Time signatures are the two fractional numbers that are written in the beginning of a musical staff, right after the key signature. Here's the why and the how!
It may seem that these two little numbers are not important enough to pay any real attention to. But actually they give us quite a lot of information that is especially useful before you start learning a piece!
First of all, the top number tells how many beats there are per measure. Why is this good to know? Well, it tells you something about the style of the piece.
Every musical composition that you listen to has some form of underlying music beat, or pulse.
Sometimes it is very obvious, like in a rap, or in a rock piece. The beat is heavy and pronounced. It is easy to move or dance to and often organized in groups of four beats.
Sometimes it is more vague and floating... like in Clair De Lune by Debussy. The pulse is there, but it is changing, moving and not so obvious.
Whereas a march is meant to.... march to! (Duh..) And unless you have three legs : ) the beat is felt in groups of two; Right, left.
So, music comes in different styles and has different purposes (listen to, dance to, march to...etc).
The most fundamental difference is in the beat, and how the beats are organized into groups. This organization of the beats in groups is called musical meter. And the time signature tells us all this in only two numbers!
So if the top number tells us how many beats there are in each group, or measure, what about the bottom number?
When reading the music we see that there are bar lines dividing the staff into «compartments» called measures or bars.
Since each measure represents the grouping of the beats in the piece, all rhythms have to add up to exactly the correct number of beats (top number) for each «group».
But in order to do that, you need to know what note is worth one beat.
As in fractions, the bottom number represents what we count. In music it is the particular note value that is «worth» one beat.
This is important for being able to read the music notes; a number 4 means that the quarter note (or crotchet) is worth one beat, for example.
Knowing this, we also know that on one beat there could alternatively be two eight notes (quavers) or four sixteenth notes (semi quavers), or any combination of note values adding up to one quarter note. (This is what creates the rhythm of the piece.)
So, if the bottom number is a 4 it means a quarter/crotchet is worth one beat. What about other numbers? The most common are: