The Magic Continuum

The Magic tuning continuum is named after the magic comma, which is the interval 3125/3072. This comma is described at Answers.com and somewhet tersely in the article in the online Tonalsoft encyclopedia of microtonal music theory.


The interval of 5/4 is a just major third, 2/1 is the octave, and 3/2 is a just fifth. The magic comma is the difference between a just fifth and five just major thirds minus an octave. Answers.com says this slightly differently, but they represent the same interval.

The magic comma completely defines the 5-limit magic continuum, which has an ordinal tuning range that spans 3-tet, through 22-tet, 19-tet, (and many others) and all the way to 10-tet.

When combined with other commas, the magic 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).