Functional Just System

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The Functional Just System (FJS) is a logical notation system for the entirety of just intonation (JI) which claims to be both more coherent and more succinct than both Helmholtz-Ellis notation and Ben Johnston's notation.

The Functional Just System can be seen as an extension of the pythagorean system: the base name of a note (G, D, Ab, etc.) or interval (P5, M2, m6) is calculated by a fifth distance superscript or subscript numbers are added to mark the deviation from the pythagorean base. The chain of fifths used is controlled by a threshold value (or "radius of tolerance") that is λ=65/63 by default (in “The radius of tolerance is a constant, by definition equal to 65/63.”[1])


Quick reference

Formal commas

Formal commas below 32-limit
Prime Formal Comma
5 80/81
7 63/64
11 33/32
13 1053/1024
17 4131/4096
19 513/512
23 736/729
29 261/256
31 248/243

Harmonic series

Overtones 1–32 with root C
1–8 C C G C E5 G Bb7 C
9–16 D E5 F11 G Ab13 Bb7 B5 C
17–24 Db17 D Eb19 E5 F7 F11 F#23 G
25–32 G#25 Ab13 A Bb7 Bb29 B5 B31 C