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.