Rastmic rank-3 clan: Difference between revisions

Line 5:

* [[Jove]] (+441/440 or 540/539) → [[Breed family #Jove|Breed family]]

* ''[[Hagrid]]'' (+9801/9800) → [[Cataharry family #Hagrid|Cataharry family]]

* ''[[Rabic]]'' (+131769/131072) → [[Alphaxenic rank ~~three~~ clan #Betarabian|Alphaxenic rank-3 clan]]

* ''[[Rabic]]'' (+131769/131072) → [[Alphaxenic rank-3 clan #Betarabian|Alphaxenic rank-3 clan]]

== Spectacle ==

Spectacle, named by [[Gene Ward Smith]] in 2010<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_17700.html Yahoo! Tuning Group | ''Spectacle temperament?'']</ref>, can be described as the 31 & 34 & 41 temperament. It tempers out 225/224, making it a sort of marvel infested with neutral thirds. It is therefore generated by octaves, major thirds, and neutral thirds. 3/2 is equated with ~~two~~ a stack of two 11/9's as a corollary of 243/242 being tempered out, 7/4 is equated with a stack of four 11/9's and two 5/4's, 11/8 is equated with a stack of five 11/9's, 13/8 is equated with a stack of two 18/11's and four 5/4's, and 17/16 is equated with three 18/11's and three 5/4's. Every harmonic is reached with help of other intervals at most with three 5/4's.

Spectacle, named by [[Gene Ward Smith]] in 2010<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_17700.html Yahoo! Tuning Group | ''Spectacle temperament?'']</ref>, can be described as the {{nowrap| 31 & 34 & 41 }} temperament. It tempers out 225/224, making it a sort of marvel infested with neutral thirds. It is therefore generated by octaves, major thirds, and neutral thirds. 3/2 is equated with a stack of two 11/9's as a corollary of 243/242 being tempered out, 7/4 is equated with a stack of four 11/9's and two 5/4's, 11/8 is equated with a stack of five 11/9's, 13/8 is equated with a stack of two 18/11's and four 5/4's, and 17/16 is equated with three 18/11's and three 5/4's. Every harmonic is reached with help of other intervals at most with three 5/4's.

[[Subgroup]]: 2.3.5.7.11

Line 19:

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000, ~11/9 = 350.377, ~5/4 = 384.370

* [[CTE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.377{{c}}, ~5/4 = 384.370{{c}}

* [[CWE]]: ~2 = 1200.000, ~11/9 = 350.176, ~5/4 = 384.095

* [[CWE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.176{{c}}, ~5/4 = 384.095{{c}}

[[Minimax tuning]]:

Line 28:

{{Optimal ET sequence|legend=1| 31, 41, 72, 247c, 281, 353c, 425bc, 497bc }}

[[Badness]]: 0.499 × 10-3

[[Badness]] (Smith): 0.499 × 10-3

[[Projection pair]]s: 3 242/81, 7 366025/52488, 11 644204/59049 to 2.5.11/9

Line 44:

Optimal tunings:

* CTE: ~2 = 1200.000, ~11/9 = 350.239, ~5/4 = 384.998

* CTE: ~2 = 1200.000{{c}}, ~11/9 = 350.239{{c}}, ~5/4 = 384.998{{c}}

* CWE: ~2 = 1200.000, ~11/9 = 350.039, ~5/4 = 384.587

* CWE: ~2 = 1200.000{{c}}, ~11/9 = 350.039{{c}}, ~5/4 = 384.587{{c}}

{{Optimal ET sequence|legend=0| 31, 72, 103, 175f }} <nowiki>*</nowiki>

Line 51:

<nowiki>*</nowiki> optimal patent val: [[240edo|240]]

Badness: 1.009 × 10-3

Badness (Smith): 1.009 × 10-3

== Cuckoo ==

Line 63:

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000, ~11/9 = 350.355, ~5/4 = 389.555

* [[CTE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.355{{c}}, ~5/4 = 389.555{{c}}

