I always have had trouble understanding the time signature in music. I have read about this, of course, but I don't understand it completely.
Days ago, I think I got something that I want to confirm with you.
This is my reasoning:
If you play an instrument that can only play one note at a time, like a trumpet, you don't really need the time signature, since you always have to play one note completely to play the next note.
If you play an instrument that can play more that one note at a time, like the piano or guitar, or play more than one instrument (like in a band), you need the time signature because without it, you can't know when to play the next note.
For example: you have a piano score. In the first measure you have 4 quarter notes all of them different notes in that measure. The tempo is "quarter note equals 60." In this way, you can play the first note at t = 0 s, the second note at t = 0.25 s, the third note at t = 0.5 s and the last note at t = 0.75 s. The four notes are held exactly one second. Or you can play the first note at t = 0 s, the second note at t = 1 s, the third note at t = 2 s and the last note at t = 3 s.
So without time signatures, in the last case, an ambiguity arises and the whole purpose of the time signature is to eliminate this ambiguity.
Thanks for your help.