The Hanson Continuum

The Hanson tuning continuum is named after the Hanson comma, which is the interval 15552/15625. This comma has been discussed at various times in the alternate tuning group (search the messages for Hanson).


The interval of 6/5 is a just minor third, 2/1 is the octave, and 3/2 is a just fifth. This equation shows that the Hanson comma is the difference between a just fifth and six just minor thirds, minus an octave.

The Hanson comma completely defines the 5-limit Hanson continuum, which has an ordinal tuning range that spans 11-tet, through 15-tet, 19-tet (and many others) and all the way to 4-tet.

When combined with other commas, the Hanson 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).