You said something interesting about how you can describe music as having three elements (melody, chord, lyric). At first I thought that including lyric in those three was a little silly but then I realized that that actually makes complete sense.
there are other variations to this, but when it comes right down to it, music and non-music rely on each other. another example would be the underscore to a scene in a movie. no lyric, but instead we have characters and things happening. and again, in that case, all 3 should be considered together, because their reliance on each other is so intimate