Here’s an excerpt from an outstanding article I found online:

Music and Mathematics – A Divine Relationship

Most people know the aesthetic beauty music and art can offer. Many, however, may not be aware of the mathematical principles which exist in music and composition. The aesthetic perception of music is governed by the right half of the brain. Mathematical relationships and spatial reasoning are controlled by the left half. This brief article is based on the premise that music theory reflects the laws of mathematics and nature, and that great composition contains mathematical relationships which enhance the perception of its aesthetic beauty. In other words, knowing music exercises the whole-brain, the whole-person.

Composers have long been fascinated by numerology. The ancient Greeks knew of the relationships between numbers and what they considered perfection in architectural design. The Golden Sequence, also known as the Golden Section, the Golden Number, or the Divine Proportion, is one such mathematical relationship, the formula of which often occurs in the natural world. (A preliminary internet search on this phenomenon turned up over thirty million hits!) This proportion can be created by dividing a line into two parts. The point of the division should be in such a place that the square of the longer subdivision is equal to the product of the shorter subdivision times the length of the entire line. Put as a formula, A (shorter subdivision) x C (entire line) = B2 (longer subdivision), or proportionally A/B = B/C. Line B is roughly 1.62 times the length of A (B/A), or conversely, line A is approximately .62 times that of B (A/B). The same relationships hold for lines B and C. To the Greeks, the 1.62 figure is known as Phi and the .62 figure is phi.

The ancient Greeks believed that a rectangle whose sides were in this proportion were the most aesthetically pleasing and based their architectural principles upon it. The most well-known such building is the Parthenon in Athens. It is also a fundamental formula used by the ancient Egyptians and is most notably seen in the pyramids.

The Golden Sequence is also found in the Fibonacci series 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55… wherein each new digit is the sum of the preceding two. In the Fibonacci series, dividing the larger of two successive numbers by the smaller yields a result approximating 1.62 [Phi]. Or, using the above formula, the product of the outer two of three consecutive numbers very nearly equals the square of the inner.

Unfortunately, the article, published in the summer of 2007, is no longer online.