Simple and Compound Beat Division

Every beat has a built-in way of breaking into smaller pieces, and that way is either two or three. In simple meter, the beat splits into two equal subdivisions, like a quarter note splitting into two eighth notes. In compound meter, the beat splits into three equal subdivisions, like a dotted quarter note splitting into three eighth notes. Same beat, same tempo even, but a totally different feel underneath because one divides evenly in half and the other divides evenly in thirds.

To read a time signature correctly you need two things: the beat unit, which is the note value that gets one main beat, and the beat division, how that unit splits. In simple meters like 3/4 and 2/2, the bottom number names the beat unit directly: a quarter note gets the beat in 3/4, a half note in 2/2, and each beat divides into two. In compound meters like 6/8 and 9/8, the bottom number is misleading on its own. In 6/8, the six eighth notes group into two beats of three eighths each, so the beat unit is a dotted quarter note and the division is three. 9/8 works the same way: nine eighths group into three beats of three, a dotted quarter beat unit, compound triple.

This is why 6/8 and 3/4 can trick the ear. Both can be counted in groups of three eighth notes, but 6/8 treats those sixes as two beats of three, compound duple, while 3/4 treats its measure as three separate beats each splitting into two eighths, simple triple. Tempo never changes which meter you're in; the grouping of beats is what decides it, and that grouping is exactly what later work on time signatures and rhythm notation builds on.