Duple, Triple and Quadruple Meter
The top number of the time signature tells us the number of main beats in each group/measure.
Time signatures with 2 main beats per group are called duple, with 3; triple, and with 4; quadruple. Easy-just look at the top number when you have simple time signatures.
So, for example a time signature of 4/4 is also called Simple Quadruple Time. 2/2 is called Simple Duple Time, and 3/8 is called Simple Triple Time.
A Caveat: The triple time signature 3/8 could- if played so fast that you have to “switch gears” to feel 1 beat per measure instead of 3- seem as if it would fall into the category of compound meter. If so- having only 1 main beat per measure (divided in 3 sub beats) it would be single compound. Not everyone agrees on this though...
So, what about the bottom number?
When listening to music, it is impossible to tell what the “bottom” number in the time signature is.
But you can easily learn to figure out if it is in simple time (main beat can be subdivided in 2) and if it is duple, triple or quadruple meter.
So you could listen to a piece and say (very snazzy!): ”This piece is in simple quadruple time, you guys!” How cool is that!