[manlon]

If you start with the 12 chromatic tones and start addding notes to a scale going up a circle of fifths, there are two natural stopping points where you have spanned the octave with a complete-sounding set of notes with relatively equal spacing and no gaps: five notes, which gives whole-step and minor-third intervals; and seven notes, which gives whole-step and half-step intervals. These two scales correspond to the spacing of the black notes and the white notes, which are mirror images of each other around the circle of fifths. Any other choice of scale size would have gaps, I believe.

[nix]

The drawback to this explanation is that the diatonic scale is 10,000 years older than the "circle of fifths". So it presumably had some appeal to musicians as well as to music theorists.

[dmoney]

Where do you find 10,000 year old music?

[nix]

You infer it from the existence of 10,000 year old musical instruments.

See http://en.wikipedia.org/wiki/Diatonic_scale#Prehistory - which also says that the circle of fifths was described much earlier than I thought.