In music, the septimal major third, also called the supermajor third (by eg Helmholtz) and sometimes BP third is the musical interval exactly or approximately equal to a 9/7 ratio of frequencies. In terms of cents, it is 435 cents, a quartertone of size 36/35 sharper than a just major third of 5/4. 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 major third is the larger of two commonly occuring musical intervals that span three diatonic scale degrees. ...

The septimal major third has a characteristic brassy sound which is much less sweet than a pure major third, but is classed as a 9-limit consonance. Together with the septimal minor third of 7/6, it makes up the septimal major triad, or supermajor triad. However, in terms of the overtone series, this is a utonal rather than otonal chord, being an inverted 6:7:9, ie a 1/6:1/7:1/9 chord. 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 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. ... 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. ...

In the early meantone era the interval made its appearance as the alternative major third in remote keys, under the name diminished fourth. Tunings of the meantone fifth in the neighborhood of Zarlino's 2/7 comma meantone will give four septimal thirds among the twelve major thirds of the tuning; this entails that three septimal major triads appear along with one chord containing a septimal major third with an ordinary minor third above it, making up a wolf fifth. Meantone temperament is a system of musical tuning. ... A major third is the larger of two commonly occurring musical intervals that span three diatonic scale degrees. ... Gioseffo Zarlino (January 31 or March 22, 1517 – February 4, 1590), was an Italian music theorist and composer of the Renaissance. ...

References

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