Septimal whole tone

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In music, the septimal whole tone is the musical interval exactly or approximately equal to a 8/7 ratio of frequencies. It is about 231 cents wide. The term septimal refers to the fact that it utilizes the seventh harmonic of the harmonic series.

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.

v • d • e Intervals Perfect unison (0) · fourth (5) · fifth (7) · octave (12) Major second (2) · third (4) · sixth (9) · seventh (11) Minor second (1) · third (3) · sixth (8) · seventh (10) Augmented unison (1) · second (3) · third (5) · fourth (6) · fifth (8) · sixth (10) · seventh (12) Diminished second (0) · third (2) · fourth (4) · fifth (6) · sixth (7) · seventh (9) · octave (11) Septimal major (supermajor) second (2½) · third (4½) · sixth (9½) · seventh (11½) Neutral second (1½) · third (3½) · sixth (8½) · seventh (10½) Septimal minor (subminor) second (½) · third (2½) · sixth (7½) · seventh (9½) Semitones are given in brackets. Fractional semitones are approximate.