In music, theseptimal minor third, also called thesubminor third (e.g., byEllis^[3][4]) orseptimal subminor third, is themusical interval exactly or approximately equal to a 7/6 ratio of frequencies.^[5] In terms ofcents, it is 267 cents, aquartertone of size 36/35 flatter than a justminor third of 6/5. In24-tone equal temperament five quarter tones approximate theseptimal minor third at 250 cents (Play^ⓘ). A septimal minor third is almost exactly two-ninths of an octave, and thus all divisions of the octave into multiples of nine (72 equal temperament being the most notable) have an almost perfect match to this interval. The septimal major sixth, 12/7, is the inverse of this interval.

The septimal minor third may be derived in theharmonic series from theseventh harmonic, and as such is in inharmonic ratios with all notes in the regular 12TET scale, with the exception of the fundamental and the octave.^[6] It has a darker but generally pleasing character when compared to the 6/5 third. A triad formed by using it in place of the minor third is called a "septimal minor" or "subminor triad"play^ⓘ.

In themeantone era the interval made its appearance as the alternative minor third in remote keys, under the nameaugmented second. Tunings of the meantone fifth in the neighborhood ofquarter-comma meantone will give three septimal minor thirds among the twelve minor thirds of the tuning; since thewolf fifth appears with an ordinary minor third, this entails there are three septimal minor triads, eight ordinary minor triads and one triad containing thewolf fifth arising from an ordinary minor third followed by aseptimal major third.

ComposerBen Johnston uses a small "7" as an accidental to indicate a note is lowered49 cents, or an upside down seven ("ㄥ") to indicate a note is raised 49 cents.^[7]

The position of this note also appears on the scale of theMoodswinger.Yuri Landman indicated the harmonic positions of his instrument in a color dotted series. The septimal minor third position is cyan blue as well as the other knotted positions of the seventh harmonic (5/7,4/7, 3/7, 2/7 and 1/7 of the string length of the open string).^[8]

Twelve-toneequal temperament (12-TET), as commonly used in Western music, does not provide a good approximation for this interval, andquarter tones (24-TET) do not match it well either.19-TET,22-TET,31-TET,41-TET, and72-TET each offer successively better matches (measured incents difference) to this interval.

Several non-Western andjust intonation tunings, such as the43-tone scale developed byHarry Partch, do feature the (exact) septimal minor third.

Because of its position in theharmonic series, the sixth harmonic (frequency ratio 6:1) being aperfect fifth and two octaves above theroot, the septimal minor third implies adifference tone aperfect fifth below the lower note in the interval. Depending on the timbre of the pitches, humans sometimes perceive this root pitch even if it is not played. The phenomenon of hearing this root pitch is evident in the following sound file, which uses a puresine wave. For comparison, the root pitch is played after the interval has been played.