9/8

Interval information

Ratio	9/8
Factorization	2-3 × 32
Monzo	[-3 2⟩
Size in cents	203.91¢
Name	whole tone
Color name	w2, wa 2nd
FJS name	[math]\displaystyle{ \text{M2} }[/math]
Special properties	square superparticular, reduced, reduced harmonic
Tenney height (log2 nd)	6.16993
Weil height (log2 max(n, d))	6.33985
Wilson height (sopfr(nd))	12
[sound info]
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9/8 is the Pythagorean whole tone or major second, 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 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.

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.

Temperaments

When this ratio is taken as a comma to be tempered, it produces antitonic temperament. EDOs that temper it out include 2edo and 4edo. If it is instead used as a generator, it produces Baldy.

See also

• 16/9 – its octave complement
• 4/3 – its fifth complement
• 32/27 – its fourth complement
• Gallery of just intervals
• List of superparticular intervals
• Wikipedia: Major second