Single-pitch tuning: Difference between revisions

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== In regular temperament theory ==

Single-pitch tuning corresponds to the [[regular temperament]] in any given [[subgroup]] where all [[prime]]s in that subgroup are [[tempering out|tempered out]], resulting in a rank-0 temperament with no [[generator]]. The mapping for this is the 0-val, {{val| 0 0 … 0 }}, or more precisely, the rank-0 matrix, [ ].

Single-pitch tuning corresponds to the [[regular temperament]] in any given [[subgroup]] where all [[prime]]s in that subgroup are [[tempering out|tempered out]], resulting in a rank-0 temperament with no [[generator]]. The mapping for this is the 0-val, {{val| 0 0 … 0 }}, or more precisely, the rank-0 matrix, [ ]. Since it maps all intervals to the same pitch, it [[tempering out|tempers out]] all commas and is [[consistent]] in all [[limit]]s.

~~Being an example of~~ a [[~~trivial temperament~~]], single-pitch tuning ~~[[tempering out|tempers out]] everything~~, ~~and~~ is ~~[[consistent]] in~~ all [[~~limit~~]]s.

Single-pitch tuning can also be considered a rank-0 temperament in the empty subgroup, which contains no primes. It tempers no commas and the pitch represents only the [[1/1|unison]], so it is also empty-subgroup JI. (Tempering everything and tempering nothing are the same in this case, because there is nothing to temper.) This is closer to representing how single-pitch tuning is actually used, when it is used at all.

Both are examples of [[trivial temperament]]s.

== Music ==

@@ Line 20: / Line 20: @@
 == In regular temperament theory ==
-Single-pitch tuning corresponds to the [[regular temperament]] in any given [[subgroup]] where all [[prime]]s in that subgroup are [[tempering out|tempered out]], resulting in a rank-0 temperament with no [[generator]]. The mapping for this is the 0-val, {{val| 0 0 … 0 }}, or more precisely, the rank-0 matrix, [&nbsp;].
+Single-pitch tuning corresponds to the [[regular temperament]] in any given [[subgroup]] where all [[prime]]s in that subgroup are [[tempering out|tempered out]], resulting in a rank-0 temperament with no [[generator]]. The mapping for this is the 0-val, {{val| 0 0 … 0 }}, or more precisely, the rank-0 matrix, [&nbsp;]. Since it maps all intervals to the same pitch, it [[tempering out|tempers out]] all commas and is [[consistent]] in all [[limit]]s.
-Being an example of a [[trivial temperament]], single-pitch tuning [[tempering out|tempers out]] everything, and is [[consistent]] in all [[limit]]s.
+Single-pitch tuning can also be considered a rank-0 temperament in the empty subgroup, which contains no primes. It tempers no commas and the pitch represents only the [[1/1|unison]], so it is also empty-subgroup JI. (Tempering everything and tempering nothing are the same in this case, because there is nothing to temper.) This is closer to representing how single-pitch tuning is actually used, when it is used at all.
+Both are examples of [[trivial temperament]]s.
 == Music ==