In music, the septimal minor third, also called the subminor third (by eg Helmholtz) is the musical interval exactly or approximately equal to a 7/6 ratio of frequencies. In terms of cents, it is 267 cents, a quartertone of size 36/35 flatter than a just minor third of 6/5. Hermann Ludwig Ferdinand von Helmholtz (August 31, 1821 – September 8, 1894) was a German physician and physicist. ... The cent is a logarithmic unit of measure used for musical intervals. ... A minor third is the smaller of two commonly occurring musical intervals compounded of two steps of the diatonic scale. ...

The septimal minor third 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; however in fact that chord is a part of the overtone series, or in other words is an otonal chord, with ratios of 6:7:9, whereas the ordinary minor third is a utonal chord. While the septimal minor third is classed as a 7-limit interval, and the septimal minor triad as a 9-limit chord, the fact that the chord is otonal makes it sound perhaps about as consonant as the just minor triad. Otonality and Utonality are terms introduced by Harry Partch to describe chords whose notes are the overtones (multiples) or undertones (divisors) of a given fixed tone. ... Otonality and Utonality are terms introduced by Harry Partch to describe chords whose notes are the overtones (multiples) or undertones (divisors) of a given fixed tone. ... Just intonation tunings and scales can be described by giving an upper bound on the complexity of the harmonies admitted by the tuning or scale. ...

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 1/4 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. Meantone temperament is a system of musical tuning. ... The musical interval of a minor third is the relationship between the first note (the root or tonic) and the third note in a minor scale. ...

See also

Septimal major third

References

Hermann Helmholz and Alexander Ellis (trans), On the Sensation of Tone, Dover Publications