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.
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This is the second part of my musings on connections between music and color which started here.

I left off with the arithmetic progression. Now for the second of the three: Geometric. Again, this is a three-term proportion where a > b > c. In the language of ratios, a and c are the extremes and b is the mean. As with an arithmetic progression, begin with two of the differences in the numbers: a—b and b—c. In a geometric or harmonic progression, these differences are to each other in the same way as one of these numbers is to one of the other numbers, not as one of the numbers is to itself as in an arithmetic proportion.

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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?

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