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, 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]})
Weblinks
- The FJS website
- Calculator
- Custom FJS Explorer
- misotanni [old] - YouTube – (abandoned channel)
Quick reference
Formal commas
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
1–8 | C | C | G | C | E^{5} | G | B♭^{7} | C |
---|---|---|---|---|---|---|---|---|
9–16 | D | E^{5} | F^{11} | G | A♭^{13} | B♭^{7} | B^{5} | C |
17–24 | D♭^{17} | D | E♭^{19} | E^{5} | F^{7} | F^{11} | F♯^{23} | G |
25–32 | G♯^{25} | A♭^{13} | A | B♭^{7} | B♭^{29} | B^{5} | B^{31} | C |