Why is There No 4/3 Time in Music?

Hi, this is Robert Estrie at virtualsheetmusic.com and livingpianos.com, with a great question I got the other day, and actually, the answer is more complex than I thought. The question is: "Why isn't there 4/3 time?"

Time signatures, you see them in the beginning of pieces of music all the time. Typically, you might have 3/4 or 4/4, or even 6/8 or 12/8, or something like that. Well, why can't you have a '3' on the bottom? Well, there's a very good reason, and it comes down to, what does a time signature mean?

Well, the top number of a time signature is simply how many beats there are in a measure, for each box of music, how many total beats there are. The bottom number, though, it's important to remember, what the bottom number stands for. The bottom number stands for the kind of note getting one beat. So, a '1' would stand for a whole note, so a time signature that has a '1' on the bottom, a whole note gets one beat. A time signature that has a '2' on the bottom, a half-note gets one beat. If you have a '4' on the bottom, a quarter-note gets one beat. It goes on and on. An '8' on the bottom is an eighth-note. So, why can't you have a '3'?

Well, there isn't really a three-note, or is there? What about triplets? Couldn't you possibly have a triplet getting one beat? Well, yes and no. Here is the way composers are able to make triple divisions as part of a time signature.

When you have a time signature like 6/8 or 12/8, these are actually functioning differently from what you might think. You might think there are six beats, which indeed there are, but the way it divides is interesting. Consider this for a moment.

If you have 6/8 time, that means that there are six eighth-notes to a measure. Well then, the question is, how is that different from 3/4 time where you have three quarter-notes in a measure? After all, three quarter-notes equals six eighth-notes, so it's exactly the same amount of time that's measured. So, what's the difference?

The difference is this. When you have 6/8 time or 9/8 or 12/8, it really is a triple division. The way it works is this. 6/8 time is actually two groups of three, sometimes referred to as a duple meter. So, 6/8 time, sure, you could have a piece that's very slow, you'd count 1-2-3-4-5-6, and that's perfectly all right because that's what a time signature tells you. But, more often, when it's a little faster, it's 1-2-3, 4-5-6, 1-2-3, 4-5-6. And when it gets very fast, instead of counting 1-2-3, 4-5-6, 1-2-3, 4-5-6, you just count 1-2, 1-2, two groups of three - 1-2-3, 4-5-6.

So, that's the way triple meters are approached, is by basically, the bottom number is a dotted quarter-note. When you have 6/8 time, it's two over a dotted quarter-note. I hope I'm not confusing you now, but the whole idea is that when you have the eighth-note getting one beat, it is generally dividing the measure into dotted quarter-notes, so 9/8 would be three dotted quarter-notes, and could be, indeed, counted in three, three groups of three.

But, sadly, there is no way to put a '3' on the bottom of a time signature because nothing is really a three-note. You have quarter-notes, eighth-notes. So, that's the long and short of why you can't have a '3' or 4/3 time.

Thanks for the great questions. It's very thought-provoking and interesting to describe the answer to that one.

Again, Robert Estrie here at virtualsheetmusic.com and livingpianos.com.

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