* [[CWE]]: ~2 = 1200.000, ~11/9 = 350.421, ~5/4 = 389.731

* [[CWE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.421{{c}}, ~5/4 = 389.731{{c}}

{{Optimal ET sequence|legend=1| 24d, 27e, 31, 58, 89, 154, 185 }}

[[Badness]]: 0.933 × 10-3

[[Badness]] (Smith): 0.933 × 10-3

=== 13-limit ===

Line 78:

Optimal tunings:

* CTE: ~2 = 1200.000, ~11/9 = 350.585, ~5/4 = 389.302

* CTE: ~2 = 1200.000{{c}}, ~11/9 = 350.585{{c}}, ~5/4 = 389.302{{c}}

* CWE: ~2 = 1200.000, ~11/9 = 350.568, ~5/4 = 389.610

* CWE: ~2 = 1200.000{{c}}, ~11/9 = 350.568{{c}}, ~5/4 = 389.610{{c}}

Line 95:

: mapping generators: ~2, ~128/105, ~5

[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000, ~128/105 = 350.174, ~5/4 = 384.014

[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~128/105 = 350.174{{c}}, ~5/4 = 384.014{{c}}

[[Badness]]: 0.770 × 10-3

[[Badness]] (Smith): 0.770 × 10-3

=== 11-limit ===

Line 109:

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000, ~11/9 = 350.217, ~5/4 = 383.962

* [[CTE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.217{{c}}, ~5/4 = 383.962{{c}}

* [[CWE]]: ~2 = 1200.000, ~11/9 = 350.003, ~5/4 = 384.078

* [[CWE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.003{{c}}, ~5/4 = 384.078{{c}}

{{Optimal ET sequence|legend=1| 17, 24, 31, 41, 72, 312bd, 384bcd, 456bcde, 528bcde, 631bcde }}

[[Badness]]: 0.641 × 10-3

[[Badness]] (Smith): 0.641 × 10-3

== Mirage ==

Line 126:

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000, ~15/14 = 116.711, ~13/8 = 840.528

* [[CTE]]: ~2 = 1200.000{{c}}, ~15/14 = 116.711{{c}}, ~13/8 = 840.528{{c}}

* [[CWE]]: ~2 = 1200.000, ~15/14 = 116.647, ~13/8 = 838.212

* [[CWE]]: ~2 = 1200.000{{c}}, ~15/14 = 116.647{{c}}, ~13/8 = 838.212{{c}}

{{Optimal ET sequence|legend=1| 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef }}

Badness: 0.738 × 10-3

Badness (Smith): 0.738 × 10-3

=== 17-limit===

Line 141:

Optimal tunings:

* CTE: ~2 = 1200.000, ~15/14 = 116.704, ~13/8 = 839.452

* CTE: ~2 = 1200.000{{c}}, ~15/14 = 116.704{{c}}, ~13/8 = 839.452{{c}}

* CWE: ~2 = 1200.000, ~15/14 = 116.640, ~13/8 = 837.142

* CWE: ~2 = 1200.000{{c}}, ~15/14 = 116.640{{c}}, ~13/8 = 837.142{{c}}

Line 156:

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000, ~11/9 = 350.145, ~5/4 = 389.708

* [[CTE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.145{{c}}, ~5/4 = 389.708{{c}}

* [[CWE]]: ~2 = 1200.000, ~11/9 = 350.555, ~5/4 = 390.269

* [[CWE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.555{{c}}, ~5/4 = 390.269{{c}}

[[Badness]]: 0.751 × 10-3

[[Badness]] (Smith): 0.751 × 10-3

=== 13-limit ===

Line 171:

Optimal tunings:

* CTE: ~2 = 1200.000, ~11/9 = 350.293, ~5/4 = 389.979

* CTE: ~2 = 1200.000{{c}}, ~11/9 = 350.293{{c}}, ~5/4 = 389.979{{c}}

* CWE: ~2 = 1200.000, ~11/9 = 351.155, ~5/4 = 391.123

* CWE: ~2 = 1200.000{{c}}, ~11/9 = 351.155{{c}}, ~5/4 = 391.123{{c}}

Badness: 0.923 × 10-3

Badness (Smith): 0.923 × 10-3

== Parahemif ==

Line 188:

