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 Time signiatures are like fractions.

They tell us how many notes are in each bar - and what kind of notes they are.

The top digit tells us how many notes are in a bar  - and the bottom digit is what each note is.

If the lower digit is 4 then we're talking crotchets (or whole notes -1s);

if it's 2- we're talking minims (2s); and if its 8 then we're talking quavers or 1/2s

In fact the bottom number is the fraction of a semibreve the note is 

So 3/4 means 3 'quarters of 4' = 3 one's ie 3 crotchets (or 'quarter notes')  

and 6/8 means 6 'eighths of 4' = 6 halves so six quavers (or half-notes)

Like good accounting, every bar must add up to the same total count.

Simple, Compound and Complex Time

In the beginning, life was Simple. Notes = beats. So a 4/4 bar had just 4 crotchets in it- and 4 beats. Then to vary things a bit, there were then either two notes to a beat- or a note every two beats - or a bit of both. And maybe doubling or halving the notes again.  

Then we wanted to have 3 notes to a beat! And so came compound time!

Compound time marks a departure between notes and beats. Whereas before, we could be pretty sure 3/4 meant 3 counts in a bar - but also 3 beats per bar, 6/8 may mean there's 6 quavers in a bar - but not 6 beats!

In 6/ 9/ or 12/ time (ie multiples of 3), notes are bundled into 3s. So the beat count in a bar is how many groups of three - the multiple of 3.

So 6/8 time is 2 beats to a bar; 9/8 time is 3 beats to a bar; 12/8 time being 4 beats to a bar.

When writing music, notes are beamed in 3's to represent this and distinguish the beats more easily. Note that each beat is 3 notes in length.

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