Time Signatures
Simple Time is a time-division in which each beat in the bar is divisible into two

Compound Time is a time-division in which each beat in the bar is divisible into three

Simple Time
e.g.
Duple
2/4, 2/2
Triple
3/8, 3/4, 3/2
Quadruple
4/8, 4/4, 4/2
Compound Time
e.g.
Duple
6/8, 6/16, 6/4
Triple
9/8, 9/16, 9/4
Quadruple
12/8, 12/16, 2/4
Irregular Time will have a top number that is greater than four. It will not, however, be divisible by two or three.
Irregular Time
e.g.
Quintuple
5/8, 5/4
Septuple
7/8, 7/4