With the design of this keyboard, only one note (maximum) can be in tune with the 440Hz equal temperament tuning, at least apart from octaves. No complicated proof of this is necessary since the ratio between any two notes in equal temperament is irrational and every note combination on this keyboard is rational. The irrationality of equal temperament is likely part of the reason why equal temperament was no common until relatively recently in human history.
I think the example also highlights why equal temperament is pretty good if you can't change tuning on the fly. Certain keys (the musical theory kind, not the keyboard kind) will sound completely different. At least equal temperament is equally out of tune from just intonation (how singers and instruments with variable pitch tune chords) for every key.
Something from the well-tempered clavier by Bach would likely work a lot better as a demonstration because it doesn't stray nearly as far from the home key. You could also make it work better by maybe adding in some keybindings to adjust the key like harps use. You probably wouldn't even need to add in 12 modes for it since harmonically related keys still work pretty well. Keys like F and Bb work well together because they are close on the circle of fifths, but F and B (natural) will not since they are basically as far apart as possible.
I think the example also highlights why equal temperament is pretty good if you can't change tuning on the fly. Certain keys (the musical theory kind, not the keyboard kind) will sound completely different. At least equal temperament is equally out of tune from just intonation (how singers and instruments with variable pitch tune chords) for every key.
Something from the well-tempered clavier by Bach would likely work a lot better as a demonstration because it doesn't stray nearly as far from the home key. You could also make it work better by maybe adding in some keybindings to adjust the key like harps use. You probably wouldn't even need to add in 12 modes for it since harmonically related keys still work pretty well. Keys like F and Bb work well together because they are close on the circle of fifths, but F and B (natural) will not since they are basically as far apart as possible.