Key is described as choosing a certain set of notes from all the available ones. A key is not just a collection of allowed notes, there is a kindof frequency d

Key is described as choosing a certain set of notes from all the available ones. A key is not just a collection of allowed notes, there is a kindof frequency distribution to them too, so that the tonic is either the most used or the most implied. The fifth is often the second-most-used. Its sortof like a key has a 'center of gravity' in the tonic note. Either it will be used a lot or alluded to a lot by the other notes. Is there any popular music that belongs to multiple keys because they only use the notes that are shared between them? Sortof - the notes might technically be part of a few different keys - but usually there is an 'implied center of gravity' pointing to a tonic note and that tells you what key you are actually in. But if you make it ambiguous for a few bars it can be a useful musical effect, sorotf suspense. And then you resolve to one or the other possible candidates and it sounds cool. But if you do it for too long it sounds muddy. A good key change is sortof like that, you hover in a space that could be either key for a bit then resolve to something specific. Or, is there anything that doesn't belong to any key because it uses more notes than are allowed by any key? Jazz goes all over the place. Accidentals, key changes. An accidental is like a single note that isn't 'in' the key. Perhaps like a one note key change. The keys are still part of it but its more adventurous. If you completely ignore key altogether its polytonal and it sounds kindof annoying. Or people invent their own ones, e.g. Aleksi Perälä and the Colundi Sequence https://thequietus.com/articles/20493-aleksi-perl-perala-colundi-sequence-clone-basement-review https://thequietus.com/articles/20493-aleksi-perl-perala-col... Althought there's a big argument as to whether western keys are all just conditioning or something intrinsic. e.g. Does Major sound 'happy' and Minor sound 'sad' to all humans? Octaves are pretty universal in human music but after that it gets complicated. I think there's some good pointers to how overtones in in inner ear correspond to frequency ratios which correspond to classic intervals such as the third or fifth. And then how best to construct a scale that squeezes in the most useful thirds and fifths and so on. If you follow that exercise then the white keys/black keys on a piano start to look quite optimal. BUT social conditioning, anthropology and so on so maybe not.