE: ~7/5 = 598.3048{{c}}, ~3/2 = 705.4512{{c}}
+* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 707.9238{{c}}
-{{Optimal ET sequence|legend=1| 10e, 12f, 22f }}
+{{Optimal ET sequence|legend=0| 10e, 12f, 22f, 34dff }}
-Badness: 0.022677
+Badness (Sintel): 0.937
 ===== 17-limit =====
@@ Line 310: / Line 306: @@
 Mapping: {{mapping| 2 0 11 12 26 17 5 | 0 1 -2 -2 -6 -3 1 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 707.947
+Optimal tunings:
+* WE: ~7/5 = 598.6103{{c}}, ~3/2 = 706.3076{{c}}
+* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 708.2256{{c}}
-{{Optimal ET sequence|legend=1| 10e, 12f, 22f }}
+{{Optimal ET sequence|legend=0| 10e, 12f, 22f }}
-Badness: 0.019007
+Badness (Sintel): 0.968
 === Pajarous ===
@@ Line 323: / Line 321: @@
 Mapping: {{mapping| 2 0 11 12 -9 | 0 1 -2 -2 5 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 709.578
+Optimal tunings:
+* WE: ~7/5 = 599.4055{{c}}, ~3/2 = 708.8747{{c}}
+* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 709.5508{{c}}
 Tuning ranges:
 * 11-odd-limit diamond monotone: ~3/2 = 709.091 (13\22)
 * 11-odd-limit diamond tradeoff: ~3/2 = [701.955, 715.803]
-* 11-odd-limit diamond monotone and tradeoff: ~3/2 = 709.091
-{{Optimal ET sequence|legend=1| 10, 12e, 22, 120bce, 142bce }}
+{{Optimal ET sequence|legend=0| 10, 12e, 22, 120bce, 142bce }}
+Badness (Sintel): 0.937
-Badness: 0.028349
+==== 2.3.5.7.11.17 subgroup ====
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 50/49, 52/51, 55/54, 64/63, 65/63
+Mapping: {{mapping| 2 0 11 12 -9 1 5 | 0 1 -2 -2 5 2 1 }}
+Optimal tunings:
+* WE: ~7/5 = 599.408{{c}}, ~3/2 = 708.878{{c}}
+* CWE: ~7/5 = 600.000{{c}}, ~3/2 = 709.544{{c}}
+{{Optimal ET sequence|legend=0| 10, 12e, 22 }}
+Badness (Sintel): 0.766
 ==== 13-limit ====
@@ Line 341: / Line 355: @@
 Mapping: {{mapping| 2 0 11 12 -9 1 | 0 1 -2 -2 5 2 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 710.240
+Optimal tunings:
+* WE: ~7/5 = 599.9064{{c}}, ~3/2 = 710.1289{{c}}
+* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 710.2325{{c}}
-{{Optimal ET sequence|legend=1| 10, 22, 54f, 76bdff }}
+{{Optimal ET sequence|legend=0| 10, 22 }}
-Badness: 0.025176
+Badness (Sintel): 1.04
 ===== 17-limit =====
@@ Line 354: / Line 370: @@
 Mapping: {{mapping| 2 0 11 12 -9 1 5 | 0 1 -2 -2 5 2 1 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 710.221
+Optimal tunings:
+* WE: ~7/5 = 599.8239{{c}}, ~3/2 = 710.0128{{c}}
+* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 710.2067{{c}}
-{{Optimal ET sequence|legend=1| 10, 22, 54f, 76bdff }}
+{{Optimal ET sequence|legend=0| 10, 22, 54f, 76bdff }}
-Badness: 0.018249
+Badness (Sintel): 0.930
 ==== Pajaro ====
@@ Line 367: / Line 385: @@
 Mapping: {{mapping| 2 0 11 12 -9 17 | 0 1 -2 -2 5 -3 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 710.818
+Optimal tunings:
+* WE: ~7/5 = 598.8257{{c}}, ~3/2 = 709.4266{{c}}
+* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 710.8414{{c}}
-{{Optimal ET sequence|legend=1| 10, 22f, 32f, 54ff }}
+{{Optimal ET sequence|legend=0| 10, 22f, 32f }}
-Badness: 0.027355
+Badness (Sintel): 1.13
 ===== 17-limit =====
@@ Line 380: / Line 400: @@
 Mapping: {{mapping| 2 0 11 12 -9 17 5 | 0 1 -2 -2 5 -3 1 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 710.866
+Optimal tunings:
+* WE: ~7/5 = 598.8865{{c}}, ~3/2 = 709.5472{{c}}
+* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 710.8704{{c}}
-{{Optimal ET sequence|legend=1| 10, 22f, 32f, 54ff }}
+{{Optimal ET sequence|legend=0| 10, 22f, 32f }}
-Badness: 0.019844
+Badness (Sintel): 1.01
 === Pajaric ===
@@ Line 393: / Line 415: @@
 Mapping: {{mapping| 2 0 11 12 7 | 0 1 -2 -2 0 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 705.524
+Optimal tunings:
+* WE: ~7/5 = 597.4807{{c}}, ~3/2 = 702.5616{{c}}
+* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 706.0542{{c}}
-{{Optimal ET sequence|legend=1| 10, 12, 22e, 34dee }}
+{{Optimal ET sequence|legend=0| 10, 12, 22e }}
-Badness: 0.023798
+Badness (Sintel): 0.787
 ==== 13-limit ====
@@ Line 406: / Line 430: @@
 Mapping: {{mapping| 2 0 11 12 7 17 | 0 1 -2 -2 0 -3 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 707.442
+Optimal tunings:
+* WE: ~7/5 = 597.1952{{c}}, ~3/2 = 704.1350{{c}}
+* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 708.1989{{c}}
-{{Optimal ET sequence|legend=1| 10, 12f, 22ef }}
+{{Optimal ET sequence|legend=0| 10, 12f, 22ef }}
-Badness: 0.020461
+Badness (Sintel): 0.845
 ==== 17-limit ====
@@ Line 419: / Line 445: @@
 Mapping: {{mapping| 2 0 11 12 7 17 5 | 0 1 -2 -2 0 -3 1 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 708.544
+Optimal tunings:
+* WE: ~7/5 = 597.6509{{c}}, ~3/2 = 705.7702{{c}}
+* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 708.9719{{c}}
-{{Optimal ET sequence|legend=1| 10, 12f, 22ef }}
+{{Optimal ET sequence|legend=0| 10, 12f, 22ef }}
-Badness: 0.017592
+Badness (Sintel): 0.896
 === Hemipaj ===
@@ Line 432: / Line 460: @@
 Mapping: {{mapping| 2 1 9 10 8 | 0 2 -4 -4 -1 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~11/8 = 546.383
+: mapping generators: ~2, ~16/11
-{{Optimal ET sequence|legend=1| 20, 22, 68d, 90d }}
+Optimal tunings:
+* WE: ~7/5 = 597.6509{{c}}, ~16/11 = 652.7788{{c}}
+* CWE: ~7/5 = 600.0000{{c}}, ~16/11 = 653.7119{{c}}
-Badness: 0.038890
+{{Optimal ET sequence|legend=0| 2, 20, 22 }}
+Badness (Sintel): 1.29
 === Hemifourths ===
@@ Line 444: / Line 476: @@
 Mapping: {{mapping| 2 0 11 12 -1 | 0 2 -4 -4 5 }}
+: mapping generators: ~2, ~55/32
-Optimal tuning (POTE): ~7/5 = 1\2, ~55/32 = 953.093
+Optimal tunings:
+* WE: ~7/5 = 597.6509{{c}}, ~55/32 = 950.8475{{c}}
+* CWE: ~7/5 = 600.0000{{c}}, ~55/32 = 953.1172{{c}}
-{{Optimal ET sequence|legend=1| 10, 24d, 34d }}
+{{Optimal ET sequence|legend=0| 10, 24d, 34d }}
-Badness: 0.048885
+Badness (Sintel): 1.62
 ==== 13-limit ====
@@ Line 458: / Line 493: @@
 Mapping: {{mapping| 2 0 11 12 -1 9 | 0 2 -4 -4 5 -1 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~26/15 = 953.074
+Optimal tunings:
+* WE: ~7/5 = 598.6748{{c}}, ~26/15 = 950.9691{{c}}
+* CWE: ~7/5 = 600.0000{{c}}, ~26/15 = 953.1052{{c}}
-{{Optimal ET sequence|legend=1| 10, 24d, 34d }}
+{{Optimal ET sequence|legend=0| 10, 24d, 34d }}
-Badness: 0.028755
+Badness (Sintel): 1.19
 ==== 17-limit ====
@@ Line 471: / Line 508: @@
 Mapping: {{mapping| 2 0 11 12 -1 9 5 | 0 2 -4 -4 5 -1 2 }}
-Optimal tuning (POTE): ~7/5 = 1\2, ~26/15 = 953.210
+Optimal tunings:
+* WE: ~7/5 = 598.8411{{c}}, ~26/15 = 951.3687{{c}}
+* CWE: ~7/5 = 600.0000{{c}}, ~26/15 = 953.2169{{c}}
-{{Optimal ET sequence|legend=1| 10, 24d, 34d }}
+{{Optimal ET sequence|legend=0| 10, 24d, 34d }}
-Badness: 0.021790
+Badness (Sintel): 1.11
-== Septimal diaschismic ==
+== Srutal ==
-{{Main| Diaschismic }}
 {{See also| Srutal vs diaschismic }}
-A simpler characterization than the one given by the normal comma list is that diaschismic adds [[126/125]] or [[5120/5103]] to the set of commas, and it can also be called 46 &amp; 58. However described, diaschismic has a 1/2-octave period and a sharp fifth generator like pajara, but not so sharp, giving a more accurate but more complex temperament. [[58edo]] provides an excellent tuning, but an alternative is to make [[7/4]] just by making the fifth 703.897 cents, as opposed to 703.448 cents for 58edo.