: mapping generators: ~2, ~896/729, ~5

[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000, ~896/729 = 351.416, ~5/4 = 386.314

[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~896/729 = 351.416{{c}}, ~5/4 = 386.314{{c}}

{{Optimal ET sequence|legend=1| 17c, 24, 34d, 41, 58, 99, 239, 338 }}

[[Badness]]: 0.607 × 10-3

[[Badness]] (Smith): 0.607 × 10-3

=== 11-limit ===

Line 202:

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000, ~11/9 = 351.320, ~5/4 = 386.314

* [[CTE]]: ~2 = 1200.000{{c}}, ~11/9 = 351.320{{c}}, ~5/4 = 386.314{{c}}

* [[CWE]]: ~2 = 1200.000, ~11/9 = 351.459, ~5/4 = 387.423

* [[CWE]]: ~2 = 1200.000{{c}}, ~11/9 = 351.459{{c}}, ~5/4 = 387.423{{c}}

{{Optimal ET sequence|legend=1| 17c, 24, 34d, 41, 58, 99e }} *

Line 209:

<nowiki>*</nowiki> [[optimal patent val]]: [[123edo|123]]

[[Badness]]: 1.34547 × 10-3

[[Badness]] (Smith): 1.34547 × 10-3

=== 13-limit ===

Line 219:

Optimal tunings:

* CTE: ~2 = 1200.000, ~11/9 = 351.343, ~5/4 = 386.314

* CTE: ~2 = 1200.000{{c}}, ~11/9 = 351.343{{c}}, ~5/4 = 386.314{{c}}

* CWE: ~2 = 1200.000, ~11/9 = 351.604, ~5/4 = 388.472

* CWE: ~2 = 1200.000{{c}}, ~11/9 = 351.604{{c}}, ~5/4 = 388.472{{c}}

{{Optimal ET sequence|legend=0| 17c, 24, 34d, 41, 58, 99ef, 157eff, 290cdeeefff }}

Badness: 1.19366 × 10-3

Badness (Smith): 1.19366 × 10-3

== Urania ==

Line 240:

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1200.000, ~11/9 = 348.830, ~7/4 = 968.826

* [[CTE]]: ~2 = 1200.000{{c}}, ~11/9 = 348.830{{c}}, ~7/4 = 968.826{{c}}

* [[CWE]]: ~2 = 1200.000, ~11/9 = 348.379, ~7/4 = 965.630

* [[CWE]]: ~2 = 1200.000{{c}}, ~11/9 = 348.379{{c}}, ~7/4 = 965.630{{c}}

{{Optimal ET sequence|legend=1| 7, 14c, 17c, 24, 31, 100de, 131bde, 162bde }}

[[Badness]]: 0.842 × 10-3

[[Badness]] (Smith): 0.842 × 10-3

[[Complexity spectrum]]: 11/9, 4/3, 12/11, 11/10, 10/9, 9/8, 11/8, 6/5, 5/4, 8/7, 7/6, 9/7, 14/11, 7/5

Scales: [[urania24]]

== References ==

[[Category:Temperament clans]]

