I mean Western music, classical music, circle of fifths and all that. Why can’t I have a key with, for example, three sharps -- though not the usual F, C, and G, but instead some other combination like E, B, and D? I imagine it would sound terribly dissonant. I have heard that the reason there is the conventional progression of sharps/flats (i.e. the circle of fifths) and that there cannot be other strange combinations of sharps/flats is because the keys are “built on each other”. However, I’m not sure what that means exactly.
I have a very limited understanding of music theory, and occasionally I have dabbled in (piano) composition and made a few amateur sketches. It is always the case that I find myself “gravitating” toward a certain key in any given attempt. I can never seem to, for example, make a sensible or at least not-terrible-sounding sketch without being in some conventional key, and if I want to introduce anything different I would simply notate accidentals in individual measures (but that would usually only be temporary, e.g. a single one-note dissonance). So what I am wondering is, is it possible to actually compose a solid, structural, perhaps even melodious piece strictly with an unconventional combination of accidentals in the key signature, and where individual measures or segments are not in some conventional key signature (which seems to usually be the case, e.g. a piece may be said to be “in C major” but can be in other keys at different moments), which would usually achieved by introducing accidentals? (I mean, one could put B as the only sharp in the key signature, but then simply add a natural to each B throughout the piece… so effectively it’s just C major.)
Could a key with unconventional accidentals make sound, structural, perhaps even harmonic and melodic sense... a key that is perhaps separate and distinct from the conventional key signatures, and maybe even with a different "quality", "temperament", or "feel"?