+Srutal can be described as the {{nowrap| 34d & 46 }} temperament, where 7/4 is located at 15 generator steps, or the double-augmented fifth (C–Gx). As such, it weakly extends [[leapfrog]]. 80edo and [[126edo]] are among the possible tunings. Srutal, shrutar and bidia have similar 19-limit properties, tempering out 190/189, related to rank-3 [[julius]].
-Diaschismic extends naturally to the 17-limit, for which the same tunings may be used, making it one of the most important of the higher-limit rank-2 temperaments. Adding the 11-limit adds the commas 176/175, 896/891 and 441/440. The 13-limit yields 196/195, 351/350, and 364/363; the 17-limit adds 136/135, 221/220, and 442/441. If you want to explore higher-limit harmonies, diaschismic is certainly one excellent way to do it; Mos of 34 notes and even more the 46-note mos will encompass very great deal of it. Of course 46 or 58 equal provide alternatives which in many ways are similar, particularly in the case of 58.
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: 126/125, 2048/2025
+[[Comma list]]: 2048/2025, 4375/4374
-{{Mapping|legend=1| 2 0 11 31 | 0 1 -2 -8 }}
+{{Mapping|legend=1| 2 0 11 -42 | 0 1 -2 15 }}
-{{Multival|legend=1| 2 -4 -16 -11 -31 -26 }}
-[[Optimal tuning]] ([[POTE]]): ~45/32 = 1\2, ~3/2 = 703.681
+[[Optimal tuning]]s:
+* [[WE]]: ~45/32 = 599.4046{{c}}, ~3/2 = 704.1150{{c}}
+: [[error map]]: {{val| -1.191 +0.969 +1.289 +0.044 }}
+* [[CWE]]: ~45/32 = 600.0000{{c}}, ~3/2 = 704.7646{{c}}
+: error map: {{val| 0.000 +2.810 +4.157 +2.643 }}
 [[Tuning ranges]]:
-* 7- and 9-odd-limit [[diamond monotone]]: ~3/2 = [700.000, 705.882] (7\12 to 20\34)
+* 7- and 9-odd-limit [[diamond monotone]]: ~3/2 = [703.448, 705.882] (34\58 to 20\34)
 * 7- and 9-odd-limit [[diamond tradeoff]]: ~3/2 = [701.955, 706.843]
-* 7- and 9-odd-limit diamond monotone and tradeoff: ~3/2 = [701.955, 705.882]
-{{Optimal ET sequence|legend=1| 12, 46, 58, 104c, 162c }}
+{{Optimal ET sequence|legend=1| 34d, 46, 80, 126, 206cd, 332bcd }}
-[[Badness]]: 0.037914
+[[Badness]] (Sintel): 2.32
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 126/125, 176/175, 896/891
+Comma list: 176/175, 896/891, 1331/1323
-Mapping: {{mapping| 2 0 11 31 45 | 0 1 -2 -8 -12 }}
+Mapping: {{mapping| 2 0 11 -42 -28 | 0 1 -2 15 11 }}
-Optimal tuning (POTE): ~45/32 = 1\2, ~3/2 = 703.714
+Optimal tunings:
+* WE: ~45/32 = 599.4413{{c}}, ~3/2 = 704.1999{{c}}
+* CWE: ~45/32 = 600.0000{{c}}, ~3/2 = 704.8017{{c}}
 Tuning ranges:
-* 11-odd-limit diamond monotone: ~3/2 = [700.000, 704.348] (7\12 to 27\46)
+* 11-odd-limit diamond monotone: ~3/2 = [704.348, 705.882] (27\46 to 20\34)
 * 11-odd-limit diamond tradeoff: ~3/2 = [701.955, 706.843]
-* 11-odd-limit diamond monotone and tradeoff: ~3/2 = [701.955, 704.348]
-{{Optimal ET sequence|legend=1| 12, 46, 58, 104c, 162ce }}
+{{Optimal ET sequence|legend=0| 34d, 46, 80, 126, 206cd }}
-Badness: 0.025034
+Badness (Sintel): 1.17
 === 13-limit ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 126/125, 176/175, 196/195, 364/363
+Comma list: 169/168, 176/175, 325/324, 364/363
-Mapping: {{mapping| 2 0 11 31 45 55 | 0 1 -2 -8 -12 -15 }}
+Mapping: {{mapping| 2 0 11 -42 -28 -18 | 0 1 -2 15 11 8 }}
-Optimal tuning (POTE): ~45/32 = 1\2, ~3/2 = 703.704
+Optimal tunings:
+* WE: ~45/32 = 599.5490{{c}}, ~3/2 = 704.3516{{c}}
+* CWE: ~45/32 = 600.0000{{c}}, ~3/2 = 704.8347{{c}}
 Tuning ranges:
-* 13- and 15-odd-limit diamond monotone: ~3/2 = [703.448, 704.348] (34\58 to 27\46)
+* 13- and 15-odd-limit diamond monotone: ~3/2 = [704.348, 705.882] (27\46 to 20\34)
 * 13-odd-limit diamond tradeoff: ~3/2 = [701.955, 706.843]
 * 15-odd-limit diamond tradeoff: ~3/2 = [701.955, 711.731]
-* 13- and 15-odd-limit diamond monotone and tradeoff: ~3/2 = [703.448, 704.348]
-{{Optimal ET sequence|legend=1| 46, 58, 104c, 162cef }}
+{{Optimal ET sequence|legend=0| 34d, 46, 80 }}
-Badness: 0.018926
+Badness (Sintel): 1.04
 === 17-limit ===
 Subgroup: 2.3.5.7.11.13.17
-Comma list: 126/125, 136/135, 176/175, 196/195, 256/255
+Comma list: 136/135, 169/168, 176/175, 221/220, 256/255
-Mapping: {{mapping| 2 0 11 31 45 55 5 | 0 1 -2 -8 -12 -15 1 }}
+Mapping: {{mapping| 2 0 11 -42 -28 -18 5 | 0 1 -2 15 11 8 1 }}
-Optimal tuning (POTE): ~17/12 = 1\2, ~3/2 = 703.812
+Optimal tunings:
+* WE: ~17/12 = 599.6459{{c}}, ~3/2 = 704.4237{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~3/2 = 704.8083{{c}}
 Tuning ranges:
-* 17-odd-limit diamond monotone: ~3/2 = [703.448, 704.348] (34\58 to 27\46)
+* 17-odd-limit diamond monotone: ~3/2 = [704.348, 705.882] (27\46 to 20\34)
 * 17-odd-limit diamond tradeoff: ~3/2 = [698.955, 711.731]
-* 17-odd-limit diamond monotone and tradeoff: ~3/2 = [703.448, 704.348]
-{{Optimal ET sequence|legend=1| 46, 58, 104c }}
+{{Optimal ET sequence|legend=0| 34d, 46, 80, 126 }}
+Badness (Sintel): 0.947
+=== 19-limit ===
+Subgroup: 2.3.5.7.11.13.17.19
+Comma list: 136/135, 169/168, 176/175, 190/189, 221/220, 256/255
+Mapping: {{mapping| 2 0 11 -42 -28 -18 5 -55 | 0 1 -2 15 11 8 1 20 }}
+Optimal tunings:
+* WE: ~17/12 = 599.6371{{c}}, ~3/2 = 704.4790{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~3/2 = 704.8745{{c}}
+{{Optimal ET sequence|legend=0| 34dh, 46, 80 }}
+Badness (Sintel): 1.04
+==== Srutaloo ====
+Srutaloo adds 576/575, 736/729 or 208/207, and rhymes with [[skidoo]].
