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]]s tempers out the [[dimcomp comma]], 390625/388962.


== Dimcomp ==
== Dimcomp ==
[[Subgroup]]: 2.3.5.7


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


Map: [<4 0 0 -1|, <0 1 0 -1|, <0 0 1 2|]
{{Mapping|legend=1| 4 0 0 -1 | 0 1 0 -1 | 0 0 1 2 }}


EDOs: {{EDOs| 12, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952 }}
: mapping generators: ~25/21, ~3, ~5


Badness: 0.000783
{{Optimal ET sequence|legend=1| 8d, 12, 44d, 48d, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952 }}


=== 11-limit ===
[[Badness]]: 0.783 × 10<sup>-3</sup>


Commas: 1375/1372, 6250/6237
== Undecimal dimcomp ==
[[Subgroup]]: 2.3.5.7.11


Map: [&lt;4 0 0 -1 5|, &lt;0 1 0 -1 -3|, &lt;0 0 1 2 3|]
[[Comma list]]: 1375/1372, 6250/6237


EDOs: {{EDOs| 12, 68, 72, 140, 152, 224, 364, 436, 588 }}
{{Mapping|legend=1| 4 0 0 -1 5 | 0 1 0 -1 -3 | 0 0 1 2 3 }}


Badness: 0.000624
{{Optimal ET sequence|legend=1| 68, 72, 140, 152, 224, 364, 436, 588 }}
 
[[Badness]]: 0.624 × 10<sup>-3</sup>


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


Commas: 625/624, 1375/1372, 2080/2079
Comma list: 625/624, 1375/1372, 2080/2079


Map: [&lt;4 0 0 -1 5 -16|, &lt;0 1 0 -1 -3 -1|, &lt;0 0 1 2 3 4|]
Mapping: {{mapping| 4 0 0 -1 5 -16 | 0 1 0 -1 -3 -1 | 0 0 1 2 3 4 }}


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


Badness: 0.000820
Badness: 0.820 × 10<sup>-3</sup>


== Octopod ==
== Octopod ==
Subgroup: 2.3.5.7.11.13


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


Map: [&lt;8 1 3 3 16 0|, &lt;0 3 4 5 3 0|, &lt;0 0 0 0 0 1|]
Mapping: {{mapping| 8 1 3 3 16 0 | 0 3 4 5 3 0 | 0 0 0 0 0 1 }}


EDOs: {{EDOs| 72, 144, 152, 224 }}
{{Optimal ET sequence|legend=1| 72, 144, 152f, 224, 824d }}


Badness: 0.001244
Badness: 1.244 × 10<sup>-3</sup>


[[Category:Theory]]
[[Category:Temperament families]]
[[Category:Temperament family]]
[[Category:Pages with mostly numerical content]]
[[Category:Dimcomp]]
[[Category:Dimcomp family| ]] <!-- main article -->
[[Category:Dimcomp| ]] <!-- key article -->
[[Category:Rank 3]]
[[Category:Rank 3]]

Latest revision as of 00:31, 24 June 2025

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The dimcomp family of rank-3 temperaments tempers out the dimcomp comma, 390625/388962.

Dimcomp

Subgroup: 2.3.5.7

Comma list: 390625/388962

Mapping: [⟨4 0 0 -1], ⟨0 1 0 -1], ⟨0 0 1 2]]

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

Optimal ET sequence: 8d, 12, 44d, 48d, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952

Badness: 0.783 × 10-3

Undecimal dimcomp

Subgroup: 2.3.5.7.11

Comma list: 1375/1372, 6250/6237

Mapping: [⟨4 0 0 -1 5], ⟨0 1 0 -1 -3], ⟨0 0 1 2 3]]

Optimal ET sequence: 68, 72, 140, 152, 224, 364, 436, 588

Badness: 0.624 × 10-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 625/624, 1375/1372, 2080/2079

Mapping: [⟨4 0 0 -1 5 -16], ⟨0 1 0 -1 -3 -1], ⟨0 0 1 2 3 4]]

Optimal ET sequence: 68, 72, 140, 152f, 212, 224, 364, 436, 588, 660, 1024c

Badness: 0.820 × 10-3

Octopod

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨8 1 3 3 16 0], ⟨0 3 4 5 3 0], ⟨0 0 0 0 0 1]]

Optimal ET sequence: 72, 144, 152f, 224, 824d

Badness: 1.244 × 10-3

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