Dimcomp family: Difference between revisions

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The '''dimcomp family''' of [[rank-3 temperament]]s tempers out the [[dimcomp comma]], 390625/388962.

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 ==

[[Subgroup]]: 2.3.5.7

[[Comma list]]: [[390625/388962]]

[[Comma list]]: 390625/388962

: mapping generators: ~25/21, ~3, ~5

: ~~mapping generators~~: ~25/21, ~3, ~5

[[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 }}

{{Optimal ET sequence|legend=1| ~~8d,~~ 12, 44d, 48d, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952 }}

{{Optimal ET sequence|legend=1| 12, 44d, 48d, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952 }}

[[Badness]]: 0.~~783 × 10-3~~

[[Badness]] (Sintel): 3.45

== Undecimal dimcomp ==

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{{Optimal ET sequence|legend=1| 68, 72, 140, 152, 224, 364, 436, 588 }}

[[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]]: 0.~~624 × 10-3~~

[[Badness]] (Sintel): 0.751

=== 13-limit ===

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Mapping: {{mapping| 4 0 0 -1 5 -16 | 0 1 0 -1 -3 -1 | 0 0 1 2 3 4 }}

{{~~Optimal ET sequence|legend~~=~~1| 68~~, 72, ~~140~~, ~~152f, 212, 224, 364, 436, 588, 660, 1024c~~ }}

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}}

Badness: 0.~~820 × 10-3~~

{{Optimal ET sequence|legend=0| 68, 72, 140, 152f, 212, 224, 364, 436, 588, 660, 1024c }}

Badness (Sintel): 0.767

== Octopod ==

Subgroup: 2.3.5.7.11.13

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

~~Comma list~~: ~~540~~/~~539~~, ~~1375~~/~~1372~~, ~~4000/3993~~

: mapping generators: ~12/11, ~7/5, ~13

~~Mapping~~: {{~~mapping~~| ~~8 1 3 3 16~~ 0 | 0 ~~3 4~~ 5 3 0 | 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 }}

Badness: 1.~~244 × 10-3~~

[[Badness]] (Sintel): 1.16

[[Category:Temperament families]]

~~[[Category:Pages with mostly numerical content]]~~

[[Category:Dimcomp family| ]]

~~[[Category:Dimcomp| ]] ~~

[[Category:Rank 3]]

@@ Line 1: / Line 1: @@
 {{Technical data page}}
-The '''dimcomp family''' of [[rank-3 temperament]]s tempers out the [[dimcomp comma]], 390625/388962.
+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 ==
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: [[390625/388962]]
+[[Comma list]]: 390625/388962
 {{Mapping|legend=1| 4 0 0 -1 | 0 1 0 -1 | 0 0 1 2 }}
+: mapping generators: ~25/21, ~3, ~5
-: mapping generators: ~25/21, ~3, ~5
+[[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 }}
-{{Optimal ET sequence|legend=1| 8d, 12, 44d, 48d, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952 }}
+{{Optimal ET sequence|legend=1| 12, 44d, 48d, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952 }}
-[[Badness]]: 0.783 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 3.45
 == Undecimal dimcomp ==
@@ Line 22: / Line 27: @@
 {{Mapping|legend=1| 4 0 0 -1 5 | 0 1 0 -1 -3 | 0 0 1 2 3 }}
-{{Optimal ET sequence|legend=1| 68, 72, 140, 152, 224, 364, 436, 588 }}
+[[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]]: 0.624 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.751
 === 13-limit ===
@@ Line 33: / Line 44: @@
 Mapping: {{mapping| 4 0 0 -1 5 -16 | 0 1 0 -1 -3 -1 | 0 0 1 2 3 4 }}
-{{Optimal ET sequence|legend=1| 68, 72, 140, 152f, 212, 224, 364, 436, 588, 660, 1024c }}
+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}}
-Badness: 0.820 × 10<sup>-3</sup>
+{{Optimal ET sequence|legend=0| 68, 72, 140, 152f, 212, 224, 364, 436, 588, 660, 1024c }}
+Badness (Sintel): 0.767
 == Octopod ==
-Subgroup: 2.3.5.7.11.13
+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
-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
-Mapping: {{mapping| 8 1 3 3 16 0 | 0 3 4 5 3 0 | 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 }}
 {{Optimal ET sequence|legend=1| 72, 144, 152f, 224, 824d }}
-Badness: 1.244 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 1.16
 [[Category:Temperament families]]
-[[Category:Pages with mostly numerical content]]
 [[Category:Dimcomp family| ]] <!-- main article -->
-[[Category:Dimcomp| ]] <!-- key article -->
 [[Category:Rank 3]]