Thanks to Jacob Collier’s (over)enthusiastic callback to Ernst Lévy’s concept of Negative Harmony, somehow this concept has gained some traction online in recent times. Having learnt about it, I started implementing it on OpenMusic to study it for my own purposes. What resulted wasn’t one such unique mapping (i.e., Negative Harmony) but rather six different mappings (including Negative Harmony, of course) which I have simply called mirror harmonies. Why six? Well, given any natural pair number N, there are only N/2 such mappings for N EDO (e.g., 6 for 12 EDO, 12 for 24 EDO, 24 for 48 EDO, etc.)
I post all six mirror harmonies’ mappings (for 12 EDO) below — the one on the top left corresponds to Negative Harmony:
Every single one of these mirror harmonies offers a great way of transforming pitch material which conserves (what Dmitri Tymoczko refers to as) macroharmonic consistency, i.e. none of these is more or less musical in any way than the previously supposed unique Negative Harmony.
All the best,