Dimcomp family: Difference between revisions

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-The '''dimcomp family''' of rank-three temperaments tempers out the [[dimcomp comma]], 390625/388962.
+{{Technical data page}}
+The '''dimcomp family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[dimcomp comma]] ({{monzo|legend=1| -1 -4 8 -4 }}, [[ratio]]: 390625/388962).
 == Dimcomp ==
-Commas: 390625/388962
+[[Subgroup]]: 2.3.5.7
-Map: [&lt;4 0 0 -1|, &lt;0 1 0 -1|, &lt;0 0 1 2|]
+[[Comma list]]: 390625/388962
-EDOs: 12, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952
+{{Mapping|legend=1| 4 0 0 -1 | 0 1 0 -1 | 0 0 1 2 }}
+: mapping generators: ~25/21, ~3, ~5
-Badness: 0.000783
+[[Optimal tuning]]s:
+* [[WE]]: ~25/21 = 300.0036{{c}}, ~3/2 = 702.0854{{c}}, ~5/4 = 385.6631{{c}}
+: [[error map]]: {{val| +0.014 +0.145 -0.622 +0.454 }}
+* [[CWE]]: ~25/21 = 300.0000{{c}}, ~3/2 = 702.0885{{c}}, ~5/4 = 385.6745{{c}}
+: error map: {{val| 0.000 +0.133 -0.639 +0.435 }}
-=== 11-limit ===
+{{Optimal ET sequence|legend=1| 12, 44d, 48d, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952 }}
-Commas: 1375/1372, 6250/6237
-Map: [&lt;4 0 0 -1 5|, &lt;0 1 0 -1 -3|, &lt;0 0 1 2 3|]
+[[Badness]] (Sintel): 3.45
-EDOs: 12, 68, 72, 140, 152, 224, 364, 436, 588
+== Undecimal dimcomp ==
+[[Subgroup]]: 2.3.5.7.11
-Badness: 0.000624
+[[Comma list]]: 1375/1372, 6250/6237
+{{Mapping|legend=1| 4 0 0 -1 5 | 0 1 0 -1 -3 | 0 0 1 2 3 }}
+[[Optimal tuning]]s:
+* [[WE]]: ~25/21 = 300.0093{{c}}, ~3/2 = 701.9976{{c}}, ~5/4 = 385.6591{{c}}
+: [[error map]]: {{val| +0.037 +0.080 -0.580 +0.597 -0.176 }}
+* [[CWE]]: ~25/21 = 300.0000{{c}}, ~3/2 = 702.0009{{c}}, ~5/4 = 385.6895{{c}}
+: error map: {{val| 0.000 +0.046 -0.624 +0.552 -0.252 }}
+{{Optimal ET sequence|legend=1| 12, …, 68, 72, 140, 152, 224, 364, 436, 588 }}
+[[Badness]] (Sintel): 0.751
 === 13-limit ===
-Commas: 625/624, 1375/1372, 2080/2079
+Subgroup: 2.3.5.7.11.13
-Map: [&lt;4 0 0 -1 5 -16|, &lt;0 1 0 -1 -3 -1|, &lt;0 0 1 2 3 4|]
+Comma list: 625/624, 1375/1372, 2080/2079
-EDOs: 68, 72, 140, 212, 224, 364, 436, 588, 660
+Mapping: {{mapping| 4 0 0 -1 5 -16 | 0 1 0 -1 -3 -1 | 0 0 1 2 3 4 }}
-Badness: 0.000820
+Optimal tunings:
+* WE: ~25/21 = 300.0140{{c}}, ~3/2 = 701.9679{{c}}, ~5/4 = 385.5977{{c}}
+* CWE: ~25/21 = 300.0000{{c}}, ~3/2 = 701.9549{{c}}, ~5/4 = 385.6140{{c}}
+{{Optimal ET sequence|legend=0| 68, 72, 140, 152f, 212, 224, 364, 436, 588, 660, 1024c }}
+Badness (Sintel): 0.767
 == Octopod ==
-Commas: 540/539, 1375/1372, 4000/3993
+Octopod is [[octoid]] with an independent generator for [[prime interval|prime]] [[13/1|13]].
+[[Subgroup]]: 2.3.5.7.11.13
+[[Comma list]]: 540/539, 1375/1372, 4000/3993
+{{Mapping|legend=1| 8 1 3 3 16 0 | 0 3 4 5 3 0 | 0 0 0 0 0 1 }}
+: mapping generators: ~12/11, ~7/5, ~13
-Map: [&lt;8 1 3 3 16 0|, &lt;0 3 4 5 3 0|, &lt;0 0 0 0 0 1|]
+[[Optimal tuning]]s:
+* [[WE]]: ~12/11 = 150.0093{{c}}, ~7/5 = 583.9356{{c}}, ~13/8 = 840.6906{{c}}
+: [[error map]]: {{val| -0.055 -0.155 -0.592 +0.832 +0.380 -0.001 }}
+* [[CWE]]: ~12/11 = 150.0000{{c}}, ~7/5 = 583.9477{{c}}, ~13/8 = 840.6394{{c}}
+: error map: {{val| 0.000 -0.112 -0.523 +0.913 +0.525 +0.112 }}
-EDOs: 72, 144, 152, 224
+{{Optimal ET sequence|legend=1| 72, 144, 152f, 224, 824d }}
-Badness: 0.001244
+[[Badness]] (Sintel): 1.16
-[[Category:Theory]]
+[[Category:Temperament families]]
-[[Category:Temperament family]]
+[[Category:Dimcomp family| ]] <!-- main article -->
-[[Category:Dimcomp]]
 [[Category:Rank 3]]