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The most common time signature is 4/4. In fact it is so common that it is also referred to as common time. But what does 4/4 time mean? It means that there are four measures, and four beats in a measure. The number on top is the number of measures, and the number on the bottom can be thought of as a fraction. In this case it equals 1/4 notes.
Another popular time signature is 3/4 time. Taking what we have learned we will see that this time signature has 3 quarter notes in each measure. This time signature is most famous for its use in waltzes.
Yet another popular time signature is 6/8. So there are 6 beats per measure and each beat is played as eighth notes. The trick with 6/8 times is that it often sounds like two separate triplets in each measure. If you watch the video, you'll hear what I mean.
There are other time signatures too. 7/8 has seven beats in a measure and each is an eighth note. There's 9/4, 12/4, 2/4, and even 4/2 time. That last one isn't so common, but consists of four beats in a measure with each one being a half note.
So there you have a basic introduction to time signatures. As you see them in sheet music and use them in your playing, they should become more familiar to you.