Functional Just System: Difference between revisions

The '''Functional Just System''' ('''FJS''') is a logical notation system for ∞-limit [[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&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>) Depending on the radius of tolerance used, some primes will differ in formal commas. Below is a table of formal commas calculated with the standard lambda, Flora Canou's proposal (λ&nbsp;=&nbsp;sqrt(2187/2048)), and neutral FJS (λ&nbsp;=&nbsp;sqrt(134217728/129140163)).

|+ style="font-size: 105%;" | Formal commas up to the 89-limit

! Standard

!FloraC

| colspan="3" | [[81/80|80/81]]

| colspan="3" | [[64/63|63/64]]

| colspan="2" | [[33/32]]

|[[180224/177147]]

| colspan="2" | [[1053/1024]]

|[[6656/6561]]

| colspan="3" | [[4131/4096]]

| colspan="3" | [[513/512]]

| colspan="3" | [[736/729]]

| colspan="2" | [[261/256]]

|+ style="font-size: 105%;" | Overtones 1–32 with root C [Default]