A time signature is a set of two numbers, one on top of the other one, written right after the key signature in a piece of music. The two numbers in a time signature tell you how many of one kind of note there are in each measure in the song. For example, means that there are four quarter notes, or notes that last one beat, in each measure.
The number in the top of the time signature tells a player how many of a certain kind of note there are in each measure. The number in the bottom of the time signature tells what kind of note is used a certain number of times in each measure. The number on the bottom of the time signature can be any number that follows the pattern1, 2, 4, 8, 16, 32..., where each number in the pattern is two times the number that came before it. So, 64 could be a number that is put in the bottom of the time signature, but 65 could not be one.
Number on the bottom of the time signature
What it means
A whole note lasts one beat
A half note lasts one beat
A quarter note lasts one beat
An eighth note lasts one beat
A sixteenth note lasts one beat
This table shows different numbers that could be the bottom of a time signature, and what they mean. Note that each note down lasts for one-half of the amount the note above it lasted. For example, one quarter note lasts one beat, and one-half note lasts one half of a beat, because one divided by two is one-half.
The symbol "" is called "cut time" (alla breve) and has been used instead of using time, where every note is cut in half. So, in "cut time", a quarter note, which usually gets one beat, gets one-half of a beat.