The point of any time signature (4/4, 6/8, 13/16 etc etc) is to tell you how many notes are in each bar. _(Is is more true to say that it’s the simplest amount of equal length notes per bar but it’s not so important)._
The bottom number tells you how big each note (or ‘beat’) is, ie a quarter note, an eighth note or anything else divisible by 4 (also 1 and 2 are used).
The top number indicates how many of that type of note is in each bar. 4/4 implies four quarter notes in every bar. 13/16 implies thirteen sixteenth notes.
Although 2/2, 4/4 and 8/8 are very similar, they are slightly different in their ‘feel’, but there is lots to argue about this.
4/4 is the most common time signature in popular music. “Money” by Pink Floyd is worth listening to as it has 7 quarter notes in every bar (7/4) and this is quite uncommon.
This is an absolutely gigantic topic and I look forward to lots of wonderful replies and argument about it.
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