Time signatures appear at the beginning of a song and stay until the time changes or until the end of the song. They're those two numbers as you can see in the image above. The time signature is simple, it tells you how to count the beats in the song and how to feel the music.
The top number of a time signature tells you the quantity of beats per measure. In that first measure we'd have 4 beats, the second 3, and the third 9. Most songs are written with the quarter note having the beat, which is where it gets the name quarter note (its a quarter of each measure). This is not always the case and the bottom number tells us about that. The bottom number tells us the type of note that matches the beat. So in 4/4 time the quarter note is the beat and there are 4 of them in a measure. If you don't get why the 4 tells us its a quarter note, think of it being a fraction with x/4 being a quarter. With that same mentality, the third measure in the example above would have a sixteenth note getting the beat (because its x/16). The next would have an eighth note, followed by a half note, and ending with a sixty fourth note.
As I've shown in the example, you can put almost any number on top. The measures are only there for counting and feel purposes, so if you can justify a huge number like 210 beats with how it wouldn't work with a smaller number the last example is possible. The bottom number can only match existing notes. So you can only see 1, 2, 4, 8, 16, 32, 64, or 128 on bottom. I have personally never performed a song with anything other than 1, 2, 4, 8, or 16 though.
If you have further questions on how time signatures work or why some options seem similar, feel free to reach out or sign up for a lesson by clicking here! The most common question I get is why 2/2 and 4/4 aren't the same thing, but that's for another day.
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