The Golden Mean in Harmony Part 1

If you ride chaos all the way out to its edge, you find beauty and order… and the Blues

Chaos: complete disorder and confusion; behavior so unpredictable as to appear random, owing to great sensitivity to small changes in conditions; the formless matter supposed to have existed before the creation of the universe.

Chaos theory: The branch of mathematics that deals with complex systems whose behavior is highly sensitive to slight changes in conditions, so that small alterations can give rise to strikingly great consequences.

Phi: The twenty-first letter of the Greek alphabet ( Φ ).

Golden Section: The division of a line so that the whole is to the greater part as that part is to the smaller part (i.e., in a ratio of 1 to 1/2(√5 + 1)), a proportion that is considered to be particularly pleasing to the eye.

Mandelbrot, Benoit (1924– ), French mathematician, born in Poland. He is known as the pioneer of fractal geometry.

Fractal: A curve or geometric figure, each part of which has the same statistical character as the whole. Fractals are useful in modeling structures (such as eroded coastlines or snowflakes) in which similar patterns recur at progressively smaller scales, and in describing partly random or chaotic phenomena such as crystal growth, fluid turbulence, and galaxy formation.

The concept of harmony goes all the way back to the Greek philosopher Pythagoras (580–500 bc). Pythagoras said that whether two notes sounded good together had to do with simple ratios:
1:1 unison
1:2 octave
2:3 fifth
3:4 fourth

We also find the 1:2, 2:3 and 3:4 proportions in the first and strongest overtones (also called partials or harmonics) which exist within every musical sound (except for a pure sine wave), blending with the fundamental tone.

This natural kinetics gave birth to Western harmony, including the circle of fifths, major and minor scales, and dominant and subdominant harmony which, by the way, is the building blocks of The Blues.