music Music is generally defined as the art of arranging sound to create some combination of form, harmony, melody, rhythm or otherwise expressive content. Exact definitions of music vary considerably around the world, though it is an aspect ...

, the septimal major third , also called the supermajor third (by

Hermann von Helmholtz Hermann Ludwig Ferdinand von Helmholtz (31 August 1821 – 8 September 1894) was a German physicist and physician who made significant contributions in several scientific fields, particularly hydrodynamic stability. The Helmholtz Association, ...

among others Hermann L. F. von Helmholtz (2007). ''

Sensations of Tone ''On the Sensations of Tone as a Physiological Basis for the Theory of Music'' (German ), commonly referred to as ''Sensations of Tone'', is a foundational work on music acoustics and the perception of sound by Hermann von Helmholtz. The first ...

'', p. 187. .) and sometimes '' Bohlen–Pierce third'' is the musical interval exactly or approximately equal to a just 9:7 ratioAndrew Horner, Lydia Ayres (2002). ''Cooking with Csound: Woodwind and Brass Recipes'', p. 131. . "Super-Major Second". of frequencies, or alternately 14:11. It is equal to 435 cents, sharper than a just

major third In classical music, a third is a musical interval encompassing three staff positions (see Interval number for more details), and the major third () is a third spanning four semitones. Forte, Allen (1979). ''Tonal Harmony in Concept and P ...

(5:4) by the

septimal quarter tone A septimal quarter tone (in music) is an Interval (music), interval with the ratio of 36:35, which is the difference between the septimal minor third and the Just minor third, or about 48.77 Cent (music), cents wide. The name derives from the in ...

(36:35) (). In

24-TET A quarter tone is a pitch halfway between the usual notes of a chromatic scale or an interval about half as wide (aurally, or logarithmically) as a semitone, which itself is half a whole tone. Quarter tones divide the octave by 50 cents each, a ...

the septimal major third is approximated by 9 quarter tones, or 450 cents (). Both 24 and 19 equal temperament map the septimal major third and the septimal narrow fourth (21:16) to the same interval. 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

root In vascular plants, the roots are the organs of a plant that are modified to provide anchorage for the plant and take in water and nutrients into the plant body, which allows plants to grow taller and faster. They are most often below the sur ...

1:1 and the

perfect fifth In music theory, a perfect fifth is the Interval (music), musical interval corresponding to a pair of pitch (music), pitches with a frequency ratio of 3:2, or very nearly so. In classical music from Western culture, a fifth is the interval fro ...

of 3:2, it makes up the septimal major triad, or supermajor triad . However, in terms of the overtone series, this is a

utonal ''Otonality'' and ''utonality'' are terms introduced by Harry Partch to describe chords whose pitch classes are the harmonics or subharmonics of a given fixed tone (identity), respectively. For example: , , ,... or , , ,.... Definition ...

rather than otonal chord, being an inverted 6:7:9, i.e. a :: chord. The septimal major triad can also be represented by the ratio 14:18:21. The septimal major triad contains an interval of a

septimal minor third In music, the septimal minor third, also called the subminor third (e.g., by Ellis), 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 ...

between its third and fifth ( 3:2 / 9:7 = 7:6 ). Similarly, the septimal major third is the interval between the third and the fifth of the septimal minor triad. In the early

meantone Meantone temperament is a musical temperament, that is a tuning system, obtained by narrowing the fifths so that their ratio is slightly less than 3:2 (making them ''narrower'' than a perfect fifth), in order to push the thirds closer to pure. Me ...

era the interval made its appearance as the alternative major third in remote keys, under the name

diminished fourth In classical music from Western culture, a diminished fourth () is an interval produced by narrowing a perfect fourth by a chromatic semitone.Benward & Saker (2003). ''Music: In Theory and Practice, Vol. I'', p.54. . Specific example of an d4 ...

. Tunings of the meantone fifth in the neighborhood of

Zarlino Gioseffo Zarlino (31 January or 22 March 1517 – 4 February 1590) was an Italian music theorist and composer of the Renaissance. He made a large contribution to the theory of counterpoint as well as to musical tuning. Life and career Zarlino w ...

's -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 In music theory, the wolf fifth (sometimes also called Procrustean fifth, or imperfect fifth) Paul, Oscar (1885). A manual of harmony for use in music-schools and seminaries and for self-instruction', p.165. Theodore Baker, trans. G. Schirmer. ...

. 22 equal temperament has a very close match to this interval. In this temperament, four fifths minus two octaves equals a septimal major third, not an ordinary major third.

References

{{Intervals 7-limit tuning and intervals Major intervals Thirds (music)