The typical way to represent a beat in music notation is with a "quarter note." (I'll tell you why it's a quarter note later.) The symbol for a quarter note is:
quarter note
It is also possible to draw the note with the stem pointing down. It is not allowed to put the stem on the other side of the note. It's on the right side when pointing up and the left side when pointing down:
quarter note, down stem
But one beat is not so interesting. Beats establish a rhythm when the occur in sequence. We write a sequence of beats by arranging them left-to-right on a line, like this:
four beats
If you clap your hands 4 times at a steady pulse, you will be performing this little piece of music.
We might represent rhythms on the computer as an array of time points, e.g. the little piece above could be represented by:
[0, 1, 2, 3]
Measures
Music is often described as hierarchical. There are beats, but you will probably notice that not all beats are the same. Most popular music has a higher level organization called a measure that consists of 4 beats. Try listening to some rock music and see if you can hear the 4-beat measures. You should feel something "big" happening every 4 beats. (Hint: rock is usually pretty fast. For fast rock, you'll be tapping about 2 or 3 beats per second. If you feel that something "big" happens every 2 beats instead of 4 beats, don't worry -- musical organization exists at many levels, so the 4-beat measure is partly a matter of perception.)
print "measure:", m, ", beat: ", b, " at time ", 4 * m + b
Duration
Music would be really boring if it only had quarter notes. This would mean that all events take place on the beat and last for one beat. Music notation allows for different durations. As you might imagine, a 2-beat duration is a half note, and a 4-beat duration is a whole note. Going to shorter durations, half a quarter note is an eighth note, etc. Here's what they look like:
whole, half, quarter, eight, sixteenth notes
Each measure still has four beats, but in some measures the durations are shorter so more notes fit into those 4 beats. Notice that the last measure has 4 sixteenth notes in the first beat and quarter notes in the remaining three. I did this mainly to save space, but it makes the point that you can combine durations any way you like as long as durations add up to 4 beats.
Here's an array representation:
[[0],
[4, 6],
[8, 9, 10, 11],
[12, 12.5, 13, 13.5, 14, 14.5, 15, 15.5],
[16, 16.25, 16.5, 16.75, 17, 18, 19]]
