Rastmic rank-3 clan: Difference between revisions

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 * [[Jove]] (+441/440 or 540/539) → [[Breed family #Jove|Breed family]]
 * ''[[Hagrid]]'' (+9801/9800) → [[Cataharry family #Hagrid|Cataharry family]]
-* ''[[Rabic]]'' (+131769/131072) → [[Alphaxenic rank-3 clan #Betarabian|Alphaxenic rank-3 clan]]
-Considered below are spectacle, mirwomo, mandos, cuckoo, parahemif, urania, and mirage.
+Considered below are spectacle, mirwomo, mandos, cuckoo, parahemif, urania, rabic, and mirage.
 == Spectacle ==
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 {{Mapping|legend=1| 1 1 0 -3 2 | 0 2 0 4 5 | 0 0 1 2 0 }}
 : mapping generators: ~2, ~11/9, ~5
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 {{Mapping|legend=1| 1 1 0 6 2 | 0 2 0 -3 5 | 0 0 1 -1 0 }}
+: mapping generators: ~2, ~11/9, ~5
 [[Optimal tuning]]s:
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 {{Mapping|legend=1| 1 1 0 6 2 | 0 2 0 5 5 | 0 0 1 -2 0 }}
 : mapping generators: ~2, ~11/9, ~5
@@ Line 122: / Line 120: @@
 {{Mapping|legend=1| 1 1 0 -3 2 | 0 2 0 -4 5 | 0 0 1 3 0 }}
 : mapping generators: ~2, ~11/9, ~5
@@ Line 160: / Line 157: @@
 {{Mapping|legend=1| 1 1 0 -1 2 | 0 2 0 13 5 | 0 0 1 0 0 }}
+: mapping generators: ~2, ~11/9, ~5
 [[Optimal tuning]]s:
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 {{Mapping|legend=1| 1 1 0 0 2 | 0 2 8 0 5 | 0 0 0 1 0 }}
 : mapping generators: ~2, ~11/9, ~7
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 Scales: [[urania24]]
+== Rabic ==
+If the rastma is added to the list of commas along with the [[Alpharabian comma]], you end up with rabic, which splits the octave into 24 equal parts. This temperament is named as such by [[Aura]] in 2022 because tempering out both the Alpharabian comma and the rastma automatically tempers out the [[Betarabian comma]].
+[[Subgroup]]: 2.3.5.7.11
+[[Comma list]]: 243/242, 131769/131072
+{{Mapping|legend=1| 24 38 0 0 83 | 0 0 1 0 0 | 0 0 0 1 0 }}
+: mapping generators: ~33/32, ~5, ~7
+[[Optimal tuning]]s:
+* [[WE]]: ~33/32 = 50.0220{{c}}, ~5/4 = 385.0647{{c}}, ~7/4 = 967.3158{{c}}
+: [[error map]]: {{val| +0.538 -1.104 -0.002 -0.002 +0.541 }}
+* [[CWE]]: ~33/32 = 50.0000{{c}}, ~5/4 = 385.0647{{c}}, ~7/4 = 967.3158{{c}}
+: error map: {{val| 0.000 -1.955 -0.937 -1.133 -1.318 }}
+{{Optimal ET sequence|legend=1| 24, 48(d), 72, 264, 336b, 408b, 480bcde }}
+[[Badness]] (Sintel): 7.30
+=== Gunn ===
+{{Todo|inline=1|complete section|unify precision|comment= Sort the comma basis. Normalize the mapping. Unify the cent values in optimal tunings to 4 decimal places. Add the optimal ET sequence. <br>Add the data for the 13- and 17-limit versions. }}
+==== 19-limit ====
+Subgroup: 2.3.5.7.11.13.17.19
+Comma list: 729/728, 273/272, 153/152, 364/363, 1729/1728
+Mapping: {{mapping| 24 38 48 48 83 108 98 102 | 0 0 1 0 0 0 0 0 | 0 0 0 1 0 -1 0 0 }}
+Optimal tunings:
+* WE: ~33/32 = 50.030{{c}}, ~5/4 = 384.859{{c}}, ~7/4 = 965.679{{c}}
+: error map: {{val| +0.724 -0.809 -0.007 -1.700 +1.185 -2.949 -2.000 +5.563 }}
+* CWE: ~33/32 = 50.000{{c}}, ~5/4 = 384.837{{c}}, ~7/4 = 965.136{{c}}
+: error map: {{val| -0.000 -1.955 -1.476 -3.690 -1.318 -5.663 -4.955 2.487 }}
+Supporting ETs: {{Edos| 24p, 72, 48f, 24c, 24df, 48cf, 48d, 96d, 48cd, 24cdf }}
+Badness (Sintel): 3.285
 == Mirage ==
 Mirage is [[miracle]] with an independent generator for prime 13.
 [[Subgroup]]: 2.3.5.7.11.13
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 {{Mapping|legend=1| 1 1 3 3 2 0 | 0 6 -7 -2 15 0 | 0 0 0 0 0 1 }}
 : mapping generators: ~2, ~15/14, ~13
 [[Optimal tuning]]s:
-* [[WE]]: ~2 = 1200.7626{{c}}, ~15/4 = 116.7069{{c}}, ~13/8 = 838.2364{{c}}
+* [[WE]]: ~2 = 1200.7626{{c}}, ~15/14 = 116.7069{{c}}, ~13/8 = 838.2364{{c}}
 : [[error map]]: {{val| +0.763 -0.951 -0.974 +0.048 +0.810 -0.004 }}
 * [[CWE]]: ~2 = 1200.0000{{c}}, ~15/14 = 116.6469{{c}}, ~13/8 = 838.2123{{c}}
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 === 17-limit ===
+Mirage is very naturally a 17-limit temperament, relating 13 and 17 by tempering out [[273/272]], [[715/714]], [[833/832]], and [[936/935]]. Instead of 13/8, the second generator can also be the small comma tempered out by [[miraculous]].
 Subgroup: 2.3.5.7.11.13.17
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 Badness (Sintel): 0.715
+=== 19-limit ===
+Subgroup: 2.3.5.7.11.13.17.19
+Comma list: 210/209, 225/224, 243/242, 273/272, 343/342
+{{Todo|complete temperament data|inline=1}}
+==== 23-limit ====
+Subgroup: 2.3.5.7.11.13.17.19.23
+Comma list: 210/209, 225/224, 243/242, 273/272, 300/299, 385/384
+{{Todo|complete temperament data|inline=1}}
+=== Prism ===
+{{Redirect|Prism|the scale|Prism (scale)}}
+Subgroup: 2.3.5.7.11.13.17.19
+Comma list: 225/224, 243/242, 273/272, 324/323, 385/384
+{{Todo|complete temperament data|inline=1}}
+==== 23-limit ====
+Subgroup: 2.3.5.7.11.13.17.19.23
+Comma list: 225/224, 243/242, 273/272, 300/299, 324/323, 385/384
+{{Todo|complete temperament data|inline=1}}
 == References ==
+[[Category:Rastmic rank-3 clan| ]] <!-- main article -->
 [[Category:Temperament clans]]
-[[Category:Rastmic rank-3 clan| ]] <!-- main article -->
+[[Category:Catalogs of rank-3 temperaments]]
-[[Category:Rastmic| ]] <!-- key article -->
-[[Category:Rank 3]]