What determines the time signature of a piece of music?

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I know that most music comes in 4/4, but why? What’s preventing someone from just putting more bars into the sheet music and making that 2/4?

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You could absolutely do that. In fact, with enough effort any piece of music could be written in any time signature. However, time signatures hold important information about phrasing and emphasis. In a 2/4 time signature, every other beat is emphasized. In a 4/4 time signature, you know to emphasize the 1st beat the most, then the 3rd, then the 2nd and 4th. In a 3/4 time signature, you emphasize every 3rd beat, and phrases tend to come in lengths of 3. So unless you were careful to annotate the sheet music to indicate that you really want 4/4-type phrasing despite the music being written in 2/4, the 2/4 version would sound subtly different when performed by professional musicians, and a theoretical 3/4 version would sound much different.

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