9/8: Difference between revisions

9/8 is the Pythagorean whole tone, measuring approximately 203.9¢. It can be arrived at by stacking two just perfect fifths ([[3/2|3/2]]) and reducing the result by one octave. However, it is also a relatively low overtone in its own right, octave-reduced. It can be treated as a dissonance or a consonance, depending on compositional context.

Two 9/8's stacked produce [[81/64|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|10/9]] yields [[5/4|5/4]]. This distinction, between a major whole tone and minor whole tone, has been completely obliterated in [[12edo|12edo]], and so we are unaccustomed to thinking of more than one size of whole tone comprising a major third. Other systems which temper out this difference (which is [[81/80|81/80]], the syntonic comma of about 21.5¢) include [[19edo|19edo]], [[26edo|26edo]], [[31edo|31edo]], and all [[Meantone|meantone]] temperaments.

9/8 is well-represented in [[6edo|6edo]] and its multiples. [[EDO|Edo]]s which tune [[3/2|3_2]] close to just ([[29edo|29edo]], [[41edo|41edo]], [[53edo|53edo]], to name three) will tune 9/8 close as well.

See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]     [[Category:3-limit]]

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[[Category:just_interval]]

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[[Category:whole_tone]]