8/7
| Interval information |
supermajor second,
septimal major second
reduced,
reduced subharmonic
(Shannon, [math]\sqrt{nd}[/math])
[sound info]
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.