Functional Just System: Difference between revisions

Line 7:

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, 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 ==

Line 13:

* [https://misotanni.github.io/fjs/en/calc.html Calculator]

* [https://www.yacavone.net/fjs-explorer/ Custom FJS Explorer]

* [https://www.youtube.com/channel/UCrKUfsh5r1uMEx8EBevPflw misotanni [old] - YouTube] – (abandoned channel)

== Quick reference ==

Line 53:

{| class="wikitable center-all"

|+ Overtones 1–32 with root C

! ~~1–8~~

! 1–8

| C

Line 60:

| E5

| G

| Bb7

| B♭7

| C

|-

! ~~9–16~~

! 9–16

| D

| E5

| F11

| G

| Ab13

| A♭13

| Bb7

| B♭7

| B5

| C

|-

! ~~17–24~~

! 17–24

| Db17

| D♭17

| D

| Eb19

| E♭19

| E5

| F7

| F11

| F#23

| F♯23

| G

|-

! ~~25–32~~

! 25–32

| G#25

| G♯25

| Ab13

| A♭13

| A

| Bb7

| B♭7

| Bb29

| B♭29

| B5

| B31

@@ Line 7: / Line 7: @@
 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, 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&nbsp;=&nbsp;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 ==
@@ Line 13: / Line 13: @@
 * [https://misotanni.github.io/fjs/en/calc.html Calculator]
 * [https://www.yacavone.net/fjs-explorer/ Custom FJS Explorer]
-* [https://www.youtube.com/channel/UCrKUfsh5r1uMEx8EBevPflw misotanni &#91;old&#93; &#45; YouTube] – (abandoned channel)
+* [https://www.youtube.com/channel/UCrKUfsh5r1uMEx8EBevPflw misotanni &#91;old&#93; &#45; YouTube] &ndash; (abandoned channel)
 == Quick reference ==
@@ Line 53: / Line 53: @@
 {| class="wikitable center-all"
 |+ Overtones 1&ndash;32 with root C
-! 1–8
+! 1&ndash;8
 | C
 | C
@@ Line 60: / Line 60: @@
 | E<sup>5</sup>
 | G
-| Bb<sup>7</sup>
+| B♭<sup>7</sup>
 | C
 |-
-! 9–16
+! 9&ndash;16
 | D
 | E<sup>5</sup>
 | F<sup>11</sup>
 | G
-| Ab<sup>13</sup>
+| A♭<sup>13</sup>
-| Bb<sup>7</sup>
+| B♭<sup>7</sup>
 | B<sup>5</sup>
 | C
 |-
-! 17–24
+! 17&ndash;24
-| Db<sup>17</sup>
+| D♭<sup>17</sup>
 | D
-| Eb<sup>19</sup>
+| E♭<sup>19</sup>
 | E<sup>5</sup>
 | F<sup>7</sup>
 | F<sup>11</sup>
-| F#<sup>23</sup>
+| F♯<sup>23</sup>
 | G
 |-
-! 25–32
+! 25&ndash;32
-| G#<sup>25</sup>
+| G♯<sup>25</sup>
-| Ab<sup>13</sup>
+| A♭<sup>13</sup>
 | A
-| Bb<sup>7</sup>
+| B♭<sup>7</sup>
-| Bb<sup>29</sup>
+| B♭<sup>29</sup>
 | B<sup>5</sup>
 | B<sup>31</sup>