Balanced Steps

Just a quick note on something funny I noticed in Richard Cohn's Audacious Euphony that led me to a mild (and daft) reharm of Giant Steps.

At the point of interest Cohn is interested in the voice-leading possibilities when all harmonies form one of the two basic tonal triads and one voice at a time moves by a single semitone.

He produces the following diagram showing how each triad can move if only one voice can change, and only by one semitone, and the result has to be a major or minor triad:

Cohn uses a capital letter and a + to mean a major triad and a lowercase letter and - for a minor triad.

As you can see, if you start on a major triad your options are to flatten the third (taking you clockwise to the minor on the same root) or to flatten the root (taking you anticlockwise to the major triad a major third above). Similarly, if you start on a minor triad you can raise the third to get to the parallel major or you can raise the fifth to get to the major triad a tritone above.

This yields four little "islands" -- there's no way to get from one to the other just by pushing notes up or down a semitone as long as every step is constrained to being a major or minor triad.

Jazz musicians will probably notice that each island's major chords are the key centres of Giant Steps, since they're separated by major thirds. So here is that old jam session favourite, with is voice-leading "balanced" using Cohn's scheme:

This kind of thing is actually not bad to practice if you have trouble changing one note in a chord while sustaining the others, so it might be of some practical use to you, but otherwise it just amused me to try it.

Here's how it sounds: