8/7

Interval information

Ratio	8/7
Factorization	23 × 7-1
Monzo	[3 0 0 -1⟩
Size in cents	231.1741¢
Names	septimal whole tone, supermajor second, septimal major second
Color name	r2, ru 2nd
FJS name	[math]\displaystyle{ \text{M2}_{7} }[/math]
Special properties	superparticular, reduced, reduced subharmonic
Tenney norm (log2 nd)	5.80735
Weil norm (log2 max(n, d))	6
Wilson norm (sopfr(nd))	13
[sound info]
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Septimal whole tone

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.

See also

• 7/4 – its octave complement
• 21/16 – its fifth complement
• 7/6 – its fourth complement
• Gallery of just intervals
• 8/7 equal-step tuning