Q: What does the bottom part of a time signature even mean? I've watched so many videos on it and I still can't grasp its purpose
A: that is supposed to be what note a beat is. so if the bottom number is 4, the 'quarter' note is supposed to be the beat. if the bottom note is 8, then the 8th note is supposed to be a beat. so "4/4" is supposed to mean there is 4 beats per bar, and a quarter note is 1 beat. "6/2" would mean there is 6 beats in a bar and the half note is one beat. There are some problems with this system-- one problem is that in some countries the notes are not named like this (quarter, eigth, etc). And the other problem is that when the top number is a multiple of 3 and the bottom note is 8, it's usually not actually the 8th note that gets one beat, it's usually actually 3 eighth notes that get one beat. but at least the bar length will adhere correctly to the number system, so for example what i'm trying to say is, 6/8 in the real world usually does not actually mean 6 beats per bar with the 8th note getting one beat. instead it usually actually means there's 2 beats per bar and the dotted quarter note gets one beat. this is mathematically equivalent, but felt differently, for speed. but let's face it, who really wants to write 2/2.667