Pythagorean tuning: Difference between revisions
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{{Wikipedia|Pythagorean tuning}} | {{Wikipedia|Pythagorean tuning}} | ||
The '''Pythagorean tuning''' is the 3-limit version of [[just intonation]]. It is the rank-2 temperament in the 2.3 subgroup that tempers out no commas. In other words, it is a [[trivial temperament]]. | The '''Pythagorean tuning''' is the 3-limit version of [[just intonation]]. It is the rank-2 temperament in the 2.3 subgroup that tempers out no commas. In other words, it is a [[trivial temperament]]. | ||
The Pythagorean temperament consists of all intervals generated by a just 3/2 and 2/1. Musically, the 2/1 is most often interpreted as an equave, and as such Pythagorean tuning mirrors the structure of the [[chain of fifths]]. | |||
See [[3-limit]] for more information. | See [[3-limit]] for more information. | ||
== Scales == | == Scales == | ||
Because Pythagorean tuning is a rank-2 temperament, its | Because Pythagorean tuning is a rank-2 temperament, the moment-of-symmetry scales generated by its fifth can be named the same way scales corresponding to other rank-2 temperaments are, as follows: | ||
* [[Pythagorean5]] – proper [[2L 3s]]. Also known as pythagorean pentic scale | * [[Pythagorean5]] – proper [[2L 3s]]. Also known as pythagorean pentic scale | ||
*[[Pythagorean7]] – improper [[5L 2s]]. Also known as pythagorean diatonic scale | *[[Pythagorean7]] – improper [[5L 2s]]. Also known as pythagorean diatonic scale | ||