10/9
| 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{n\cdot d}[/math]) |
~4.56419 bits |
[sound info] | |
| open this interval in xen-calc | |
In 5-limit just intonation, 10/9 is the small, classic(al), or ptolemaic whole tone[1] 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