9/8: Difference between revisions
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Two 9/8's stacked produce [[81/64]], the Pythagorean major third, a rather bright major third of approximately 407.8¢. However, a 9/8 plus the minor whole tone [[10/9]] yields [[5/4]]. This distinction, between a major whole tone and minor whole tone, has been completely obliterated in [[12edo]], and so we are unaccustomed to thinking of more than one size of whole tone comprising a major third. Other systems that temper out this difference (which is [[81/80]], the syntonic comma of about 21.5¢), such as [[19edo]], [[26edo]], and [[31edo]], are called [[meantone]] temperaments. | Two 9/8's stacked produce [[81/64]], the Pythagorean major third, a rather bright major third of approximately 407.8¢. However, a 9/8 plus the minor whole tone [[10/9]] yields [[5/4]]. This distinction, between a major whole tone and minor whole tone, has been completely obliterated in [[12edo]], and so we are unaccustomed to thinking of more than one size of whole tone comprising a major third. Other systems that temper out this difference (which is [[81/80]], the syntonic comma of about 21.5¢), such as [[19edo]], [[26edo]], and [[31edo]], are called [[meantone]] temperaments. | ||
A stack of six intervals of 9/8 exceeds the octave by the [[Pythagorean comma]]. | |||
== History == | == History == | ||
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== Temperaments == | == Temperaments == | ||
When this ratio is taken as a comma to be [[tempering out|tempered out]], it produces [[Very low accuracy temperaments #Antitonic|antitonic]] temperament. Edos that temper it out include [[2edo]] and [[4edo]]. If it is instead used as a generator, it produces, among others, [[Subgroup temperaments #Baldy|baldy]]. | When this ratio is taken as a comma to be [[tempering out|tempered out]], it produces [[Very low accuracy temperaments #Antitonic|antitonic]] temperament. Edos that temper it out include [[2edo]] and [[4edo]]. If it is instead used as a generator, it produces, among others, [[Subgroup temperaments #Baldy|baldy]]. | ||
== Approximation == | == Approximation == | ||
9/8 is well-represented in [[6edo]] and its multiples, though only multiples of [[12edo]] (up to [[300edo]]) map 9/8 to 1\6 by [[patent val]]. [[Edo]]s which tune [[3/2]] close to just, such as [[29edo]], [[41edo]], and [[53edo]], will tune 9/8 close to just as well. | |||
{{Interval edo approximation|9/8}} | {{Interval edo approximation|9/8}} | ||