Septimal whole tone

septimal major second

Inverse	harmonic seventh
Name
Other names	Septimal whole tone, Supermajor second
Abbreviation	M2
Size
Semitones	~2.5
Interval class	~2.5
Just interval	8:7
Cents
12-Tone equal temperament	200
24-Tone equal temperament	250
Just intonation	231

In music, the septimal whole tone or supermajor second is the musical interval exactly or approximately equal to a 8/7 ratio of frequencies. It is about 231 cents wide in just intonation and 250 cents in the quarter tone scale. The term septimal refers to the fact that it utilizes the seventh harmonic of the harmonic series, which is combined with the eighth.

This interval does not fit easily into equally-tempered tuning systems. The standard 12 equal temperament used in most western music does not come close to this interval. The 19 equal temperament offers a closer, but still poor match for this interval, but it does not distinguish between this interval and the septimal minor third, which it has a better fit for. The 22 equal temperament distinguishes between these two intervals, but it still matches the septimal whole tone poorly. The 31 equal temperament is the smallest widely used equal temperament that matches this interval closely; 26 equal temperament provides an even closer match to the septimal whole tone (and its inversion, the harmonic seventh), but due to the significant flatness of its major thirds and fifths, this tuning is little used.