Functional Just System: Difference between revisions
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Fractions are normally given in normalized form (since easier to lookup and link to). The information in the table doesn't say anything about the direction (i.e. if the exponent is positive or negative). Tag: Undo |
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Revision as of 19:26, 6 January 2021
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])
Weblinks
Quick reference
Formal commas
| Prime | Formal Comma |
|---|---|
| 5 | 81/80 |
| 7 | 64/63 |
| 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 | 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 |