Associated temperament: Difference between revisions

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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.

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 [[cocmma basis]] for the rank-2 temperament.

== 7-limit ==

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| 56/55

| [[36edo]]

| [[~~Catcall~~]]

| [[Catnip]]

| 56/55, 81/80, 128/125

|-

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-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.
+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 [[cocmma basis]] for the rank-2 temperament.
 == 7-limit ==
@@ Line 195: / Line 195: @@
 | 56/55
 | [[36edo]]
-| [[Catcall]]
+| [[Catnip]]
 | 56/55, 81/80, 128/125
 |-