Recently I’ve been fooling around with different figures to display chord relations, to some extent inspired by Euler’s and Riemann’s Tonnetz. I now came up with a 5×5 grid containing all 24 major and minor triads (with the middle position left blank) and tried to find a meaningful layout for such a triad square. There seems to be no entirely consistent way of arranging the chords so as to adhere to one single rule for the derivation of adjacent fields. Yet I found two interesting layouts, one of which tends to emphasise third relations, while the other prefers hexatonic poles. I’m curious what you think of these figures, and if they might be of any use in a transformational harmonic theory, apart from illustrating cycles of minor thirds and octatonic regions in symmetrical patterns.

To be sure, this is just thought-in-progress and by no means a fully developed approach, so I’ll be glad to hear your opinions and suggestions. In case I might have unconsciously reproduced some recent findings from Neo-Riemannian Theory which I was unaware of, I’d appreciate if somebody pointed out a source to me. Also, if you can think of another more convincing 5×5 layout, please let me know.