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This is the third part of a series of posts on the three mediating proportions – arithmetic, geometric and harmonic – and my playing with the idea of mapping the latter of these to my next body of work, working title Fourths and Fifths. The first post in this series is here.

The harmonic progression, or proportion, looks like this:

a—b:b—c::a:c

the formula for which is:

b = 2ac/(a+c)

which results in the harmonic, or musical, proportion:

1, 4/3, 3/2, 2

where 1 is the fundamental, 4/3 is a fourth, 3/2 is a fifth, and 2 the octave above 1.

If you’re interested in a full discussion of the math behind this, see Richard Lawlor’s Sacred Geometry 1. For a fascinating and in-depth history of how geometry becomes music and the development of our octave, see Richard Merrick’s Interference 2. For my purposes, I’m interested in how this might get mapped to the color wheel, music becomes color becomes music. And when I began playing with this idea, it made more sense to use four primaries for painting (red, yellow, green, blue) instead of the traditional three color primaries (red, yellow, blue).

A short digression before I go on:

Color is vibration, as music is vibration. In the visible light spectrum color moves from violet (the shortest wavelength) through blue, then green, yellow, orange, and red (the longest wavelength). The difference between the colors of visible light (additive color) and the colors mixed for painting (subtractive color) can be charted as:

Additive Color Subtractive Color
Physical Perceived
Mixing adds light Mixing subtracts light
Transmitted Reflected (light that is not absorbed)
All colors = white All colors = black

The primaries of additive color are red, green and blue; of subtractive color are magenta, cyan and yellow (even though this isn’t really reflected – no pun intended – in traditional color wheels or in most discussions of color theory). When two of the additive color primaries are mixed, these are called secondaries. The secondaries of additive color are the primaries of subtractive color, and vice versa. I find this fascinating.

But, as I said, I’m basing my colors for Fourths and Fifths on primaries of red, yellow, green and blue. I have planned three triads (triptychs) that will look something like this:

R → Y → G, where yellow is the fundamental and red is the octave below, green the octave above. The fourth of the R-Y octave will be a red-orange. The fifth of the Y-G octave will be a yellow-green.

And so on. Now it’s time to get into the studio.


References / Additional Reading

  1. Johannes Itten, The Elements of Color (John Wiley & Sons, 2003)
  2. Mark David Gottsegen, The Painter’s Handbook (Watson-Guptill Publications, 2006)
  3. Paul Zelanski and Mary Pat Fisher, Color (Prentice Hall, 2003)
  4. Lawrence D. Woolf, It’s a Colorful Life (General Atomics Sciences Education Foundation, 2000)
  5. Ian Stewart and Martin Golubitsky, Fearful Symmetry: Is God a Geometer? (Dover Publications, 2011)

  1. Robert Lawlor, Sacred Geometry (London: Thames and Hudson Ltd., 1982) 80-89.
  2. Richard Merrick, Interference: A Grand Scientific Musical Theory (Richard Merrick, first revised edition, 2010)