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Since the release last month of "The SUPER 4" Shortbook™ and blogpost, I've subsequently come across a few additional interesting and potentially useful musical relationships between aspects of this "super" 4-note grouping, known technically as a tetratonic.
Specifically, I've been checking out the effect of expressing them in intervals of a minor 3rd, which divides the octave into four equal parts - forming the diminished cycle.
As mentioned, the results proved to be quite interesting - and musically useful to boot.