8/7
Ratio | 8/7 |
Factorization | 2^{3} × 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 |
Tenney height (log_{2} nd) | 5.80735 |
Weil height (log_{2} 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.