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Encyclopedia of Microtonal Music Theory

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skhismic major-3rd / schismic major-third

[John Chalmers, Divisions of the Tetrachord]

An interval of 384 cents [¢] (8192/6561) produced by tuning 8 Fifths down from the tonic and five octaves upwards. It may be spelled as Fb in the key of C.

It differs from the Major Third of Just Intonation, 5/4 (386¢), by the Skhisma, an interval of about 2¢.

. . . . . . . . .
[Joe Monzo]

The definition above describes the 2,3-monzo of the skhismic-3rd, which is [13 -8, >; the exponent of prime-factor 2 (= 5) is derived from adding the exponents of 2 occuring from both the subtraction of 8 "5ths" (giving 28) and the addition of 5 octaves (25), thus, 2(8+5) = 213. Using vector addition, the skhisma difference is calculated thus:

  2,3,5-monzo        ratio        ~cents

  | -2  0, 1 >       5 / 4      386.3137139
- | 13 -8, 0 >    8192 / 6561   384.3599931
------------
  |-15  8, 1 >   32805 / 32768    1.953720788
		

Below is a Monzo lattice illustrating the "skhismic major-3rd":

skhismic-major-3rd: Monzo lattice
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