The next note is never more than a whole-tone away

I first learned of the exercise of running different scales into each other from Barry Harris. You start near the top of your instrument, and as the chords change, you change your scale but keep going in the same direction. Relatively easy on a tune like Autumn Leaves, pretty difficult on a tune like Giant Steps. My teacher Mark Sherman also emphasizes this drill, and has in fact taken it to a whole new level.

In discussing this drill a few weeks ago, Mark told me, the next note is always either a semitone or a whole-tone away. I thought of a simple way to prove this.

First off, we need to review the concept of locally diatonic scales. In short, they are scale in which all groups of three consecutive notes can be mapped onto three consecutive notes of the diatonic scale. There are only four scales that qualify: diatonic, melodic minor, whole-tone, and diminished. None of these scales contains an interval greater than a whole-tone. Both the harmonic minor, and its inversion, the harmonic major, contain an augmented second, that’s why they are not included.

Ok, so moving between any of our four scales, at any transposition, the next note will always be a semitone of a whole-tone away, and here’s the proof.

  • The current note will either be a member of the next scale or not
  • If the current note is a member of the next scale, the next note will either be a semitone or a whole-tone away
  • If the current note is not a member of the next scale, then the next note has to be a semitone away, by definition
  • Therefore, the next note is always a semitone or a whole-tone away

By the way, when running locally diatonic scales into each other, the aggregate result is definitely not guaranteed to be locally diatonic. It should be easy to think of examples where running two scales together results in two consecutive semitones, which would break the rules for locally diatonic.

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