@@ Line 5: / Line 5: @@
 * [[Jove]] (+441/440 or 540/539) → [[Breed family #Jove|Breed family]]
 * ''[[Hagrid]]'' (+9801/9800) → [[Cataharry family #Hagrid|Cataharry family]]
-* ''[[Rabic]]'' (+131769/131072) → [[Alphaxenic rank three clan #Betarabian|Alphaxenic rank-3 clan]]
+* ''[[Rabic]]'' (+131769/131072) → [[Alphaxenic rank-3 clan #Betarabian|Alphaxenic rank-3 clan]]
 == Spectacle ==
-Spectacle, named by [[Gene Ward Smith]] in 2010<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_17700.html Yahoo! Tuning Group | ''Spectacle temperament?'']</ref>, can be described as the 31 & 34 & 41 temperament. It tempers out 225/224, making it a sort of marvel infested with neutral thirds. It is therefore generated by octaves, major thirds, and neutral thirds. 3/2 is equated with two a stack of two 11/9's as a corollary of 243/242 being tempered out, 7/4 is equated with a stack of four 11/9's and two 5/4's, 11/8 is equated with a stack of five 11/9's, 13/8 is equated with a stack of two 18/11's and four 5/4's, and 17/16 is equated with three 18/11's and three 5/4's. Every harmonic is reached with help of other intervals at most with three 5/4's.
+Spectacle, named by [[Gene Ward Smith]] in 2010<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_17700.html Yahoo! Tuning Group | ''Spectacle temperament?'']</ref>, can be described as the {{nowrap| 31 & 34 & 41 }} temperament. It tempers out 225/224, making it a sort of marvel infested with neutral thirds. It is therefore generated by octaves, major thirds, and neutral thirds. 3/2 is equated with a stack of two 11/9's as a corollary of 243/242 being tempered out, 7/4 is equated with a stack of four 11/9's and two 5/4's, 11/8 is equated with a stack of five 11/9's, 13/8 is equated with a stack of two 18/11's and four 5/4's, and 17/16 is equated with three 18/11's and three 5/4's. Every harmonic is reached with help of other intervals at most with three 5/4's.
 [[Subgroup]]: 2.3.5.7.11
@@ Line 19: / Line 19: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1200.000, ~11/9 = 350.377, ~5/4 = 384.370
+* [[CTE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.377{{c}}, ~5/4 = 384.370{{c}}
-* [[CWE]]: ~2 = 1200.000, ~11/9 = 350.176, ~5/4 = 384.095
+* [[CWE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.176{{c}}, ~5/4 = 384.095{{c}}
 [[Minimax tuning]]:
@@ Line 28: / Line 28: @@
 {{Optimal ET sequence|legend=1| 31, 41, 72, 247c, 281, 353c, 425bc, 497bc }}
-[[Badness]]: 0.499 × 10<sup>-3</sup>
+[[Badness]] (Smith): 0.499 × 10<sup>-3</sup>
 [[Projection pair]]s: 3 242/81, 7 366025/52488, 11 644204/59049 to 2.5.11/9
@@ Line 44: / Line 44: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~11/9 = 350.239, ~5/4 = 384.998
+* CTE: ~2 = 1200.000{{c}}, ~11/9 = 350.239{{c}}, ~5/4 = 384.998{{c}}
-* CWE: ~2 = 1200.000, ~11/9 = 350.039, ~5/4 = 384.587
+* CWE: ~2 = 1200.000{{c}}, ~11/9 = 350.039{{c}}, ~5/4 = 384.587{{c}}
 {{Optimal ET sequence|legend=0| 31, 72, 103, 175f }} <nowiki>*</nowiki>
@@ Line 51: / Line 51: @@