+Subgroup: 2.3.5.7.11.13.17.19.23
+Comma list: 136/135, 169/168, 176/175, 190/189, 208/207, 221/220, 256/255
+Mapping: {{mapping| 2 0 11 -42 -28 -18 5 -55 -10 | 0 1 -2 15 11 8 1 20 6 }}
+Optimal tunings:
+* WE: ~17/12 = 599.6690{{c}}, ~3/2 = 704.5098{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~3/2 = 704.8713{{c}}
+{{Optimal ET sequence|legend=0| 34dh, 46, 80 }}
+Badness (Sintel): 0.971
+===== 29-limit =====
+Subgroup: 2.3.5.7.11.13.17.19.23.29
+Comma list: 136/135, 169/168, 176/175, 190/189, 208/207, 221/220, 232/231, 256/255
+Mapping: {{mapping| 2 0 11 -42 -28 -18 5 -55 -10 -76 | 0 1 -2 15 11 8 1 20 6 27 }}
+Optimal tunings:
+* WE: ~17/12 = 599.6664{{c}}, ~3/2 = 704.5138{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~3/2 = 704.8807{{c}}
+{{Optimal ET sequence|legend=0| 34dhj, 46, 80 }}
-Badness: 0.016425
+Badness (Sintel): 1.10
-==== Na"Naa' ====
+===== 31-limit =====
-<b>Na"Naa'</b> is a remarkable subgroup temperament of 46&amp;58 with a prime harmonic of 23.
+Subgroup: 2.3.5.7.11.13.17.19.23.29.31
-Subgroup: 2.3.5.7.11.13.17.23
+Comma list: 136/135, 169/168, 176/175, 190/189, 208/207, 217/216, 221/220, 232/231, 256/255
-Comma list: 126/125, 136/135, 176/175, 196/195, 231/230, 256/255
+Mapping: {{mapping| 2 0 11 -42 -28 -18 5 -55 -10 -76 48 | 0 1 -2 15 11 8 1 20 6 27 -12 }}
-Sval mapping: {{mapping| 2 0 11 31 45 55 5 63 | 0 1 -2 -8 -12 -15 1 -17 }}
+Optimal tunings:
+* WE: ~17/12 = 599.8115{{c}}, ~3/2 = 704.5958{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~3/2 = 704.8086{{c}}
-Optimal tuning (POTE): ~17/12 = 1\2, ~3/2 = 703.870
+{{Optimal ET sequence|legend=0| 46, 80, 126 }}
-{{Optimal ET sequence|legend=1| 46, 58i, 104ci }}
+Badness (Sintel): 1.44
 == Keen ==
-Keen adds 875/864 as well as 2240/2187 to the set of commas. It may also be described as the 22 &amp; 56 temperament. [[78edo]] is a good tuning choice, and remains a good one in the 11-limit, where keen, {{multival| 2 -4 18 -12 … }}, is really more interesting, adding 100/99 and 385/384 to the commas.
+Keen adds 875/864 as well as 2240/2187 to the set of commas. It may also be described as the {{nowrap| 22 & 34 }} temperament. [[78edo]] is a good tuning choice, and remains a good one in the 11-limit, where the temperament is really more interesting, adding 100/99 and 385/384 to the list of commas.
 [[Subgroup]]: 2.3.5.7
@@ Line 581: / Line 670: @@
 {{Mapping|legend=1| 2 0 11 -23 | 0 1 -2 9 }}
-{{Multival|legend=1| 2 -4 18 -11 23 53 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~45/32 = 599.6603{{c}}, ~3/2 = 707.1707{{c}}
+: [[error map]]: {{val| -0.679 +4.536 -3.033 -2.591 }}
+* [[CWE]]: ~45/32 = 600.0000{{c}}, ~3/2 = 707.5294{{c}}
+: error map: {{val| 0.000 +5.574 -1.373 -1.061 }}
-[[Optimal tuning]] ([[POTE]]): ~45/32 = 1\2, ~3/2 = 707.571
+{{Optimal ET sequence|legend=1| 22, 56, 78, 134b }}
-{{Optimal ET sequence|legend=1| 22, 56, 78, 134b, 212b, 290bb }}
+[[Badness]] (Sintel): 2.13
-[[Badness]]: 0.083971
 === 11-limit ===
@@ Line 596: / Line 687: @@
 Mapping: {{mapping| 2 0 11 -23 26 | 0 1 -2 9 -6 }}
-Optimal tuning (POTE): ~45/32 = 1\2, ~3/2 = 707.609
+Optimal tunings:
+* WE: ~45/32 = 599.6286{{c}}, ~3/2 = 707.1712{{c}}
+* CWE: ~45/32 = 600.0000{{c}}, ~3/2 = 707.5984{{c}}
-{{Optimal ET sequence|legend=1| 22, 56, 78, 212be, 290bbe }}
+{{Optimal ET sequence|legend=0| 22, 56, 78 }}
-Badness: 0.045270
+Badness (Sintel): 1.50
 ==== 13-limit ====
@@ Line 609: / Line 702: @@
 Mapping: {{mapping| 2 0 11 -23 26 -18 | 0 1 -2 9 -6 8 }}
-Optimal tuning (POTE): ~45/32 = 1\2, ~3/2 = 707.167
+Optimal tunings:
+* WE: ~45/32 = 599.3498{{c}}, ~3/2 = 706.4009{{c}}
+* CWE: ~45/32 = 600.0000{{c}}, ~3/2 = 707.1309{{c}}
-{{Optimal ET sequence|legend=1| 22f, 34, 56f }}
+{{Optimal ET sequence|legend=0| 22f, 34, 56f }}
-Badness: 0.044877
+Badness (Sintel): 1.85
 ===== 17-limit =====
@@ Line 622: / Line 717: @@
 Mapping: {{mapping| 2 0 11 -23 26 -18 5 | 0 1 -2 9 -6 8 1}}
-Optimal tuning (POTE): ~17/12 = 1\2, ~3/2 = 707.155
+Optimal tunings:
+* WE: ~17/12 = 599.4053{{c}}, ~3/2 = 706.4544{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~3/2 = 707.1243{{c}}
-{{Optimal ET sequence|legend=1| 22f, 34, 56f }}
+{{Optimal ET sequence|legend=0| 22f, 34, 56f }}
-Badness: 0.030297
+Badness (Sintel): 1.54
 ==== Keenic ====
@@ Line 635: / Line 732: @@
 Mapping: {{mapping| 2 0 11 -23 26 36 | 0 1 -2 9 -6 -9 }}
-Optimal tuning (POTE): ~45/32 = 1\2, ~3/2 = 707.257
+Optimal tunings:
+* WE: ~45/32 = 599.8547{{c}}, ~3/2 = 707.0858{{c}}
+* CWE: ~45/32 = 600.0000{{c}}, ~3/2 = 707.2596{{c}}
-{{Optimal ET sequence|legend=1| 22, 34, 56 }}
+{{Optimal ET sequence|legend=0| 22, 34, 56 }}
-Badness: 0.040351
+Badness (Sintel): 1.67
 ===== 17-limit =====
@@ Line 648: / Line 747: @@
 Mapping: {{mapping| 2 0 11 -23 26 36 5 | 0 1 -2 9 -6 -9 1 }}
-Optimal tuning (POTE): ~17/12 = 1\2, ~3/2 = 707.252
+Optimal tunings:
+* WE: ~17/12 = 599.8338{{c}}, ~3/2 = 707.0558{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~3/2 = 707.2537{{c}}
-{{Optimal ET sequence|legend=1| 22, 34, 56 }}
+{{Optimal ET sequence|legend=0| 22, 34, 56 }}
-Badness: 0.026917
+Badness (Sintel): 1.37
 == Bidia ==
-Bidia adds [[3136/3125]] to the commas, splitting the period into 1/4 octave. It may be called the 12 &amp; 56 temperament.
+Bidia adds [[3136/3125]] to the commas, splitting the period into 1/4 octave. It may be called the {{nowrap| 12 & 68 }} temperament; its ploidacot is tetraploid monocot. Scales of bidia [[cluster temperament|cluster]] around [[12edo]], with a small residue left behind when three semitones exceed the quarter-octave period. This residue represents [[64/63]], and somewhat peculiarly, [[81/80]] is represented by ''two'' of these intervals.
