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There are lots of bad reasons to count lines of code, but lots of good reasons too. If you're porting some old code from one language to another, the more LOC in the old code, the longer it will probably take. If you're hunting for a bug, the more code you have to look through to find it, the harder it might be. Etc. It wasn't asked super eloquently but I think it's a highly constructive question.
It's not constructive to ask why a language is designed the way it is, particularly if that design asks us to type four extra characters for no obvious benefit? What am I missing?
It seems to me that it might be helpful to think about what you want to do with these note/chord/scale classes. Are you going to produce sheet music? Midi files? Do transformations on scores (transposition, doubling all the note lengths, adding trills to all whole notes above a certain note, etc.)? Once you have a possible class structure, think about how you would accomplish those tasks. If it seems awkward, maybe you want a different class structure.
"If you consider it a design issue where one interface has one contract for that method and the other interface has other contract then not allowing it would not solve the issue." Why not? It would force you to rename one of the interface methods. If the interfaces are coming from third-party code, that might involving asking that third party to change it, but it would effectively solve the problem, wouldn't it?