I think perhaps the way I would state the subset problem is that white keys are in a way the "subset that sounds good" to the culture where the piano keyboard arose. More in the vein of discussion than suggesting you'd need to change anything :)
The black keys are means of transposing that subset.
It is a very interesting but in a way unrelated insight that the black keys also form a consonant group.
And then music and musicians naturally coevolve with instruments and do whatever they please!
I think perhaps the way I would state the subset problem is that white keys are in a way the "subset that sounds good" to the culture where the piano keyboard arose. More in the vein of discussion than suggesting you'd need to change anything :)
The black keys are means of transposing that subset.
It is a very interesting but in a way unrelated insight that the black keys also form a consonant group.
And then music and musicians naturally coevolve with instruments and do whatever they please!