 [[Subgroup]]: 2.3.5.7
@@ Line 662: / Line 763: @@
 {{Mapping|legend=1| 4 0 22 43 | 0 1 -2 -5 }}
+: mapping generators: ~25/21, ~3
-{{Multival|legend=1| 4 -8 -20 -22 -43 -24 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~25/21 = 299.6887{{c}}, ~3/2 = 704.6318{{c}}
-[[Optimal tuning]] ([[POTE]]): ~25/21 = 1\4, ~3/2 = 705.364
+: [[error map]]: {{val| -1.245 +1.432 +0.064 +0.854 }}
+* [[CWE]]: ~25/21 = 300.0000{{c}}, ~3/2 = 705.5070{{c}}
+: error map: {{val| 0.000 +3.552 +2.672 +3.639 }}
-{{Optimal ET sequence|legend=1| 12, 56, 68, 80, 148d }}
+{{Optimal ET sequence|legend=1| 12, …, 56, 68, 80, 148d }}
-[[Badness]]: 0.056474
+[[Badness]] (Sintel): 1.43
 === 11-limit ===
@@ Line 678: / Line 782: @@
 Mapping: {{mapping| 4 0 22 43 71 | 0 1 -2 -5 -9 }}
-Optimal tuning (POTE): ~25/21 = 1\4, ~3/2 = 705.087
+Optimal tunings:
+* WE: ~25/21 = 299.6809{{c}}, ~3/2 = 704.3367{{c}}
+* CWE: ~25/21 = 300.0000{{c}}, ~3/2 = 705.2170{{c}}
-{{Optimal ET sequence|legend=1| 12, 68, 80 }}
+{{Optimal ET sequence|legend=0| 12, 56e, 68, 80 }}
-Badness: 0.040191
+Badness (Sintel): 1.33
 === 13-limit ===
@@ Line 691: / Line 797: @@
 Mapping: {{mapping| 4 0 22 43 71 -36 | 0 1 -2 -5 -9 8 }}
-Optimal tuning (POTE): ~25/21 = 1\4, ~3/2 = 705.301
+Optimal tunings:
+* WE: ~25/21 = 299.7538{{c}}, ~3/2 = 704.7222{{c}}
+* CWE: ~25/21 = 300.0000{{c}}, ~3/2 = 705.3241{{c}}
-{{Optimal ET sequence|legend=1| 12, 68, 80, 148d, 228bcd, 376bbcddf }}
+{{Optimal ET sequence|legend=0| 12, 68, 80, 148d, 228bcd, 376bbcddf }}
-Badness: 0.041137
+Badness (Sintel): 1.70
 === 17-limit ===
@@ Line 704: / Line 812: @@
 Mapping: {{mapping| 4 0 22 43 71 -36 10 | 0 1 -2 -5 -9 8 1 }}
-Optimal tuning (POTE): ~25/21 = 1\4, ~3/2 = 705.334
+Optimal tunings:
+* WE: ~25/21 = 299.7883{{c}}, ~3/2 = 704.8365{{c}}
+* CWE: ~25/21 = 300.0000{{c}}, ~3/2 = 705.3496{{c}}
-{{Optimal ET sequence|legend=1| 12, 68, 80, 148d, 228bcd, 376bbcddf }}
+{{Optimal ET sequence|legend=0| 12, 68, 80, 148d }}
-Badness: 0.028631
+Badness (Sintel): 1.46
 === 19-limit ===
@@ Line 717: / Line 827: @@
 Mapping: {{mapping| 4 0 22 43 71 -36 10 17 | 0 1 -2 -5 -9 8 1 0 }}
-Optimal tuning (POTE): ~19/16 = 1\4, ~3/2 = 705.339
+Optimal tunings:
+* WE: ~19/16 = 299.7967{{c}}, ~3/2 = 704.8609{{c}}
+* CWE: ~19/16 = 300.0000{{c}}, ~3/2 = 705.3519{{c}}
-{{Optimal ET sequence|legend=1| 12, 68, 80, 148d, 376bbcddfh }}
+{{Optimal ET sequence|legend=0| 12, 68, 80, 148d }}
-Badness: 0.020590
+Badness (Sintel): 1.25
 === 23-limit ===
@@ Line 731: / Line 843: @@
 Optimal tunings:
-* [[TE]]: ~19/16 = 299.797 (~2 = 1199.188), ~3 = 1904.048 (~3/2 = 704.860)
+* WE: ~19/16 = 299.7961{{c}}, ~3/2 = 704.8577{{c}}
-* [[CWE]]: ~19/16 = 1\4, ~3/2 = 705.341
+* CWE: ~19/16 = 300.0000{{c}}, ~3/2 = 705.3413{{c}}
-* [[POTE]]: ~19/16 = 1\4, ~3/2 = 705.337
-{{Optimal ET sequence|legend=1| 12, 68, 80, 148di }}
+{{Optimal ET sequence|legend=0| 12, 68, 80, 148di }}
-Badness: 0.017301
+Badness (Sintel): 1.24
-== Echidna ==
+== Shrutar ==
-Echidna adds 1728/1715 to the commas and takes 9/7 as a generator. It may be called the 22 &amp; 58 temperament. [[58edo]] or [[80edo]] make for good tunings, or their vals can be added to {{val| 138 219 321 388 }} (138cde). In most of the tunings it has a significantly sharp 7/4 which some prefer.
+Shrutar adds 245/243 to the commas, and also tempers out [[6144/6125]]. It can also be described as {{nowrap| 22 & 46 }}. Its generator can be taken as either ~36/35 or ~35/24; the latter is interesting since along with 15/14 and 21/20, it connects opposite sides of a hexany. Its ploidacot is diploid alpha-dicot. [[68edo]] makes for a good tuning, but another excellent choice is a generator of 14<sup>(1/7)</sup>, making 7's just.
-Echidna becomes more interesting when extended to be an 11-limit temperament by adding 176/175, 540/539 or 896/891 to the commas, where the same tunings can be used as before. It then is able to represent the entire 11-odd-limit diamond to within about six cents of error, within a compass of 24 notes. The 22-note 2mos gives scope for this, and the 36-note mos much more. Better yet, it is related to three important 11-limit edos: 22edo, a trivial tuning, is the smallest consistent in the 11-odd-limit, corresponding to the merge of this temperament with [[hedgehog]]; [[58edo]] is the smallest tuning that is distinctly consistent in the 11-odd-limit and [[80edo]] is the third smallest distinctly consistent in the 11-odd-limit.
+By adding 121/120 or 176/175 to the commas, shrutar can be extended to the 11-limit, which loses a bit of accuracy, but picks up low-complexity 11-limit harmony, making shrutar quite an interesting 11-limit system. 68, 114 or a 14<sup>(1/7)</sup> generator can again be used as tunings.
-The generator can be interpreted as 11/10, the period complement of 9/7, as a stack of 11/10 and 9/7 makes [[99/70]] which is extremely close to 600{{cent}} and is equal to it if we temper out [[9801/9800|S99]]. Three 11/10's then make a 4/3 (tempering out [[4000/3993|S10/S11]] thus making 10/9 and 12/11 equidistant from 11/10), implying a flat tuning of 4/3.
-Like most srutal extensions, the 13- and 17-limit interpretations are possible by observing that since we have tempered out [[176/175]], tempering out [[351/350]] and [[352/351]] which sum to 176/175 is very elegant. In the 17-limit we can equate the half-octave with 17/12 and 24/17 and we can take advantage of the sharp fifth by combining echidna with [[srutal archagall]], leading to a particularly beautiful temperament (one that prefers a very slightly less sharp fifth than srutal archagall). This mapping of 13 and 17 is supported by the patent vals of the three main echidna edos of 22, 58 and 80, of which all except 22 are consistent in the [[17-odd-limit]].
+Additionally, shrutar can employ the standard diaschismic mapping of prime 17, and most naturally represents the 2.3.5.7.11.17 subgroup temperament where 15:16:17:18 and 32:33:34:35:36 are equalized. Shrutar canonically maps primes 13, 19, and 23 as the 46 & 68 temperament; these mappings are significantly more complex and need finer tuning, however.
