When listening to music, you might find yourself tapping your foot to the beat. And you probably tap your foot in "groups" of beats, without even realizing it.
For waltzes, the groups of beats are 3... and you can count along as "1,2,3...1,2,3"
For a song like Hey Jude, the groups of beats are 4... counting along as "1,2,3,4...1,2,3,4"
Bar lines group those notes on "paper".
Time signatures are different from bar lines, but related.
If you heard things like "4/4 time" or "3/4 time", those are "time signatures".
The time signature gives you 2 numbers: (i) the first number tells you what grouping of notes to count along with the song, and (ii) the second number tells you what type of note (quarter note, eighth note, etc) is valued at 1 beat. The first number is about feel, the second number is about notation.
To fully understand how to interpret the 2 numbers of time signatures, here are examples.
The most common time signature in Western music is 4/4 ["four-four"] time.
Notice the two numbers given as a fraction? — "4/4" time.
The first 4 (at the top of the 4/4 "fraction") tells you the grouping of beats to count the song.
You'll therefore count along to 4/4 time as "1,2,3,4...1,2,3,4...", because the top number is a 4.
The 1/4, at the bottom of the "4/4" fraction, tells you what note (quarter note, eighth note, etc) is valued as 1 beat. For 4/4 time, 1/4 at the bottom tells you that quarter notes will be valued at 1 beat. As a consequence, if 1/4 notes are valued at 1 beat, 1/2 notes will be valued at 2 beats, 1/8th notes will be valued at half a beat, so on and so forth.
For 6/8 time, the top number being "6" tells you that you'll count along with the song as "1,2,3,4,5,6...1,2,3,4,5,6..."
The bottom number, "1/8" tells you that you'll treat eighth notes as 1 beat in the bar. Therefore, all other notes change with respect to this reference; so 1/4 notes will be worth 2 full beats, and 1/2 notes will be worth 4 full beats,
Now keep going with these other time signatures! Interpret the top and bottom numbers, and listen to the audio examples to double-check your intuition.
Here's a look at how 2/4 time is notated, alongside an example.
Grouping: the 2 at the top tells you that each bar will "store" 2 beats of time, so you'll count along with the song as "1,2...1,2...1,2...etc"
Notation: since the number at the bottom is 1/4, quarter notes will be valued at 1 beat. Therefore, since each bar stores 2 beats, 2 quarter notes will fill each bar of 2/4 time.
Here's that waltz again. You probably know what to expect with a waltz, because this time signature is so common, but try dissecting it in the same way.
Grouping: the 3 at the top tells you to count along as "1,2,3...1,2,3..."
Notation: the bottom number is 1/4, so each quarter note will be valued at 1 beat. Therefore, since each bar is grouped with 3 beats, 3 quarter notes will be enough to fill each bar.
Now, here's the crowd favorite, 4/4 time. You already know how this one works, but let's review again!
Grouping: the "4" at the top means you'll "feel" the music in groups of 4 beats.
Notation: similarly, the "1/4" at the bottom tells you that one 1/4 note will be valued as 1 beat of time. In a bar of 4/4 time, four quarter notes will therefore fill each bar.
Now, when you stare at a sheet of music, you'll know how to: (i) count along with the music, and (2) value the duration of each note on the page.
To hammer the point home, check out these songs in various time signatures. Count along and see if it's what you expected.
3/4 Time: Slim Dusty - A Pub With No Beer
4/4 Time: Van Morrison - Brown Eyed Girl
5/4 Time: Paul Desmond & Dave Brubeck - Take Five
7/4 Time: Pink Floyd - Money
9/8 Time: Sting - I Hung My Head
12/8 Time: Tool - Schism
6/12 Time: Del Amitri - Nothing Ever Happens