In December l989 I was introduced to the ancient principle governing harmonic resonance in art: the Golden Ratio (ø), sometimes referred to as the Golden Section. A friend, Hugh Joudry, pointed out to me a number of examples from paintings completed during the previous five to eight years in which my choice of proportions very closely approached the Golden Ratio. Through our many conversations I became aware of the infinite ramifications and possibilities for the aesthetic application of this and related mathematical concepts.

Resonance can be defined as the recurrence or "echo" of a primary principle. If one begins a painting on ø rectangle ABCD (see diagram) where the ratio between the smaller side A to the larger side B is equal to the ratio between side B and the sum of sides A and B, we get A : B = B : A + B. Already we have established a resonance, an echo of the initial A : B ratio. Proceeding further, if we divide side B into segments E and H so that A : B = E : H a second ø rectangle (AEFG) results. Rectangle AEFG also resonates with the initial rectangle ABCD but on a different scale. This procedure can be repeated indefinitely, establishing resonance and correspondence between the large (macrocosm) and the small (microcosm). Thus a single ratio--aside from the recurring squares adjacent to each ø rectangle--permeates the evolving imagery as an underlying reality motif.

Resonance in visual art is similar to "overtones" in music. If we sound a middle C on the piano a higher octave C can also be heard. The Golden Ratio generates a similar and infinite series of visual and numerical overtones. Far from being a mere mechanical formula, it expresses in numerical/visual terms the link between heaven and earth as symbolized by the arc or rainbow, and the dynamic connection between individual human beings and their common ground.