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: 1728/1715, 2048/2025
+[[Comma list]]: 245/243, 2048/2025
-{{Mapping|legend=1| 2 1 9 2 | 0 3 -6 5 }}
+{{Mapping|legend=1| 2 1 9 -2 | 0 2 -4 7 }}
+: mapping generators: ~45/32, ~35/24
-{{Multival|legend=1| 6 -12 10 -33 -1 57 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~45/32 = 599.5401{{c}}, ~35/24 = 652.3108{{c}}
+: [[error map]]: {{val| -0.920 +2.207 +0.304 -1.730 }}
+* [[CWE]]: ~45/32 = 600.0000{{c}}, ~35/24 = 652.7736{{c}}
+: error map: {{val| 0.000 +3.592 +2.592 +0.589 }}
-[[Optimal tuning]] ([[POTE]]): ~45/32 = 1\2, ~9/7 = 434.856
+{{Optimal ET sequence|legend=1| 22, 46, 68, 182b, 250bc }}
-{{Optimal ET sequence|legend=1| 22, 58, 80, 138cd, 218cd }}
-[[Badness]]: 0.058033
+[[Badness]] (Sintel): 1.20
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 176/175, 540/539, 896/891
+Comma list: 121/120, 176/175, 245/243
-Mapping: {{mapping| 2 1 9 2 12 | 0 3 -6 5 -7 }}
+Mapping: {{mapping| 2 1 9 -2 8 | 0 2 -4 7 -1 }}
-Optimal tuning (POTE): ~45/32 = 1\2, ~9/7 = 434.852
+Optimal tunings:
+* WE: ~45/32 = 599.7721{{c}}, ~16/11 = 652.4321{{c}}
+* CWE: ~45/32 = 600.0000{{c}}, ~16/11 = 652.6672{{c}}
-Minimax tuning:
+{{Optimal ET sequence|legend=0| 22, 46, 68, 114 }}
-* 11-odd-limit: ~9/7 = {{monzo| 5/12 0 0 1/12 -1/12 }}
-: [{{monzo| 1 0 0 0 0 }}, {{monzo| 7/4 0 0 1/4 -1/4 }}, {{monzo| 2 0 0 -1/2 1/2 }}, {{monzo| 37/12 0 0 5/12 -5/12 }}, {{monzo| 37/12 0 0 -7/12 7/12 }}]
-: Eigenmonzo (unchanged-interval) basis: 2.11/7
-{{Optimal ET sequence|legend=1| 22, 58, 80, 138cde, 218cde }}
+Badness (Sintel): 0.876
-Badness: 0.025987
 === 13-limit ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 176/175, 351/350, 364/363, 540/539
+Comma list: 121/120, 176/175, 196/195, 245/243
-Mapping: {{mapping| 2 1 9 2 12 19 | 0 3 -6 5 -7 -16 }}
+Mapping: {{mapping| 2 1 9 -2 8 -10 | 0 2 -4 7 -1 16 }}
-Optimal tuning (POTE): ~45/32 = 1\2, ~9/7 = 434.756
+Optimal tunings:
+* WE: ~45/32 = 599.7699{{c}}, ~16/11 = 652.4035{{c}}
+* CWE: ~45/32 = 600.0000{{c}}, ~16/11 = 652.6374{{c}}
-{{Optimal ET sequence|legend=1| 22, 58, 80, 138cde }}
+{{Optimal ET sequence|legend=0| 22f, 46, 68, 114 }}
-Badness: 0.023679
+Badness (Sintel): 1.16
-=== 17-limit ===
+==== 17-limit ====
 Subgroup: 2.3.5.7.11.13.17
-Comma list: 136/135, 176/175, 221/220, 256/255, 540/539
+Comma list: 121/120, 136/135, 154/153, 176/175, 196/195
+Mapping: {{mapping| 2 1 9 -2 8 -10 6 | 0 2 -4 7 -1 16 2 }}
+Optimal tunings:
+* WE: ~17/12 = 599.7995{{c}}, ~16/11 = 652.4287{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~16/11 = 652.6334{{c}}
+{{Optimal ET sequence|legend=0| 22f, 46, 68, 114 }}
+Badness (Sintel): 0.953
-Mapping: {{mapping| 2 1 9 2 12 19 6 | 0 3 -6 5 -7 -16 3 }}
+==== 19-limit ====
+Subgroup: 2.3.5.7.11.13.17.19
-Optimal tuning (POTE): ~17/12 = 1\2, ~9/7 = 434.816
+Comma list: 121/120, 136/135, 154/153, 176/175, 196/195, 343/342
-{{Optimal ET sequence|legend=1| 22, 58, 80, 138cde }}
+Mapping: {{mapping| 2 1 9 -2 8 -10 6 -10 | 0 2 -4 7 -1 16 2 17 }}
-Badness: 0.020273
+Optimal tunings:
+* WE: ~17/12 = 599.8060{{c}}, ~16/11 = 652.5190{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~16/11 = 652.7164{{c}}
-== Echidnic ==
+{{Optimal ET sequence|legend=0| 22fh, 46, 68, 114, 182bef }}
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 686/675, 1029/1024
+Badness (Sintel): 1.07
-{{Mapping|legend=1| 2 2 7 6 | 0 3 -6 -1 }}
+==== 23-limit ====
+Subgroup: 2.3.5.7.11.13.17.19.23
-{{Multival|legend=1| 6 -12 -2 -33 -20 29 }}
+Comma list: 121/120, 136/135, 154/153, 176/175, 196/195, 253/252, 343/342
-[[Optimal tuning]] ([[POTE]]): ~45/32 = 1\2, ~8/7 = 234.492
+Mapping: {{mapping| 2 1 9 -2 8 -10 6 -10 -4 | 0 2 -4 7 -1 16 2 17 12 }}
-{{Optimal ET sequence|legend=1| 10, 36, 46, 194bcd, 240bcd, 286bcd, 332bccdd }}
+Optimal tunings:
+* WE: ~17/12 = 599.7879{{c}}, ~16/11 = 652.4776{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~16/11 = 652.6926{{c}}
-[[Badness]]: 0.072246
+{{Optimal ET sequence|legend=0| 22fh, 46, 68, 114 }}
-=== 11-limit ===
+Badness (Sintel): 1.03
-Subgroup: 2.3.5.7.11
-Comma list: 385/384, 441/440, 686/675
+== Shru ==
+Shru tempers out 392/375 and slices the compound semitone into two generators of ~10/7. Its ploidacot is diploid alpha-dicot, the same as shrutar.
-Mapping: {{mapping| 2 2 7 6 3 | 0 3 -6 -1 10 }}
+[[Subgroup]]: 2.3.5.7
-Optimal tuning (POTE): ~45/32 = 1\2, ~8/7 = 235.096
+[[Comma list]]: 392/375, 1323/1280
-{{Optimal ET sequence|legend=1| 10, 36e, 46, 102, 148, 342bcdd }}
+{{Mapping|legend=1| 2 1 9 11 | 0 2 -4 -5 }}
+: mapping generators: ~45/32, ~10/7
-Badness: 0.045127
+[[Optimal tuning]]s:
+* [[WE]]: ~45/32 = 600.2519{{c}}, ~10/7 = 650.4083{{c}}
+: [[error map]]: {{val| +0.504 -0.887 +14.321 -18.096 }}
+* [[CWE]]: ~45/32 = 600.0000{{c}}, ~10/7 = 650.1017{{c}}
+: error map: {{val| 0.000 -1.752 +13.279 -19.334 }}
-=== 13-limit ===
+{{Optimal ET sequence|legend=1| 2, 22d, 24 }}
-Subgroup: 2.3.5.7.11.13
-Comma list: 91/90, 169/168, 385/384, 441/440
+[[Badness]] (Sintel): 3.99
-Mapping: {{mapping| 2 2 7 6 3 7 | 0 3 -6 -1 10 1 }}
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
-Optimal tuning (POTE): ~45/32 = 1\2, ~8/7 = 235.088
+Comma list: 56/55, 77/75, 1323/1280
-{{Optimal ET sequence|legend=1| 10, 46, 102, 148f, 194bcdf }}
+Mapping: {{mapping| 2 1 9 11 8 | 0 2 -4 -5 -1 }}
-Badness: 0.028874
+Optimal tunings:
+* WE: ~17/12 = 600.2356{{c}}, ~10/7 = 650.3856{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~10/7 = 650.1008{{c}}
-=== 17-limit ===
+{{Optimal ET sequence|legend=0| 2, 22d, 24 }}
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 91/90, 136/135, 154/153, 169/168, 256/255
+Badness (Sintel): 2.10
-Mapping: {{mapping| 2 2 7 6 3 7 7 | 0 3 -6 -1 10 1 3 }}
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
-Optimal tuning (POTE): ~17/12 = 1\2, ~8/7 = 235.088
+Comma list: 56/55, 77/75, 105/104, 507/500
-{{Optimal ET sequence|legend=1| 10, 46, 102, 148f, 194bcdf }}
+Mapping: {{mapping| 2 1 9 11 8 15 | 0 2 -4 -5 -1 -7 }}
-Badness: 0.019304
+Optimal tunings:
+* WE: ~45/32 = 599.9067{{c}}, ~10/7 = 649.4907{{c}}
+* CWE: ~45/32 = 600.0000{{c}}, ~10/7 = 649.5950{{c}}
-; Compositions
+{{Optimal ET sequence|legend=0| 2, 24 }}
-* [https://untwelve.org/competition/2011 ''A Stiff Shot of Turpentine''] [https://untwelve.org/static/audio/competition/2011/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3 play] by [[Peter Kosmorsky]]
-* [https://www.youtube.com/watch?v=VsBXIvBZY6A ''56edo Track (Echidnic16 Scale)''] by [[Budjarn Lambeth]] (2025)
-== Shrutar ==
+Badness (Sintel): 2.12
-Shrutar adds 245/243 to the commas, and also tempers out 6144/6125. It can also be described as 22&amp;46. Its generator can be taken as either 36/35 or 35/24; the latter is interesting since along with 15/14 and 21/20, it connects opposite sides of a hexany. [[68edo]] makes for a good tuning, but another excellent choice is a generator of 14<sup>(1/7)</sup>, making 7's just.
-By adding 121/120 or 176/175 to the commas, shrutar can be extended to the 11-limit, which loses a bit of accuracy, but picks up low-complexity 11-limit harmony, making shrutar quite an interesting 11-limit system. 68, 114 or a 14<sup>(1/7)</sup> generator can again be used as tunings.
+== Sruti ==
+Sruti tempers out 19683/19600, setting itself up as a [[hemipyth]] temperament. It has the same semi-octave period as diaschismic, but the generator can be taken as a neutral third or a hemitwelfth. The temperament can be described as {{nowrap| 24 & 34d }}; its ploidacot is diploid dicot. [[58edo]] may be recommended as a tuning.
