Septimal major third

Infobox Interval| main_interval_name = Septimal major third
inverse = Septimal minor sixth
complement = Septimal minor sixth
other_names = Supermajor third | abbreviation = M3
semitones = ~4 | interval_class = ~4 | just_interval = 9:7| cents_equal_temperament = 400| cents_just_intonation = 435In music, the septimal major third Audio|Septimal major third on C.mid|play, also called the "supermajor third" (by Hermann Helmholtz) and sometimes "Bohlen-Pierce third" is the musical interval exactly or approximately equal to a 9:7 ratio of frequencies. In terms of cents, it is 435 cents, sharper than a just major third of 5:4 by the septimal quarter tone, 36:35 (Audio|Septimal quarter tone on C.mid|play).

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 Audio|Septimal major triad on C.mid|play. However, in terms of the overtone series, this is a utonal rather than otonal chord, being an inverted6:7:9, ie a #if:|1+⁶⁄_{3}|#if:6|¹⁄₆|¹⁄₁:#if:|1+⁷⁄_{3}|#if:7|¹⁄₇|¹⁄₁:#if:|1+⁹⁄_{3}|#if:9|¹⁄₉|¹⁄₁ chord.

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 #if:|2+⁷⁄_{3}|#if:7|²⁄₇|¹⁄₂-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.

References

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