editing disabled

9/8
|-3 2>
203.91000 cents
sound sample

9/8 is the Pythagorean whole tone, measuring approximately 203.9¢. It can be arrived at by stacking two just perfect fifths (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, 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 which temper out this difference (which is 81/80, the syntonic comma of about 21.5¢) include 19edo, 26edo, 31edo, and all meantone temperaments.

9/8 is well-represented in 6edo and its multiples. Edos which tune 3_2 close to just (29edo, 41edo, 53edo, to name three) will tune 9/8 close as well.

See: Gallery of Just Intervals