8/7
| Ratio | 8/7 |
| Factorization | 23 × 7-1 |
| Monzo | [3 0 0 -1⟩ |
| Size in cents | 231.17409¢ |
| Names | septimal whole tone, supermajor second, septimal major second |
| Color name | r2, ru 2nd |
| FJS name | [math]\text{M2}_{7}[/math] |
| Special properties | superparticular, reduced, reduced subharmonic |
| Tenney height (log2 nd) | 5.80735 |
| Weil height (log2 max(n, d)) | 6 |
| Wilson height (sopfr(nd)) | 13 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.19168 bits |
[sound info] | |
| open this interval in xen-calc | |
In just intonation, 8/7 is the supermajor second or septimal major second of approximately 231.2 ¢. Although it falls between the familiar major second and minor third of 12edo, it generally sounds more like a wide second than a narrow third. It can be found between the 7th and 8th harmonics and is thus a superparticular ratio. In 7-limit JI and higher, it is treated as a consonance, particularly in the context of a chord such as 4:5:6:7:8, where it appears between the harmonic seventh (7/4) and octave. It differs from the Pythagorean major second of 9/8 by 64/63, a microtone of about 27.3 ¢. It is close in size to one step of 5edo = 240 ¢.
A stack of three supermajor seconds is close to a perfect fifth (3/2). The difference is 1029/1024 (about 8.4 ¢), which is tempered out in slendric and 31edo.