Functional Just System: Difference between revisions
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* [https://misotanni.github.io/fjs/en/calc.html Calculator] | * [https://misotanni.github.io/fjs/en/calc.html Calculator] | ||
* [https://www.yacavone.net/fjs-explorer/ Custom FJS Explorer] | * [https://www.yacavone.net/fjs-explorer/ Custom FJS Explorer] | ||
* [https://www.youtube.com/channel/UCrKUfsh5r1uMEx8EBevPflw misotanni [old] - YouTube] | * [https://www.youtube.com/channel/UCrKUfsh5r1uMEx8EBevPflw misotanni [old] - YouTube] – (abandoned channel) | ||
== Quick reference == | == Quick reference == | ||
=== Formal commas === | === Formal commas === | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|+ Formal commas below 32-limit | |+ style="font-size: 105%;" | Formal commas below 32-limit | ||
|- | |||
! Prime | ! Prime | ||
! Formal Comma | ! Formal Comma | ||
| Line 52: | Line 53: | ||
=== Harmonic series === | === Harmonic series === | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|+ Overtones | |+ style="font-size: 105%;" | Overtones 1–32 with root C | ||
! | |- | ||
! 1–8 | |||
| C | | C | ||
| C | | C | ||
| Line 63: | Line 65: | ||
| C | | C | ||
|- | |- | ||
! | ! 9–16 | ||
| D | | D | ||
| E<sup>5</sup> | | E<sup>5</sup> | ||
| Line 73: | Line 75: | ||
| C | | C | ||
|- | |- | ||
! | ! 17–24 | ||
| D♭<sup>17</sup> | | D♭<sup>17</sup> | ||
| D | | D | ||
| Line 83: | Line 85: | ||
| G | | G | ||
|- | |- | ||
! | ! 25–32 | ||
| G♯<sup>25</sup> | | G♯<sup>25</sup> | ||
| A♭<sup>13</sup> | | A♭<sup>13</sup> | ||
| Line 94: | Line 96: | ||
|} | |} | ||
{{Navbox notation}} | |||
{{ | |||
[[Category:Notation]] | [[Category:Notation]] | ||
[[Category:Just intonation]] | [[Category:Just intonation]] | ||
Revision as of 18:28, 11 February 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 |
| 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. | |