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Comment by hugh3 | Hacker News Reader

I think there are different answers at different levels.

On one level, the white notes are the notes of the C major scale, and the black notes are the semitones which are left over. Why not put all the semitones in one row? That would be much harder to play. Why split it into "C major" and "leftovers"? A bunch of semi-arbitrary decisions made by early harpsichord manufacturers, I guess, which happen to make the instrument easier to play than most alternatives.

If you're looking for an explanation of why the notes of the major scale sound good together whereas most alternative modes sound weird, that's a more difficult question.

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Supposedly there is a mathematical reason for the 2-2-1-2-2-2-1 spacing of the major scale. If you take all possible pairs of notes in the diatonic scale, you get a richer distribution of intervals than you can produce with any other seven-note selection from the twelve note scale. Similarly, the classic pentatonic scale provides the best set of intervals for any five-note selection from the twelve. A better set of intervals might lead to a better choice of chords too.

This is my somewhat fuzzy recollection from a paper I read a long time ago. Someone out there can check with three lines of R, right?

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.

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.

Where do you find 10,000 year old music?

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.

So if we stard from C, and take steps of fifths, we get the notes in the order: C, G, D, A, E, B, F#, C#, G#, D#, A#, F (and then C again).

It is true that if you take the first 5, you get a scale with pattern of intervals C-<2>-D-<2>-E-<3>-G-<2>-A-<3>-C, and then it you'd add the sixth note (B), that would be only 1 step from C. So if we aim for a "nice" distribution of intervals, 5-note scale is a good stopping point.

But your explanation doesn't give any light on why the 7-note scale would be the next stopping point.

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