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]]. All rank-2 temperaments generated by 3/2 and 2/1 in the 5-limit or higher are extensions of pythagorean. | ||
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]]. | 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]]. | ||