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: 245/243, 2048/2025
+[[Comma list]]: 2048/2025, 19683/19600
-{{Mapping|legend=1| 2 1 9 -2 | 0 2 -4 7 }}
+{{Mapping|legend=1| 2 0 11 -15 | 0 2 -4 13 }}
+: mapping generators: ~45/32, ~140/81
-{{Multival|legend=1| 4 -8 14 -22 11 55 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~45/32 = 599.2764{{c}}, ~140/81 = 950.7284{{c}}
+: [[error map]]: {{val| -1.447 -0.498 +2.813 +1.497 }}
+* [[CWE]]: ~45/32 = 600.0000{{c}}, ~140/81 = 951.8227{{c}}
+: error map: {{val| 0.000 +1.690 +6.395 +4.869 }}
-[[Optimal tuning]] ([[POTE]]): ~45/32 = 1\2, ~35/24 = 652.811
+{{Optimal ET sequence|legend=1| 24, 34d, 58, 150cd, 208ccdd, 266ccdd }}
-{{Optimal ET sequence|legend=1| 22, 46, 68, 182b, 250bc }}
-[[Badness]]: 0.189510
+[[Badness]] (Sintel): 2.97
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 121/120, 176/175, 245/243
+Comma list: 176/175, 243/242, 896/891
-Mapping: {{mapping| 2 1 9 -2 8 | 0 2 -4 7 -1 }}
+Mapping: {{mapping| 2 0 11 -15 -1 | 0 2 -4 13 5 }}
-Optimal tuning (POTE): ~45/32 = 1\2, ~16/11 = 652.680
+Optimal tunings:
+* WE: ~45/32 = 599.1951{{c}}, ~121/70 = 950.5864{{c}}
+* CWE: ~45/32 = 600.0000{{c}}, ~121/70 = 951.7972{{c}}
-{{Optimal ET sequence|legend=1| 22, 46, 68, 114, 296bce, 410bce }}
+{{Optimal ET sequence|legend=0| 24, 34d, 58, 150cdee, 208ccddee, 266ccddeee }}
-Badness: 0.084098
+Badness (Sintel): 1.37
 === 13-limit ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 121/120, 176/175, 196/195, 245/243
+Comma list: 144/143, 176/175, 351/350, 676/675
-Mapping: {{mapping| 2 1 9 -2 8 -10 | 0 2 -4 7 -1 16 }}
+Mapping: {{mapping| 2 0 11 -15 -1 9 | 0 2 -4 13 5 -1 }}
-Optimal tuning (POTE): ~45/32 = 1\2, ~16/11 = 652.654
+Optimal tunings:
+* WE: ~45/32 = 599.1479{{c}}, ~26/15 = 950.5337{{c}}
+* CWE: ~45/32 = 600.0000{{c}}, ~26/15 = 951.8314{{c}}
-{{Optimal ET sequence|legend=1| 22f, 24f, 46, 68, 114 }}
+{{Optimal ET sequence|legend=0| 24, 34d, 58, 150cdeef, 208ccddeeff, 266ccddeeefff }}
-Badness: 0.079358
+Badness (Sintel): 0.983
 === 17-limit ===
 Subgroup: 2.3.5.7.11.13.17
-Comma list: 121/120, 136/135, 154/153, 176/175, 196/195
+Comma list: 136/135, 144/143, 170/169, 176/175, 221/220
-Mapping: {{mapping| 2 1 9 -2 8 -10 6 | 0 2 -4 7 -1 16 2 }}
+Mapping: {{mapping| 2 0 11 -15 -1 9 5 | 0 2 -4 13 5 -1 2 }}
-Optimal tuning (POTE): ~17/12 = 1\2, ~16/11 = 652.647
+Optimal tunings:
+* WE: ~17/12 = 599.3003{{c}}, ~26/15 = 950.7465{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~26/15 = 951.8142{{c}}
-{{Optimal ET sequence|legend=1| 22f, 24f, 46, 68, 114 }}
+{{Optimal ET sequence|legend=0| 24, 34d, 58 }}
-Badness: 0.049392
+Badness (Sintel): 1.05
-=== 19-limit ===
+== Anguirus ==
-Subgroup: 2.3.5.7.11.13.17.19
+As another hemipyth temperament, anguirus tempers out 49/48. It can be described as the {{nowrap| 10 & 24 }} temperament; its ploidacot is diploid dicot, the same as sruti.
-Comma list: 121/120, 136/135, 154/153, 176/175, 196/195, 343/342
-Mapping: {{mapping| 2 1 9 -2 8 -10 6 -10 | 0 2 -4 7 -1 16 2 17 }}
-Optimal tuning (POTE): ~17/12 = 1\2, ~16/11 = 652.730
-{{Optimal ET sequence|legend=1| 22fh, 24fh, 46, 68, 114, 182bef }}
-Badness: 0.044197
-=== 23-limit ===
-Subgroup: 2.3.5.7.11.13.17.19.23
-Comma list: 121/120, 136/135, 154/153, 176/175, 196/195, 253/252, 343/342
-Mapping: {{mapping| 2 1 9 -2 8 -10 6 -10 -4 | 0 2 -4 7 -1 16 2 17 12 }}
-Optimal tuning (POTE): ~17/12 = 1\2, ~16/11 = 652.708
-{{Optimal ET sequence|legend=1| 22fh, 46, 68, 114 }}
-Badness: 0.035137
-== Sruti ==
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: 2048/2025, 19683/19600
+[[Comma list]]: 49/48, 2048/2025
-{{Mapping|legend=1| 2 0 11 -15 | 0 2 -4 13 }}
+{{Mapping|legend=1| 2 0 11 4 | 0 2 -4 1 }}
+: mapping generators: ~45/32, ~7/4
-{{Multival|legend=1| 4 -8 26 -22 30 83 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~45/32 = 600.2758{{c}}, ~7/4 = 953.4593{{c}}
+: [[error map]]: {{val| +0.552 +4.964 +2.883 -14.264 }}
+* [[CWE]]: ~45/32 = 600.0000{{c}}, ~7/4 = 953.0188{{c}}
+: error map: {{val| 0.000 +4.083 +1.611 -15.807 }}
-[[Optimal tuning]] ([[POTE]]): ~45/32 = 1\2, ~140/81 = 951.876
+{{Optimal ET sequence|legend=1| 10, 24, 34 }}
-{{Optimal ET sequence|legend=1| 24, 34d, 58, 150cd, 208ccdd, 266ccdd }}
-[[Badness]]: 0.117358
+[[Badness]] (Sintel): 1.97
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 176/175, 243/242, 896/891
+Comma list: 49/48, 56/55, 243/242
-Mapping: {{mapping| 2 0 11 -15 -1 | 0 2 -4 13 5 }}
+Mapping: {{mapping| 2 0 11 4 -1 | 0 2 -4 1 5 }}
-Optimal tuning (POTE): ~45/32 = 1\2, ~121/70 = 951.863
+Optimal tunings:
+* WE: ~45/32 = 599.9250{{c}}, ~7/4 = 952.0646{{c}}
+* CWE: ~45/32 = 600.0000{{c}}, ~7/4 = 952.1784{{c}}
-{{Optimal ET sequence|legend=1| 24, 34d, 58 }}
+{{Optimal ET sequence|legend=0| 10, 24, 34 }}
-Badness: 0.041459
+Badness (Sintel): 1.63
 === 13-limit ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 144/143, 176/175, 351/350, 676/675
+Comma list: 49/48, 56/55, 91/90, 243/242
-Mapping: {{mapping| 2 0 11 -15 -1 9 | 0 2 -4 13 5 -1 }}
+Mapping: {{mapping| 2 0 11 4 -1 9 | 0 2 -4 1 5 -1 }}
-Optimal tuning (POTE): ~45/32 = 1\2, ~26/15 = 951.886
+Optimal tunings:
+* WE: ~45/32 = 599.7575{{c}}, ~7/4 = 951.9241{{c}}
+* CWE: ~45/32 = 600.0000{{c}}, ~7/4 = 952.2980{{c}}
-{{Optimal ET sequence|legend=1| 24, 34d, 58, 150cdeef, 208ccddeeff }}
+{{Optimal ET sequence|legend=0| 10, 24, 34, 58d, 92ddef }}
-Badness: 0.023791
+Badness (Sintel): 1.27
 === 17-limit ===
 Subgroup: 2.3.5.7.11.13.17
-Comma list: 136/135, 144/143, 170/169, 176/175, 221/220
+Comma list: 49/48, 56/55, 91/90, 119/117, 154/153
+Mapping: {{mapping| 2 0 11 4 -1 9 5 | 0 2 -4 1 5 -1 2 }}
+Optimal tunings:
+* WE: ~17/12 = 599.7925{{c}}, ~7/4 = 952.0004{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~7/4 = 952.3178{{c}}
+{{Optimal ET sequence|legend=0| 10, 24, 34 }}
+Badness (Sintel): 1.10
-Mapping: {{mapping| 2 0 11 -15 -1 9 5 | 0 2 -4 13 5 -1 2 }}
+== Echidna ==
+Echidna adds 1728/1715 to the commas and takes 9/7 as a generator. It may be called the {{nowrap| 22 & 58 }} temperament; its ploidacot is diploid alpha-tricot. [[58edo]] or [[80edo]] make for good tunings, or their vals can be added to {{val| 138 219 321 388 }} (138cde). In most of the tunings it has a significantly sharp 7/4 which some prefer.
