This is a question I received the other day and I was surprised about how in-depth the answer became. All musicians are familiar with time signatures at the beginning of pieces – whether it’s 3/4, 4/4, 6/8, or even something like 12/8 – but why is there no 3 at the bottom of time signatures? The answer to this question comes down to what a time signature means.
The top number in a time signature represents how many beats there are in each measure. In other words, each measure (the box around each set of notes) of music on your sheet has that many beats contained within it – for example, a piece in 3/4 would have 3 beats in each measure of music.
The bottom number in a time signature represents the kind of note getting one beat. For example, a 1 would stand for a whole note. So a time signature with a 1 at the bottom – such as 4/1 – would mean that each whole note gets 1 beat and the top number tells you that there are 4 beats in each measure of music. A 2 at the bottom of the time signature would represent a half note and that means that every half note gets one beat. A 4 on the bottom would represent a quarter note and that would mean that every quarter note would get one beat. This goes on and on with each number representing a different note. But you might have noticed we just skipped 3 and instead went from 2 to 4; why is this?
There is not really a 3 note in music. What about something like triplets? Couldn’t you have a triplet getting one beat? The answer is not a simple yes or no.
Composers are able to make triple divisions as part of a time signature but they aren’t represented by a 3 at the bottom of the time signature. When you see time signatures like 6/8 or 12/8 these are actually functioning differently than you might think. There are certainly 6 beats in a 6/8 time signature and there are 6 8th notes to a measure. The question is, how is this different from 3/4 where you have three quarter notes in a measure? After all, three quarter notes equals the same amount as six eighth notes; it is exactly the same amount of time that’s measured. So how are these different?
When you have something like 6/8 time or 9/8, or even 12/8 time it’s actually a triple division. 6/8 time is actually two groups of three – sometimes referred to as a duple meter. In these triple division time signatures, the bottom number can represents dotted quarter notes. So 6/8 time is like having 2 dotted quarter notes in each measure. 9/8 time can be thought of as a piece with 3 dotted quarter notes in each measure. (Each dotted quarter note contains 3 eighth notes.) So, this is how a triple division of the beat is achieved with time signatures.
So why can’t we just put a three at the bottom of the time signature? Because there is simply nothing we can denote as a three note – every time signature must have a note represented in the bottom number and 3 is not represented by any particular type of note.
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