Functional Just System: Difference between revisions
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Revision as of 10:45, 16 July 2025
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 | 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 |
See also
| View • Talk • EditMusical notation | |
|---|---|
| Universal | Sagittal notation |
| Just intonation | Functional Just System • Ben Johnston's notation (Johnston–Copper notation) • Helmholtz–Ellis notation • Color notation |
| MOS scales | Diamond-mos notation • KISS notation (Quasi-diatonic MOS notation) |
| Temperaments | Chain-of-fifths notation • Stein–Zimmermann–Gould notation • Ups and downs notation • Syntonic–rastmic subchroma notation • Extended meantone notation • Fractional sharp notation |
See musical notation for a longer list of systems by category. See Category:Notation for the most complete, comprehensive list, but not sorted by category. | |