Functional Just System: Difference between revisions
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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 [[ | 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.”''<ref>[https://misotanni.github.io/fjs/en/rules.html The Complete Formal FJS Description]</ref>) | 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.”''<ref>[https://misotanni.github.io/fjs/en/rules.html The Complete Formal FJS Description]</ref>) | ||
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=== Formal commas === | === Formal commas === | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|+Formal commas below 32-limit | |+ Formal commas below 32-limit | ||
! Prime | ! Prime | ||
! Formal Comma | ! Formal Comma | ||
| Line 52: | Line 52: | ||
=== Harmonic series === | === Harmonic series === | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|+Overtones | |+ Overtones 1–32 with root C | ||
! 1–8 | ! 1–8 | ||
| C | | C | ||
Revision as of 19:16, 20 May 2024
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
- 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 | 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 |