Septimal minor third
In music, the septimal minor third, also called the subminor third or septimal subminor third, is the musical interval exactly or approximately equal to a ratio. In terms of cents, it is 267 cents, a quartertone of size flatter than a minor third. In 24 tone equal temperament five quarter tones approximate the septimal minor third at 250 cents. A septimal minor third is almost exactly two-ninths of an octave, and thus all divisions of the octave into multiples of nine have an almost perfect match to this interval. The septimal major sixth,, is the inverse of this interval.
The septimal minor third may be derived in the harmonic series from the seventh harmonic, and as such is in inharmonic ratios with all notes in the regular 12 TET scale, with the exception of the fundamental and the octave. It has a darker but generally pleasing character when compared to the A triad formed by using it in place of the minor third is called a "septimal minor" or "subminor triad".
In the meantone era the interval made its appearance as the alternative minor third in remote keys, under the name augmented second. Tunings of the meantone fifth in the neighborhood of quarter-comma meantone will give three septimal minor thirds among the twelve minor thirds of the tuning; since the wolf fifth appears with an ordinary minor third, this entails there are three septimal minor triads, eight ordinary minor triads and one triad containing the wolf fifth arising from an ordinary minor third followed by a septimal major third.
Composer Ben Johnston uses a small "" as an accidental to indicate a note is lowered 49 cents, or an upside down seven to indicate a note is raised 49 cents.
The position of this note also appears on the scale of the Moodswinger. 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 [Septimal tritone|], [Harmonic seventh|],, and of the string length of the open string.
In equal temperament and non-Western scales
Twelve-tone equal temperament, as commonly used in Western music, does not provide a good approximation for this interval, and quarter tones do not match it well either. 19 TET, 22 TET, 31 TET, 41 TET, and 72 TET each offer successively better matches to this interval.Several non-Western and just intonation tunings, such as the 43 tone scale developed by Harry Partch, do feature the septimal minor third.