I play the guqin (古琴), a Chinese zither-like instrument which I believe is the oldest instrument in the world for which musical notation exists. Like the Tibetan notation, it doesn't indicate rhythm or duration of notes, just succession. Until a hundred years ago or so, people were just assuming they knew what the melody sounded like, and to this day you will hear different interpretations of the same piece that simply make different assumptions about the duration of notes.