-Optimal tuning (POTE): ~17/12 = 1\2, ~26/15 = 951.857
+Echidna becomes more interesting when extended to be an 11-limit temperament by adding 176/175, 540/539 or 896/891 to the commas, where the same tunings can be used as before. It then is able to represent the entire 11-odd-limit diamond to within about six cents of error, within a compass of 24 notes. The 22-note 2mos gives scope for this, and the 36-note mos much more. Better yet, it is related to three important 11-limit edos: 22edo, a trivial tuning, is the smallest consistent in the 11-odd-limit, corresponding to the merge of this temperament with [[hedgehog]]; [[58edo]] is the smallest tuning that is distinctly consistent in the 11-odd-limit and [[80edo]] is the third smallest distinctly consistent in the 11-odd-limit.
-{{Optimal ET sequence|legend=1| 24, 34d, 58 }}
+The generator can be interpreted as 11/10, the period complement of 9/7, as a stack of 11/10 and 9/7 makes [[99/70]] which is extremely close to 600{{cent}} and is equal to it if we temper out [[9801/9800|S99]]. Three 11/10's then make a 4/3 (tempering out [[4000/3993|S10/S11]] thus making 10/9 and 12/11 equidistant from 11/10), implying a flat tuning of 4/3.
-Badness: 0.020536
+Like most srutal extensions, the 13- and 17-limit interpretations are possible by observing that since we have tempered out [[176/175]], tempering out [[351/350]] and [[352/351]] which sum to 176/175 is very elegant. In the 17-limit we can equate the half-octave with 17/12 and 24/17 and we can take advantage of the sharp fifth by combining echidna with [[srutal archagall]], leading to a particularly beautiful temperament (one that prefers a very slightly less sharp fifth than srutal archagall). This mapping of 13 and 17 is supported by the patent vals of the three main echidna edos of 22, 58 and 80, of which all except 22 are consistent in the [[17-odd-limit]].
-== Anguirus ==
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: 49/48, 2048/2025
+[[Comma list]]: 1728/1715, 2048/2025
-{{Mapping|legend=1| 2 0 11 4 | 0 2 -4 1 }}
+{{Mapping|legend=1| 2 1 9 2 | 0 3 -6 5 }}
+: mapping generators: ~45/32, ~9/7
-{{Multival|legend=1| 4 -8 2 -22 -8 27 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~45/32 = 599.3056{{c}}, ~9/7 = 434.3524{{c}}
+: [[error map]]: {{val| -1.389 +0.408 +1.322 +1.547 }}
+* [[CWE]]: ~45/32 = 600.0000{{c}}, ~9/7 = 434.8327{{c}}
+: error map: {{val| 0.000 +2.543 +4.690 +5.338 }}
-[[Optimal tuning]] ([[POTE]]): ~45/32 = 1\2, ~7/4 = 953.021
+{{Optimal ET sequence|legend=1| 22, 58, 80, 138cd, 218cd }}
-{{Optimal ET sequence|legend=1| 10, 24, 34 }}
+[[Badness]] (Sintel): 1.47
-[[Badness]]: 0.077955
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 49/48, 56/55, 243/242
+Comma list: 176/175, 540/539, 896/891
+Mapping: {{mapping| 2 1 9 2 12 | 0 3 -6 5 -7 }}
-Mapping: {{mapping| 2 0 11 4 -1 | 0 2 -4 1 5 }}
+Optimal tunings:
+* WE: ~45/32 = 599.3085{{c}}, ~9/7 = 434.3511{{c}}
+* CWE: ~45/32 = 600.0000{{c}}, ~9/7 = 434.8647{{c}}
-Optimal tuning (POTE): ~45/32 = 1\2, ~7/4 = 952.184
+Minimax tuning:
+* 11-odd-limit: ~9/7 = {{monzo| 5/12 0 0 1/12 -1/12 }}
+: [{{monzo| 1 0 0 0 0 }}, {{monzo| 7/4 0 0 1/4 -1/4 }}, {{monzo| 2 0 0 -1/2 1/2 }}, {{monzo| 37/12 0 0 5/12 -5/12 }}, {{monzo| 37/12 0 0 -7/12 7/12 }}]
+: unchanged-interval (eigenmonzo) basis: 2.11/7
-{{Optimal ET sequence|legend=1| 10, 24, 34, 58d, 92de }}
+{{Optimal ET sequence|legend=0| 22, 58, 80, 138cde, 218cde }}
-Badness: 0.049253
+Badness (Sintel): 0.859
 === 13-limit ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 49/48, 56/55, 91/90, 243/242
+Comma list: 176/175, 351/350, 364/363, 540/539
-Mapping: {{mapping| 2 0 11 4 -1 9 | 0 2 -4 1 5 -1 }}
+Mapping: {{mapping| 2 1 9 2 12 19 | 0 3 -6 5 -7 -16 }}
-Optimal tuning (POTE): ~45/32 = 1\2, ~7/4 = 952.309
+Optimal tunings:
+* WE: ~45/32 = 599.3397{{c}}, ~9/7 = 434.2772{{c}}
+* CWE: ~45/32 = 600.0000{{c}}, ~9/7 = 434.7864{{c}}
-{{Optimal ET sequence|legend=1| 10, 24, 34, 58d, 92ddef }}
+{{Optimal ET sequence|legend=0| 22, 36f, 58, 80, 138cde }}
-Badness: 0.030829
+Badness (Sintel): 0.978
 === 17-limit ===
 Subgroup: 2.3.5.7.11.13.17
-Comma list: 49/48, 56/55, 91/90, 119/117, 154/153
+Comma list: 136/135, 176/175, 221/220, 256/255, 540/539
+Mapping: {{mapping| 2 1 9 2 12 19 6 | 0 3 -6 5 -7 -16 3 }}
-Mapping: {{mapping| 2 0 11 4 -1 9 5 | 0 2 -4 1 5 -1 2 }}
+Optimal tunings:
+* WE: ~45/32 = 599.4645{{c}}, ~9/7 = 434.4282{{c}}
+* CWE: ~45/32 = 600.0000{{c}}, ~9/7 = 434.8340{{c}}
-Optimal tuning (POTE): ~17/12 = 1\2, ~7/4 = 952.330
+{{Optimal ET sequence|legend=0| 22, 36f, 58, 80, 138cde }}
-{{Optimal ET sequence|legend=1| 10, 24, 34, 58d, 92ddef }}
+Badness (Sintel): 1.03
-Badness: 0.021796
+== Echidnic ==
+Echidnic tempers out 686/675 and [[1029/1024]]. It has the same semi-octave period as diaschismic, but slices the generator of a fifth into three ~8/7's. It can be described as the {{nowrap| 10 & 46 }} temperament; its ploidacot is diploid tricot.
