1/2-comma meantone: Difference between revisions
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Correct math and example. 33 is actually a closer approximation than 26. |
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In '''1/2-comma [[meantone]]''' temperament, each perfect fifth is tempered by a half of a [[syntonic comma]] from its just value of [[3/2]]. This results in minor sevenths being exactly [[9/5]] (and major seconds being exactly [[10/9]]). | In '''1/2-comma [[meantone]]''' temperament, each perfect fifth is tempered by a half of a [[syntonic comma]] from its just value of [[3/2]]. This results in minor sevenths being exactly [[9/5]] (and major seconds being exactly [[10/9]]). | ||
In this system, the "major thirds" are exactly [[100/81]] or approximately 365 [[cent]]s, thus bordering on neutral thirds. The fifths of this temperament fall between those of [[26edo]] and [[33edo], but closer to 33, which is the best small number candidate for a closed system approximating this meantime. | In this system, the "major thirds" are exactly [[100/81]] or approximately 365 [[cent]]s, thus bordering on neutral thirds. The fifths of this temperament fall between those of [[26edo]] and [[33edo]], but closer to 33, which is the best small number candidate for a closed system approximating this meantime. | ||
[[Category:Meantone]] | [[Category:Meantone]] | ||
Revision as of 20:15, 2 July 2020
In 1/2-comma meantone temperament, each perfect fifth is tempered by a half of a syntonic comma from its just value of 3/2. This results in minor sevenths being exactly 9/5 (and major seconds being exactly 10/9).
In this system, the "major thirds" are exactly 100/81 or approximately 365 cents, thus bordering on neutral thirds. The fifths of this temperament fall between those of 26edo and 33edo, but closer to 33, which is the best small number candidate for a closed system approximating this meantime.