 <nowiki>*</nowiki> optimal patent val: [[240edo|240]]
-Badness: 1.009 × 10<sup>-3</sup>
+Badness (Smith): 1.009 × 10<sup>-3</sup>
 == Cuckoo ==
@@ Line 63: / Line 63: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1200.000, ~11/9 = 350.355, ~5/4 = 389.555
+* [[CTE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.355{{c}}, ~5/4 = 389.555{{c}}
-* [[CWE]]: ~2 = 1200.000, ~11/9 = 350.421, ~5/4 = 389.731
+* [[CWE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.421{{c}}, ~5/4 = 389.731{{c}}
 {{Optimal ET sequence|legend=1| 24d, 27e, 31, 58, 89, 154, 185 }}
-[[Badness]]: 0.933 × 10<sup>-3</sup>
+[[Badness]] (Smith): 0.933 × 10<sup>-3</sup>
 === 13-limit ===
@@ Line 78: / Line 78: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~11/9 = 350.585, ~5/4 = 389.302
+* CTE: ~2 = 1200.000{{c}}, ~11/9 = 350.585{{c}}, ~5/4 = 389.302{{c}}
-* CWE: ~2 = 1200.000, ~11/9 = 350.568, ~5/4 = 389.610
+* CWE: ~2 = 1200.000{{c}}, ~11/9 = 350.568{{c}}, ~5/4 = 389.610{{c}}
 {{Optimal ET sequence|legend=0| 27e, 31, 58, 96d, 154 }}
@@ Line 95: / Line 95: @@
 : mapping generators: ~2, ~128/105, ~5
-[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000, ~128/105 = 350.174, ~5/4 = 384.014
+[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~128/105 = 350.174{{c}}, ~5/4 = 384.014{{c}}
 {{Optimal ET sequence|legend=1| 17, 21, 24, 31, 41, 72, 281d }}
-[[Badness]]: 0.770 × 10<sup>-3</sup>
+[[Badness]] (Smith): 0.770 × 10<sup>-3</sup>
 === 11-limit ===
@@ Line 109: / Line 109: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1200.000, ~11/9 = 350.217, ~5/4 = 383.962
+* [[CTE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.217{{c}}, ~5/4 = 383.962{{c}}
-* [[CWE]]: ~2 = 1200.000, ~11/9 = 350.003, ~5/4 = 384.078
+* [[CWE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.003{{c}}, ~5/4 = 384.078{{c}}
 {{Optimal ET sequence|legend=1| 17, 24, 31, 41, 72, 312bd, 384bcd, 456bcde, 528bcde, 631bcde }}
-[[Badness]]: 0.641 × 10<sup>-3</sup>
+[[Badness]] (Smith): 0.641 × 10<sup>-3</sup>
 == Mirage ==
@@ Line 126: / Line 126: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1200.000, ~15/14 = 116.711, ~13/8 = 840.528
+* [[CTE]]: ~2 = 1200.000{{c}}, ~15/14 = 116.711{{c}}, ~13/8 = 840.528{{c}}
-* [[CWE]]: ~2 = 1200.000, ~15/14 = 116.647, ~13/8 = 838.212
+* [[CWE]]: ~2 = 1200.000{{c}}, ~15/14 = 116.647{{c}}, ~13/8 = 838.212{{c}}
 {{Optimal ET sequence|legend=1| 10, 31, 41, 62, 72, 103, 175f, 216c, 288cdf, 391bcdef }}
-Badness: 0.738 × 10<sup>-3</sup>
+Badness (Smith): 0.738 × 10<sup>-3</sup>
 === 17-limit===
@@ Line 141: / Line 141: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~15/14 = 116.704, ~13/8 = 839.452
+* CTE: ~2 = 1200.000{{c}}, ~15/14 = 116.704{{c}}, ~13/8 = 839.452{{c}}
-* CWE: ~2 = 1200.000, ~15/14 = 116.640, ~13/8 = 837.142
+* CWE: ~2 = 1200.000{{c}}, ~15/14 = 116.640{{c}}, ~13/8 = 837.142{{c}}
 {{Optimal ET sequence|legend=0| 10, 31, 41, 62, 72, 103, 175f }}
@@ Line 156: / Line 156: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1200.000, ~11/9 = 350.145, ~5/4 = 389.708
