An infinity of new scale families are shown via Marcus Hobbs’ animation of moving generators along Wilson’s Moments of Symmetry continuum. Generators are an initial condition for a note generating formula.

Defining Moments of Symmetry

Kraig Grady’s Wilson Archives has a simple “cliff notes” definition of a Moment of Symmetry. A Moment of Symmetry is a scale that consists of:

1. A Generator (of any size, for example a 3/2 or a fifth in 12 equal temperament).
2. An Interval of Equivalence (of any size, for example most commonly an octave)
3. A Scale Degree or Scale Unit represented by no more than two sizes only (Large = L and small = s)

The Generator is repeatedly superimposed but reduced within the Interval of Equivalence with only the large and small Scale Degrees or Scale Units.

For more information, check out the excellent introduction on the subject in Kraig Grady’s Wilson Archives:

http://anaphoria.com/wilsonintroMOS.html.

You may also be interested in viewing the Moments of Symmetry As A User Interactive Circle.