My attempts to determine whether or not a rational basis exists for my intuition of a relationship between color and music led me back to Robert Lawlor’s *Sacred Geometry*, a book I first read about a decade ago, specifically chapter VIII, “Mediation: Geometry Becomes Music.” (The quotes and examples in this post are from the 1994 Thames and Hudson edition.)^{1}

As I worked through the color relationships for the new body of work, I felt there might be some such relationship. In a previous post, The closed circle and the infinite loop, my first instinct was that the colors for the series somehow related to thirds and fifths in music. I now amend this to fourths and fifths after reading Lawlor.

This is based on the concept of “mediating proportions” – binding two extremes through a single mean term.

There are three such mediating proportions: arithmetic, geometric and harmonic. It’s the latter I’m trying to puzzle through (which means I’ll need to relearn everything I’ve forgotten about music theory). So between music theory and color theory is there a correspondence we can define and talk about? It’s all vibration, right?

And now the math behind these progressions. First, these proportions are all three-term proportions, a group of three unequal numbers where *a > b > c*. In the language of ratios *a* and *c* are the extremes and *b* is the mean. The relationship between these numbers is that “two of their differences are to each other in the same relationship as one of these numbers is to itself…” (arithmetic) *or* is in the same relationship as one of these numbers is to one of the other numbers (geometric and harmonic). The two differences here are *a—b and b—c*.

**Arithmetic Progression**

In an arithmetic progression *a—b* is to *b—c* as *a* is to *a*, *b* is to *b*, *c* is to *c*:

*a—b:b—c::a:a, b:b, c:c*

To take a simple example, let’s say the extremes of this proportion are 3 and 7. To find the mean, add the two extremes and divide by two:

*b = (a+c)/2*

The mean term is 5 and the arithmetic progression is 3, 5, 7.

Next: the geometric and harmonic progressions.

- Robert Lawlor,
*Sacred Geometry*(London: Thames and Hudson Ltd., 1982) 80-89. ↩