Question

explain what both the top and the bottom numbers in a time signature mean?

Answer 1

The top number is the amount of beats you will be using and the bottom number is the maximum amount of beats possible in a measure.

For instance, \(\frac{ 3 }{ 4 }\) time has 3 beats per measure, and the amount of beats per note is the same as \(\frac{ 4 }{ 4 }\) time (half notes are 2 beats, quarter notes are 1 beat, etc.)
In \(\frac{ 6 }{ 8 }\) time, half notes would be 4 beats, quarter notes would be 2 beats, and so on.

Probably not the best explanation, but whatever :p

Answer 2

The top number of the time signature tells you how many beats to count. This could be any number. Most often the number of beats will fall between 2 and 12.

The bottom number tells you what kind of note to count. That is, whether to count the beats as quarter notes, eighth notes, or sixteenth notes. So the only numbers you will see as the bottom number (the denominator) will correspond to note values:

1 = whole note (you’ll never see this)
2 = half note
4 = quarter note
8 = eighth note
16 = sixteenth note
You could continue on with 32, 64, but you will hopefully never encounter them! After a while it gets a bit unwieldy. The most common bottom numbers are 4, 8 and 16.