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Time signatures, and what 4/2 means

A time signature is two numbers stacked. You already read the top one by instinct: it's how many beats are in a bar. The bottom one is the part that trips people up, because it isn't a count at all. It names which note value gets one beat.

Bottom numberOne beat is a…Because
1whole notea whole
2half notehalf of a whole
4quarter notea quarter of a whole
8eighth notean eighth of a whole

So everything you already know (3/4, 4/4, 5/4) has a 4 on the bottom, which means the quarter note is the beat. Three, four or five quarter-note beats per bar.

4/2

Same idea, different unit: four beats per bar, and each beat is a half note. A full bar holds four half notes, which is the same amount of written time as eight quarter notes.

44 42 1234 1234 4/4: four beats, each a quarter note (filled head) 4/2: four beats, each a half note (hollow head)
count both bars exactly the same way: 1, 2, 3, 4

Does it sound slower?

No, and this is the bit that clicks it into place. How fast the music goes is set by the tempo, not the time signature. The tempo marking tells you how many beats per minute, whatever note the beat happens to be. Four half-note beats at 80 per minute sound exactly like four quarter-note beats at 80 per minute. You count "1, 2, 3, 4" at the same speed either way.

What changes is the writing. In 4/2, the notes that sound like quarter notes are written as half notes, the ones that sound like eighths are written as quarters, and so on. Everything is one size bigger on the page.

Same sound, written two ways in 4/4 in 4/2 beat = quarter note half-beat = eighth note beat = half note half-beat = quarter note

Then why bother?

Hear it

Pick one. The strong beat of each bar is the higher click. 4/4 and 4/2 are set to the same beats per minute so you can hear that they're identical. 2/2 and 6/8 are there because they're the two you'll meet next.

tap a time signature

The two you'll meet next

2/2, "cut time". Two half-note beats per bar, often written as a C with a line through it. Same bar length as 4/4, but you feel two big steps instead of four. Marches and fast show tunes live here: written like 4/4, felt in two.

6/8. This one breaks the rule a little. On paper it's six eighth notes per bar, but at any normal speed you feel two beats, each split into three: ONE-two-three TWO-two-three. Signatures with 6, 9 or 12 on top are called compound, and their beat is three of the bottom note. That's the lilt in a jig or "House of the Rising Sun".

The one-line version

Top number: how many beats in a bar. Bottom number: which note counts as one beat. The tempo decides how fast it goes. So 42 is four beats a bar, each written as a half note, and it can be just as fast as 4/4.