Functional Just System: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
BudjarnLambeth (talk | contribs)
m {{Notation navbox}}
ArrowHead294 (talk | contribs)
mNo edit summary
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] – (abandoned channel)
* [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 1–32 with root C
|+ style="font-size: 105%;" | Overtones 1–32 with root C
! 1–8
|-
! 1–8
| C
| C
| C
| C
Line 63: Line 65:
| C
| C
|-
|-
! 9–16
! 9–16
| D
| D
| E<sup>5</sup>
| E<sup>5</sup>
Line 73: Line 75:
| C
| C
|-
|-
! 17&ndash;24
! 17–24
| D♭<sup>17</sup>
| D♭<sup>17</sup>
| D
| D
Line 83: Line 85:
| G
| G
|-
|-
! 25&ndash;32
! 25–32
| G♯<sup>25</sup>
| G♯<sup>25</sup>
| A♭<sup>13</sup>
| A♭<sup>13</sup>
Line 94: Line 96:
|}
|}


 
{{Navbox notation}}
{{Notation navbox}}


[[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

Quick reference

Formal commas

Formal commas below 32-limit
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

Overtones 1–32 with root C
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