The system of notating rational intervals devised by Ben Johnston. It evolved from the 1960s to the 1980s.
Johnston notation is based on typical 5-limit JI diatonic major scale, represented by the seven letter-names A B C D E F G and corresponding to the respective ratios 5/3, 15/8, 1/1, 9/8, 5/4, 4/3, and 3/2. This scale is a periodicity-block as shown on the following lattice-diagram:
The accidental symbols # and b represent an alteration of intonation by the ratio 25:24 (= ~70.67 cents), plus or minus respectively.
The symbols + and - represent an alteration of intonation by the ratio 81:80 [= ~21.506 cents], which is the syntonic comma.
Each additional accidental in Johnston's system represents an intonational inflection resulting from the incorporation of additional prime-factors in the ratio of a given pitch.
Johnston notation uses arrows pointing up or down to represent the presence of prime-factor 11, and for all higher primes his notation simply uses the prime number itself for the otonal adjustment and the prime number inverted for the utonal adjustment.
It is the opinion of several tuning-theorists that Johnston's notational idea is a good one, but that it could be improved by using a Pythagorean scale instead of a 5-limit one as a basis. See HEWM, and Monzo, JustMusic Prime-Factor Notation.
Fonville, John. 1991.
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