The Functional Just System (FJS) is a logical notation system for ∞-limit 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, A♭, 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]) Depending on the radius of tolerance used, some primes will differ in formal commas. Below is a table of formal commas calculated with the standard lambda, Flora Canou's proposal (λ = sqrt(2187/2048)), and neutral FJS (λ = sqrt(134217728/129140163)).
Weblinks
Quick reference
Formal commas
Harmonic series
Overtones 1–32 with root C [Default]
| 1–8
|
C
|
C
|
G
|
C
|
E5
|
G
|
B♭7
|
C
|
| 9–16
|
D
|
E5
|
F11
|
G
|
A♭13
|
B♭7
|
B5
|
C
|
| 17–24
|
D♭17
|
D
|
E♭19
|
E5
|
F7
|
F11
|
F♯23
|
G
|
| 25–32
|
G♯25
|
A♭13
|
A
|
B♭7
|
B♭29
|
B5
|
B31
|
C
|
Overtones 1–32 with root C [FloraC]
| 1–8
|
C
|
C
|
G
|
C
|
E5
|
G
|
B♭7
|
C
|
| 9–16
|
D
|
E5
|
F11
|
G
|
A♭13
|
B♭7
|
B5
|
C
|
| 17–24
|
D♭17
|
D
|
E♭19
|
E5
|
F7
|
F11
|
F♯23
|
G
|
| 25–32
|
G♯25
|
A♭13
|
A
|
B♭7
|
B♭29
|
B5
|
C31
|
C
|
Overtones 1–32 with root C [Neutral]
| 1–8
|
C
|
C
|
G
|
C
|
E5
|
G
|
B♭7
|
C
|
| 9–16
|
D
|
E5
|
E♯11
|
G
|
G♯13
|
B♭7
|
B5
|
C
|
| 17–24
|
D♭17
|
D
|
E♭19
|
E5
|
F7
|
E♯11
|
F♯23
|
G
|
| 25–32
|
G♯25
|
G♯13
|
A
|
B♭7
|
A♯29
|
B5
|
D𝄫31
|
C
|
See also