-== Shru ==
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: 392/375, 1323/1280
+[[Comma list]]: 686/675, 1029/1024
-{{Mapping|legend=1| 2 1 9 11 | 0 2 -4 -5 }}
+{{Mapping|legend=1| 2 2 7 6 | 0 3 -6 -1 }}
+: mapping generators: ~45/32, ~8/7
-{{Multival|legend=1| 4 -8 -10 -22 -27 -1 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~45/32 = 599.7208{{c}}, ~8/7 = 234.8330{{c}}
+: [[error map]]: {{val| -0.558 +1.986 +2.733 -5.334 }}
+* [[CWE]]: ~45/32 = 600.0000{{c}}, ~8/7 = 234.9539{{c}}
+: error map: {{val| 0.000 +2.907 +3.963 -3.780 }}
-[[Optimal tuning]] ([[POTE]]): ~45/32 = 1\2, ~10/7 = 650.135
+{{Optimal ET sequence|legend=1| 10, 26c, 36, 46 }}
-{{Optimal ET sequence|legend=1| 2, 22d, 24 }}
+[[Badness]] (Sintel): 1.83
-[[Badness]]: 0.157619
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 56/55, 77/75, 1323/1280
+Comma list: 385/384, 441/440, 686/675
-Mapping: {{mapping| 2 1 9 11 8 | 0 2 -4 -5 -1 }}
+Mapping: {{mapping| 2 2 7 6 3 | 0 3 -6 -1 10 }}
-Optimal tuning (POTE): ~45/32 = 1\2, ~10/7 = 650.130
+Optimal tunings:
+* WE: ~45/32 = 599.8022{{c}}, ~8/7 = 235.0185{{c}}
+* CWE: ~45/32 = 600.0000{{c}}, ~8/7 = 235.0893{{c}}
-{{Optimal ET sequence|legend=1| 2, 22d, 24 }}
+{{Optimal ET sequence|legend=0| 10, 36e, 46, 102, 148 }}
-Badness: 0.063483
+Badness (Sintel): 1.49
 === 13-limit ===
 Subgroup: 2.3.5.7.11.13
-Comma list: 56/55, 77/75, 105/104, 507/500
+Comma list: 91/90, 169/168, 385/384, 441/440
+Mapping: {{mapping| 2 2 7 6 3 7 | 0 3 -6 -1 10 1 }}
+Optimal tunings:
+* WE: ~45/32 = 599.9570{{c}}, ~8/7 = 235.0708{{c}}
+* CWE: ~45/32 = 600.0000{{c}}, ~8/7 = 235.0862{{c}}
+{{Optimal ET sequence|legend=0| 10, 36e, 46, 102, 148f }}
+Badness (Sintel): 1.19
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 91/90, 136/135, 154/153, 169/168, 256/255
+Mapping: {{mapping| 2 2 7 6 3 7 7 | 0 3 -6 -1 10 1 3 }}
-Mapping: {{mapping| 2 1 9 11 8 15 | 0 2 -4 -5 -1 -7 }}
+Optimal tunings:
+* WE: ~17/12 = 599.9571{{c}}, ~8/7 = 235.0709{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~8/7 = 235.0860{{c}}
-Optimal tuning (POTE): ~45/32 = 1\2, ~10/7 = 650.535
+{{Optimal ET sequence|legend=0| 10, 36e, 46, 102, 148f }}
-{{Optimal ET sequence|legend=1| 22df, 24 }}
+Badness (Sintel): 0.983
-Badness: 0.045731
+; Music
+* [https://untwelve.org/competition/2011 ''A Stiff Shot of Turpentine''] [https://untwelve.org/static/audio/competition/2011/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3 play] by [[Peter Kosmorsky]]
+* [https://www.youtube.com/watch?v=VsBXIvBZY6A ''56edo Track (Echidnic16 Scale)''] by [[Budjarn Lambeth]] (2025)
 == Quadrasruta ==
+Named by [[Xenllium]] in 2022, quadrasruta tempers out 2401/2400, the breedsma, and extends [[buzzard]]. It may be described as {{nowrap| 58 & 68 }}; its ploidacot is diploid alpha-tetracot. 126edo may be recommended as a tuning.
 [[Subgroup]]: 2.3.5.7
@@ Line 1,104: / Line 1,282: @@
 {{Mapping|legend=1| 2 0 11 8 | 0 4 -8 -3 }}
+: mapping generators: ~45/32, ~21/16
-{{Multival|legend=1| 8 -16 -6 -44 -32 31 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~45/32 = 599.4443{{c}}, ~21/16 = 475.7746{{c}}
+: [[error map]]: {{val| -1.111 +1.143 +1.377 -0.595 }}
+* [[CWE]]: ~45/32 = 600.0000{{c}}, ~21/16 = 476.2394{{c}}
+: error map: {{val| 0.000 +3.003 +3.771 +2.456 }}
-[[Optimal tuning]] ([[POTE]]): ~45/32 = 1\2, ~21/16 = 476.216
+{{Optimal ET sequence|legend=1| 10, …, 58, 68, 126, 446bbccd }}
-{{Optimal ET sequence|legend=1| 10, 38c, 48c, 58, 68, 126 }}
+[[Badness]] (Sintel): 1.86
-[[Badness]]: 0.073569
 === 11-limit ===
@@ Line 1,120: / Line 1,301: @@
 Mapping: {{mapping| 2 0 11 8 22 | 0 4 -8 -3 -19 }}
-Optimal tuning (POTE): ~45/32 = 1\2, ~21/16 = 476.118
+Optimal tunings:
+* WE: ~45/32 = 599.4648{{c}}, ~21/16 = 475.6929{{c}}
+* CWE: ~45/32 = 600.0000{{c}}, ~21/16 = 476.1507{{c}}
-{{Optimal ET sequence|legend=1| 58, 126, 184c, 310bccde }}
+{{Optimal ET sequence|legend=0| 10e, …, 58, 126, 184c, 310bccde }}
-Badness: 0.049018
+Badness (Sintel): 1.62
 ==== 13-limit ====
@@ Line 1,133: / Line 1,316: @@
 Mapping: {{mapping| 2 0 11 8 22 9 | 0 4 -8 -3 -19 -2 }}
-Optimal tuning (POTE): ~45/32 = 1\2, ~21/16 = 476.099
+Optimal tunings:
+* WE: ~45/32 = 599.3787{{c}}, ~21/16 = 475.6065{{c}}
+* CWE: ~45/32 = 600.0000{{c}}, ~21/16 = 476.1345{{c}}
-{{Optimal ET sequence|legend=1| 58, 126f, 184cff }}
+{{Optimal ET sequence|legend=0| 10e, …, 58, 126f, 184cff }}
-Badness: 0.028463
+Badness (Sintel): 1.18
 ==== 17-limit ====
@@ Line 1,146: / Line 1,331: @@
 Mapping: {{mapping| 2 0 11 8 22 9 5 | 0 4 -8 -3 -19 -2 4 }}
-Optimal tuning (POTE): ~17/12 = 1\2, ~21/16 = 476.162
+Optimal tunings:
+* WE: ~17/12 = 599.5077{{c}}, ~21/16 = 475.7713{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~21/16 = 476.1814{{c}}
-{{Optimal ET sequence|legend=1| 58, 126f }}
+{{Optimal ET sequence|legend=0| 10e, 58, 126f }}
-Badness: 0.023820
+Badness (Sintel): 1.21
 === Quadrafourths ===
@@ Line 1,159: / Line 1,346: @@
 Mapping: {{mapping| 2 0 11 8 -1 | 0 4 -8 -3 10 }}
-Optimal tuning (POTE): ~45/32 = 1\2, ~21/16 = 476.017
+Optimal tunings:
+* WE: ~45/32 = 599.2593{{c}}, ~21/16 = 475.4292{{c}}
+* CWE: ~45/32 = 600.0000{{c}}, ~21/16 = 476.0088{{c}}
-{{Optimal ET sequence|legend=1| 10, 38c, 48c, 58 }}
+{{Optimal ET sequence|legend=0| 10, 48c, 58, 184cee, 242ccdeee }}
-Badness: 0.049114
+Badness (Sintel): 1.62
 ==== 13-limit ====
@@ Line 1,172: / Line 1,361: @@
 Mapping: {{mapping| 2 0 11 8 -1 9 | 0 4 -8 -3 10 -2 }}
-Optimal tuning (POTE): ~45/32 = 1\2, ~21/16 = 476.028
+Optimal tunings:
+* WE: ~45/32 = 599.2147{{c}}, ~21/16 = 475.4052{{c}}
+* CWE: ~45/32 = 600.0000{{c}}, ~21/16 = 476.0253{{c}}
-{{Optimal ET sequence|legend=1| 10, 38c, 48c, 58 }}
+{{Optimal ET sequence|legend=0| 10, 48c, 58, 126eef, 184ceeff, 242ccdeeeff }}
-Badness: 0.026743
+Badness (Sintel): 1.11
 ==== 17-limit ====
@@ Line 1,185: / Line 1,376: @@
 Mapping: {{mapping| 2 0 11 8 -1 9 5 | 0 4 -8 -3 10 -2 4 }}
-Optimal tuning (POTE): ~17/12 = 1\2, ~21/16 = 476.077
+Optimal tunings:
+* WE: ~17/12 = 599.3353{{c}}, ~21/16 = 475.5495{{c}}
+* CWE: ~17/12 = 600.0000{{c}}, ~21/16 = 476.0691{{c}}
+{{Optimal ET sequence|legend=0| 10, 48c, 58 }}
+Badness (Sintel): 1.13
+== Subgroup extensions ==
+=== Srutal archagall (2.3.5.17) ===
+{{See also | Fiventeen }}
+Subgroup: 2.3.5.17
+Comma list: 136/135, 256/255
+Subgroup-val mapping: {{mapping| 2 0 11 5 | 0 1 -2 1 }}
+: mapping generators: ~17/12, ~3
+Optimal tunings:
+* WE: ~45/32 = 599.5585{{c}}, ~3/2 = 704.6188{{c}}
+* CWE: ~45/32 = 600.0000{{c}}, ~3/2 = 705.1356{{c}}
-{{Optimal ET sequence|legend=1| 10, 38c, 48c, 58, 126eef, 184ceeff }}
+{{Optimal ET sequence|legend=0| 10, 12, 22, 34, 80, 114, 194bc }}
-Badness: 0.022239
+Badness (Sintel): 0.212
 [[Category:Temperament families]]
 [[Category:Diaschismic family| ]] <!-- main article -->
-[[Category:Diaschismic| ]] <!-- key article -->
 [[Category:Rank 2]]

Diaschismic family: Difference between revisions