+* [[CTE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.145{{c}}, ~5/4 = 389.708{{c}}
-* [[CWE]]: ~2 = 1200.000, ~11/9 = 350.555, ~5/4 = 390.269
+* [[CWE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.555{{c}}, ~5/4 = 390.269{{c}}
 {{Optimal ET sequence|legend=1| 7, 24, 31, 58, 89 }}
-[[Badness]]: 0.751 × 10<sup>-3</sup>
+[[Badness]] (Smith): 0.751 × 10<sup>-3</sup>
 === 13-limit ===
@@ Line 171: / Line 171: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~11/9 = 350.293, ~5/4 = 389.979
+* CTE: ~2 = 1200.000{{c}}, ~11/9 = 350.293{{c}}, ~5/4 = 389.979{{c}}
-* CWE: ~2 = 1200.000, ~11/9 = 351.155, ~5/4 = 391.123
+* CWE: ~2 = 1200.000{{c}}, ~11/9 = 351.155{{c}}, ~5/4 = 391.123{{c}}
 {{Optimal ET sequence|legend=0| 7, 24, 31, 58 }}
-Badness: 0.923 × 10<sup>-3</sup>
+Badness (Smith): 0.923 × 10<sup>-3</sup>
 == Parahemif ==
@@ Line 188: / Line 188: @@
 : mapping generators: ~2, ~896/729, ~5
-[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000, ~896/729 = 351.416, ~5/4 = 386.314
+[[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~896/729 = 351.416{{c}}, ~5/4 = 386.314{{c}}
 {{Optimal ET sequence|legend=1| 17c, 24, 34d, 41, 58, 99, 239, 338 }}
-[[Badness]]: 0.607 × 10<sup>-3</sup>
+[[Badness]] (Smith): 0.607 × 10<sup>-3</sup>
 === 11-limit ===
@@ Line 202: / Line 202: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1200.000, ~11/9 = 351.320, ~5/4 = 386.314
+* [[CTE]]: ~2 = 1200.000{{c}}, ~11/9 = 351.320{{c}}, ~5/4 = 386.314{{c}}
-* [[CWE]]: ~2 = 1200.000, ~11/9 = 351.459, ~5/4 = 387.423
+* [[CWE]]: ~2 = 1200.000{{c}}, ~11/9 = 351.459{{c}}, ~5/4 = 387.423{{c}}
 {{Optimal ET sequence|legend=1| 17c, 24, 34d, 41, 58, 99e }} *
@@ Line 209: / Line 209: @@
 <nowiki>*</nowiki> [[optimal patent val]]: [[123edo|123]]
-[[Badness]]: 1.34547 × 10<sup>-3</sup>
+[[Badness]] (Smith): 1.34547 × 10<sup>-3</sup>
 === 13-limit ===
@@ Line 219: / Line 219: @@
 Optimal tunings:
-* CTE: ~2 = 1200.000, ~11/9 = 351.343, ~5/4 = 386.314
+* CTE: ~2 = 1200.000{{c}}, ~11/9 = 351.343{{c}}, ~5/4 = 386.314{{c}}
-* CWE: ~2 = 1200.000, ~11/9 = 351.604, ~5/4 = 388.472
+* CWE: ~2 = 1200.000{{c}}, ~11/9 = 351.604{{c}}, ~5/4 = 388.472{{c}}
 {{Optimal ET sequence|legend=0| 17c, 24, 34d, 41, 58, 99ef, 157eff, 290cdeeefff }}
-Badness: 1.19366 × 10<sup>-3</sup>
+Badness (Smith): 1.19366 × 10<sup>-3</sup>
 == Urania  ==
@@ Line 240: / Line 240: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~2 = 1200.000, ~11/9 = 348.830, ~7/4 = 968.826
+* [[CTE]]: ~2 = 1200.000{{c}}, ~11/9 = 348.830{{c}}, ~7/4 = 968.826{{c}}
-* [[CWE]]: ~2 = 1200.000, ~11/9 = 348.379, ~7/4 = 965.630
+* [[CWE]]: ~2 = 1200.000{{c}}, ~11/9 = 348.379{{c}}, ~7/4 = 965.630{{c}}
 {{Optimal ET sequence|legend=1| 7, 14c, 17c, 24, 31, 100de, 131bde, 162bde }}
-[[Badness]]: 0.842 × 10<sup>-3</sup>
+[[Badness]] (Smith): 0.842 × 10<sup>-3</sup>
 [[Complexity spectrum]]: 11/9, 4/3, 12/11, 11/10, 10/9, 9/8, 11/8, 6/5, 5/4, 8/7, 7/6, 9/7, 14/11, 7/5
 Scales: [[urania24]]
+== References ==
 [[Category:Temperament clans]]