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 [[Helmholtz–Ellis notation]] and [[Ben Johnston's notation]]. | 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, | 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.”''<ref>[https://misotanni.github.io/fjs/en/rules.html The Complete Formal FJS Description]</ref>) | ||
== Weblinks == | == Weblinks == | ||
| Line 13: | Line 13: | ||
* [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 == | ||
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{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|+ Overtones 1–32 with root C | |+ Overtones 1–32 with root C | ||
! | ! 1–8 | ||
| C | | C | ||
| C | | C | ||
| Line 60: | Line 60: | ||
| E<sup>5</sup> | | E<sup>5</sup> | ||
| G | | G | ||
| | | B♭<sup>7</sup> | ||
| C | | C | ||
|- | |- | ||
! | ! 9–16 | ||
| D | | D | ||
| E<sup>5</sup> | | E<sup>5</sup> | ||
| F<sup>11</sup> | | F<sup>11</sup> | ||
| G | | G | ||
| | | A♭<sup>13</sup> | ||
| | | B♭<sup>7</sup> | ||
| B<sup>5</sup> | | B<sup>5</sup> | ||
| C | | C | ||
|- | |- | ||
! | ! 17–24 | ||
| | | D♭<sup>17</sup> | ||
| D | | D | ||
| | | E♭<sup>19</sup> | ||
| E<sup>5</sup> | | E<sup>5</sup> | ||
| F<sup>7</sup> | | F<sup>7</sup> | ||
| F<sup>11</sup> | | F<sup>11</sup> | ||
| | | F♯<sup>23</sup> | ||
| G | | G | ||
|- | |- | ||
! | ! 25–32 | ||
| | | G♯<sup>25</sup> | ||
| | | A♭<sup>13</sup> | ||
| A | | A | ||
| | | B♭<sup>7</sup> | ||
| | | B♭<sup>29</sup> | ||
| B<sup>5</sup> | | B<sup>5</sup> | ||
| B<sup>31</sup> | | B<sup>31</sup> | ||
Revision as of 19:24, 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, 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 |