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 | 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.