Moments of Symmetry as a User Interactive Circle


Marcus Hobbs’ user interactive visualization of one of Wilson’s galaxy clusters of musical tunings known as Moments of Symmetry.

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What Am I Looking At?

From the Sonic Sky: An Introduction @14:48:

You’re looking at an infinite pitch field in which our twelve tone master set scale is a mere spec. Kind of like how our beloved Earth is a mere dot in the cosmos.

Our system, 12 tone equal temperament, is that ring with 12 equally spaced cells dividing the circle. Try entering the generator 0.5833333…. above. Change one little number way to the right of the decimal point in the formula that generates the radii, and the whole cosmos changes right before your eyes and a new galaxy comes into being with nested master sets each rendering a whole new set of tonal properties.

There are so many of these sonic galaxies in this cluster that you can’t count them. That’s how big and fertile this area of exploration is.

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 on Moments of Symmetry there’s an excellent introduction in the Kraig Grady’s Wilson Archives:

You may also be interested in the Moments of Symmetry represented a Morphing Rectangle.

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  • Hi this is a very interesting diagram! The patterns are beautiful, and I feel that I’m beginning to understand the potential of MOS. On a constructive note, I think you should be able to type in certain ratios into the MOS but that’s only a quibble.

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