This morning a young adult student in preparation for sight-reading Clementi's F-sharp Minor Prelude (in the splendid collection Preludes and Exercises) was ambling through the F-sharp minor scale. This young man has not been force-fed scales of any kind, and has a most accurate and astonishingly sensitive ear. As he played the upward moving scale he went beyond one octave, then began to respond to its inner tensions by altering tones. He did this entirely without plan unaware that his meanderings indicated profound auditory involvement in the mysteries of that scale, made even more poignant by the black/key - white/key half steps.
He makes his living as a computer animator so is well aware of the power of formula and of its opposite.