Associated temperament: Difference between revisions

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By an '''associated temperament''' to a ''p''-limit [[comma]] is meant a [[harmonic limit|''p''-limit]] [[regular temperament|temperament]] [[temper out|tempering out]] that comma which shares the same [[optimal patent val]] as the [[Rank and codimension|codimension one]] temperament tempering out that comma. By definition, the [[optimal patent val]] defines the unique [[ET|rank one]] associated temperament. For [[rank two temperaments]], it is possible for more than one temperament to be associated, and some of these are listed below. The column headings are the comma being associated, the optimal patent val, the rank two temperament, and a [[comma basis]] for the rank two temperament.
In [[regular temperament theory]], an '''associated temperament''' to a [[harmonic limit|''p''-limit]] [[comma]] is a ''p''-limit [[regular temperament]] [[tempering out]] that comma which shares the same [[optimal patent val]] as the [[codimension]]-1 temperament tempering out that comma. By definition, the optimal patent val defines the unique [[ET|rank-1]] associated temperament. For [[rank-2 temperament]]s, it is possible for more than one temperament to be associated, and some of these are listed below. The column headings are the comma being associated, the optimal patent val (OPV), the rank-2 temperament, and a [[comma basis]] for the rank-2 temperament.


== 7-limit ==
== 7-limit ==
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| [[36/35]]
| [[36/35]]
| [[12edo]]
| [[12edo]]
| [[Dominant]]
| [[Dominant (temperament)|Dominant]]
| 36/35, [[64/63]]
| 36/35, [[64/63]]
|-
|-
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| 56/55
| 56/55
| [[36edo]]
| [[36edo]]
| [[Catcall]]
| [[Catnip]]
| 56/55, 81/80, 128/125
| 56/55, 81/80, 128/125
|-
|-
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[[Category:Regular temperament theory]]
[[Category:Regular temperament theory]]
[[Category:Temperament]]
[[Category:Rank 2]]
[[Category:Rank 2]]