Septimal major third

Septimal major third
Inverse septimal minor sixth
Other names Supermajor third
Abbreviation S3, SM3
Semitones ~4½
Interval class ~4½
Just interval 9:7[1]
Equal temperament 400
24 equal temperament 450
Just intonation 435
9/7 major third from C to E [2]  Play . This, "extremely large third", is also found between C- and E- and may resemble a neutral third or blue note.[3]

In music, the septimal major third  play , also called the supermajor third (by Hermann Helmholtz among others[4][5][6]) and sometimes Bohlen–Pierce third is the musical interval exactly or approximately equal to a just 9:7 ratio[4][7] of frequencies, or alternately 14:11.[7] It is equal to 435 cents,[4] sharper than a just major third (5:4) by the septimal quarter tone (36:35) ( play ). In 24-TET the septimal major third is approximated by 9 quarter tones, or 450 cents ( 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 root 1:1 and the perfect fifth of 3:2, it makes up the septimal major triad, or supermajor triad  play . However, in terms of the overtone series, this is a utonal rather than otonal chord, being an inverted 6:7:9, i.e. a 99:97:96 chord. The septimal major triad can also be represented by the ratio 14:18:21.[8] The septimal major triad contains an interval of a septimal minor third 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 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 27-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.


  1. Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxiii. ISBN 0-8247-4714-3. Septimal major third.
  2. Fonville, John. "Ben Johnston's Extended Just Intonation- A Guide for Interpreters", p.112, Perspectives of New Music, Vol. 29, No. 2 (Summer, 1991), pp. 106-137.
  3. Fonville (1991), p.128.
  4. 1 2 3 Hermann L. F Von Helmholtz (2007). On the Sensations of Tone, p.187. ISBN 1-60206-639-6.
  5. Royal Society (Great Britain) (1880, digitized Feb 26, 2008). Proceedings of the Royal Society of London, Volume 30, p.531. Harvard University.
  6. Society of Arts (Great Britain) (1877, digitized Nov 19, 2009). Journal of the Society of Arts, Volume 25, p.670. The Society.
  7. 1 2 Andrew Horner, Lydia Ayres (2002). Cooking with Csound: Woodwind and Brass Recipes, p.131. ISBN 0-89579-507-8. "Super-Major Second".
  8. "Just Chord Tunings"
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