The Syntonic Continuum

The Syntonic tuning continuum is named after the syntonic comma, which is the interval 81/80. This comma has been known since antiquity, and is described in several ways in this Wikipedia article.


The interval of 5/4 is a just major third, 2/1 is an octave, and 3/2 is a just fifth. The syntonic comma is the difference between a just major third and four just fifths minus two octaves. Wikipedia says this slightly differently, but they represent the same interval.

The syntonic comma completely defines the 5-limit syntonic continuum, which has an ordinal tuning range that spans 5-tet, through 22-tet, 17-tet, 12-tet, 19-tet, (and includes many others) all the way to 7-tet. This is described in great detail in our article from the winter 2007 issue of the Computer Music Journal "Isomorphic Controllers and Dynamic Tuning: Invariant Fingering Over a Tuning Continuum."

When combined with other commas, the syntonic continuum expands to include higher limit intervals though the range of ordinal tuning contracts. In the TransFormSynth, the commas are used to define the tuning of the notes (the pitches) as well as the timbre of the sounds (i.e., the detailed placement of the overtones).