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Video Transcription

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.

You stated that the top figure in a time signature indicates how many beats in a bar, yes it does in simple time however in compound time the top figure indicates how many pulses in a bar and the bottom figure indicates what kind of pulse. i.e 6/8 is compound duple, if you divide the top figure by 3 and the bottom by two you find it has 2 dotted crotches per bar. Alan West.

You are right. How a meter divides up is another subject entirely. It's important for people to understand the simple math in a time signature first. Then they can appreciate how a waltz in 3/4 time may be felt in 1 as well as other duple meters that you bring up - good points!

John D. Beach* VSM MEMBER *on January 30, 2019 @8:24 am PST

Time signatures can become complicated fractional concepts within a measure, requiring in-course-of-play division and a theoretical arbitrary or constant on which to base such division. Three is an odd number which does not lend itself to an equality of purposeful or performable division relative to its progressive multiples.

There can be divisions of 3 within almost any time signature. Not only can each beat be divided in 3 with triplets, 2 beats can also be written as triplets where 3 notes take the time of 2.

However, the bottom number represents a note value and there is no "3" note. That's the simple explanation as to why no time signatures have a 3 on the bottom.

Mike Vitale* VSM MEMBER *on February 10, 2017 @7:56 pm PST

I thought about this one and offer another consideration from the field of mathematics. The lower number in a time signature functions as the base of a numeric system. By base, I mean our standard number system is base 10 - the rightmost position indicates the number of 10's raised to the zero power, to the left is the number of 10's raised to the first power and so on. In music, the base for the lower number in the time signature is 2. So 2 raised to the zero is 1, 2 raised to the 1 is 2, 2 raised to the 2 is 4 - giving us the familiar 1, 2, 4, 8, 16 for the lower numbers. The upper number in the key signature functions similar to our number system in that it tells you how many of the base you have in the measure. For a 3 to appear in the lower number in a time signature, we would need to switch to base 3 for our rhythmic structure. I don't think it would offer any additional expressiveness though as you can emulate triples using the top number as 3, 6, 9, 12 . .

Robert Estrin- host, on February 13, 2017 @12:55 pm PST

It's interesting how rhythmic notation has evolved. Perhaps there are other systems that are possible. But the good news is that the notation system we have works - so we're in good shape!

Excuse my English because I am a French Canadian not speaking much English.
There is an error in the released of February 6, 2017.
The video transcription following the video about 4/3 in music is about "How much does it cost to tune a piano".
I would appreciate to be able to read the right text.
Thank you.