12-tone puzzle \\ triad sequences

Example solution: Augmented triads

Here’s an easy (but ugly) solution – divide the octave into thirds, four times. That is, twelve semitones divided by three pitches per triad produces an augmented triad: an equilateral harmonic structure constructed exclusively of major third intervals. Ascend this shape chromatically to use up every note of the chromatic scale.

This is clunky to explain in words, so let’s use a 12-tone grid to visualise this:

Drawing up a 12-tone grid is a great way to explore solutions to this puzzle.

And here’s the same solution in standard notation:

Solution 1: Four augmented triads (C+ D♭+ D+ E♭+) will use up every note of the chromatic scale.

Of course, with this solution being a symmetrical intervallic structure in 12-tone equal temperament (12TET), we may find that much like the whole-tone scale this sound has relatively limited applications in the ‘normal’ music we find ourselves playing daily. So this isn’t necessarily going to be prettiest sound on earth, and it will become apparent that even though every solution to this puzzle produces a sequence that uses all 12 tones of the chromatic scale in equal proportion, each solution produces a unique musical and emotional/evocative effect.