Septimal major third

Add links
Source: Wikipedia, the free encyclopedia.
Septimal major third
septimal minor sixth
Name
Other namesSupermajor third, Septimal supermajor third
AbbreviationS3, SM3
Size
Semitones~4½
Interval class~4½
Just interval9:7[1]
Cents
12-Tone equal temperament400
24-Tone equal temperament450
Just intonation435
9/7 major third from C to E7 upside-down [2]This, "extremely large third", is also found between C and E7 upside-down and may resemble a neutral third or blue note.[3]

In music, the septimal major third playⓘ, also called the supermajor third (by Hermann von Helmholtz among others[4][5][6]), septimal supermajor third, 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ⓘ). Both 24 and 19 equal temperament map the septimal major third and the septimal narrow fourth (21:16) to the same interval.

This interval has a characteristic brassy sound which is much less sweet than a pure major third, but is classed as a

utonal rather than otonal chord, being an inverted 6:7:9, i.e. a 9⁄9:9⁄7:9⁄6 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

wolf fifth
.

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

  1. ISBN 0-8247-4714-3
    . Septimal major third.
  2. JSTOR 833435
    .
  3. ^ Fonville (1991), p. 128.
  4. ^
    ISBN 1-60206-639-6
    .
  5. doi:10.1098/rspl.1879.0155
    .
  6. JSTOR 41335396
    .
  7. ^
    ISBN 0-89579-507-8
    . "Super-Major Second".
  8. ^ ""Just Chord Tunings"". Archived from the original on 2013-11-12. Retrieved 2013-11-12.
Retrieved from "https://en.wikipedia.org/w/index.php?title=Septimal_major_third&oldid=1219740751"