10/9

Interval information

Ratio	10/9
Factorization	2 × 3-2 × 5
Monzo	[1 -2 1⟩
Size in cents	182.40371¢
Names	small whole tone, classic(al) whole tone, ptolemaic whole tone
Color name	y2, yo 2nd
FJS name	[math]\text{M2}^{5}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	6.49185
Weil height (log2 max(n, d))	6.64386
Wilson height (sopfr(nd))	13
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.20877 bits
[sound info]
open this interval in xen-calc

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Major second

In 5-limit just intonation, 10/9 is the small, classic(al), or ptolemaic whole tone of about 182.4¢. It is a superparticular interval, as you can find it in the harmonic series between the 9th and the 10th overtones. It is one of two essential whole tones in the 5-limit; the other one is 9/8 (about 203.9¢), which is 81/80 (about 21.5¢) higher than 10/9. 9/8 is an octave-reduced overtone, and it is closer to 12edo's single whole step of 200¢. Thus, 9/8 is more familiar and less difficult to tune by ear than 10/9.

The first three notes of a JI major scale – 1/1, 9/8, 5/4 – move by a step of 9/8 followed by a step of 10/9 (or alternatively 1/1, 10/9, 5/4 – move by a step of 10/9 followed by a step of 9/8). In systems where 81/80 is tempered out (in 12edo, 19edo, 31edo and other meantone systems) that distinction is lost and this sounds like two equal-sized steps. In strict JI, the difference may be hard to notice at first.

See also

• Decaononic - temperament which sets the tone to this interval, instead of to 9/8
• 9/5 – its octave complement
• 27/20 – its fifth complement
• 6/5 – its fourth complement
• Gallery of just intervals