Signature isn’t for tempo, signature is to tell you;
1) What kind of note denotes a single “beat,” and;
2) How many beats you have per measure, as well as (generally) what beats should be emphasized.
>2/4 or 6/8? Why can’t the music just be written in 4/4 or 3/4?
Because theses actually mean different things, even if they’re “mathematically” equivalent at first glance.
2/4 time would denote that the first beat gets emphasis. 4/4 time denotes that the 1st and 3rd beats get emphasis, but that the 3rd gets less emphasis.
3/4 and 6/8 are also different; 3/4 time denotes that the 1st beat gets emphasis, whereas 6/8 time denotes that the 1st and 4th beats get emphasis, with the 4th beat having less emphasis.
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