# How do time signatures relay information on the grouping of beats?

I'm trying my best to understand musical meter, but it's just not making sense to me. In particular, I don't understand how one might deduce from the two numbers in the time signature (i.e. 3/4 or 4/4 etc.) the exact number of divisions and subdivisions of the beat. That information is necessary in order to determine whether a meter is simple/compound etc.

I'll quickly expound my (likely flawed) understanding. The number on top is the number of beats per bar, the number below tells you which type of beat. As there is a choice over how fast to play a piece, the lower number is arbitrary, or at least only important as regards ease of notation. As far as I can see, the top number is more important.

Simple meter divides each beat (or pulse) into two smaller beats. Compound meter divides each pulse into 3 smaller beats. My first question is: why are these are taken to be the only types of meter? Might we not group a meter with 10 beats per bar into two pulses of 5 sub-divisions, for example? This would classify as neither simple nor compound.

Secondly, suppose I'm given a time signature of 6/8. Numerically, 6 can be divided in four ways: either one group of six, six groups of one, three groups of two, or two groups of three. Unless I'm mistaken, the time signature 6/8 is always taken to represent the last of these possibilities: two pulses of 3 semiquavers. Now, I understand that 3/4 meter can represent either 3 groups of 1, or 3 groups of 2,4,8,16, ... etc. due to the fact that the lengths of notes in musical notation are related by powers of 2 (for example, a minim is twice the length of a crotchet), which accounts for the 3 groups of 2 possibility. This still leaves the question: Why shouldn't 6/8 represent one group of six beats (or six groups of one as they amount to the same thing)?

Is there some kind of system I've not yet come across, or is the only thing relating the groupings of beats to the number of beats per bar some pre-existing conventions which students of music theory simply have to learn by heart?

• 6/8 is two pulses of three quavers (eighth notes).
– Tim
Oct 8 '15 at 11:34
• related question and this. Oct 8 '15 at 11:43
• @JamesMachin Both numbers are actually important. Typically, signatures where the bottom number is higher tend to be slower in tempo. The lower the number, the faster the music tends to be. Ex. 4/16 vs 2/2. The reason for this notation is, I believe, purely psychological, but that's another point. You can absolutely divide the pulse into any number of subdivisions. You've actually stumbled into what are known as carnatic rhythms. For meters that aren't simple or compound, we say they're asymmetric = 5/8, 11/16, 7/4 etc. To clarify how pulses are grouped in a measure...(continued) Oct 8 '15 at 18:52
• ...especially with asymmetric meters, composers will often include the subdivision in the time signature. For example, instead of 7/8, it might be 3+4/8 or 2+5/8. Writing in this way clearly defines how the pulse is organized in the the measure, as well as the subsequent rhythmic groupings. Oct 8 '15 at 18:54

a time signature is just not very precise.

it'll tell you what symbol the beat is (GENERALLY) and how long a bar is. That's about it.

It doesn't tell you how many subdivisions of the beat is the "basic smallest rhythm unit" of the song (like 16ths in most pop for example).

In situations with multiples of 3 and 2, say a timesig of 12/8, you don't know whether it's 1 e & a 2 e & a 3 e & a OR whether it's 1 & a 2 & a 3 & a 4 & a. You are forced to look through the notation and figure all the useful stuff out yourself.

One important rule about time signatures that's not often mentioned is that if the numerator is a multiple of 3, well, you're usually dealing with a waltz (3 main pulses) that are subdivided. But you can't tell for sure until you read the notes and figure out the rhythms actually in the song.

It's no wonder that people are confused by time signatures. They're just plain vague and poorly specified (says me the computer programmer).

The theory of rhythm is a relatively new field of academic study beginning with music theorists such as Joseph Schillinger and Henry Cowell in the early 20th century. In more recent years there has been much academic interest in the musics of Africa and other places with aural (as opposed to literary) traditions. Music-neuroscience cross-displinary study is also developing the tools necessary to understand how the brain processes rhythm.

Rhythm can be conceptualized as existing in layers. The foundation of these layers is the pulse. This is a steady stream of "ticks" analogous with the ticking of a clock. When pulse is accented it creates beat. Regularity of beat creates rhythm. Rhythm, or the anticipation of beat, engages the brain at its most basic level and causes our bodies to respond kinetically - foot tapping, etc.

Meter comes out of higher brain function whereby beats are grouped into patterns, typically groups of 2, 3 or combinations of both. In other words, it is an intellectual process that has its origins in music as a literary art (reading music). The music of cultures with aural traditions - particularly those such as sub-Saharan African ones whose music involves much rhythmic complexity - is difficult to analyse in a traditional metrical sense. This is because the complexity arises out of a layering of rhythmic pattern elements each having a different periodicity (metric duration). This makes clear transcriptions difficult when attempts are made to notate the rhythms in a reduction down to a single meter. It does, however, make for interesting mathematical pondering. (See Godfried T. Toussaint The Geometry of Musical Rhythm - especially the chapter on "necklace rhythms".)

3/4 is always 3 beats to the bar. Those beats are crotchets, one beat each, 1/4 notes. 3/2 exists as 3 lots of minims, and 3/8 3 quavers. 6/8 is traditionally shown to represent 6 quavers, but grouped into 2 lots of 3, thus a two count, sub-dividing each count into 3. This produces a very different feel from 3/4 which will contain the same number of crotchet, etc, but grouped to give a different rhythmic feel.

Yes, it's entirely possible to have 10/4, and 5/4 is not uncommon - 'Mars', from the Planets, Take Five', 'Mission Impossible', et al. And with 10/4 you could group just as you wish. As with 5/4, which is either 3+2 or 2+3.

As far as grouping is concerned, 1st beat is usually strongest, but the rest of the bar can be whatever, although in 4 and 6 timing, the bars should be written out so that there is an obvious centre, as in a tied note if the second note is a minim, rather than crotchet, minim, crotchet, it ought to be crotchet, crotchet-tied-to-crotchet, crotchet. But that's not always followed.

• So I could write a bar of 6/8 grouping the notes into three groups of two semi-quavers, without being technically incorrect? Looking up, maybe my question was a bit unclear, but I was kind of looking for a method of deducing the grouping of beats given a time signature. But it looks like there's more than one accepted way to group the notes per time signature? Oct 8 '15 at 12:13
• Putting 3 groups of two QUAVERS in a bar will constitute 3/4. Putting them into 2 groups of 3 will constitute 6/8. It's a simple way for a reader to establish what's going to happen. Having said that, a look at the first couple of bars will do that generally, anyway.
– Tim
Oct 8 '15 at 12:29
• Yeah sorry I meant quavers, not semi-quavers. Ok suppose I wanted to notate music that simply had 6 quavers per bar with no subdivisions (i.e one pulse of 6). Would the meter still be 6/8? Oct 8 '15 at 12:53
• It would be a strange piece with only one note per bar - that could actually be of any length in real time, thus note value.. There would be no reason to make each note 6 quavers long over an alternative 3 or 4 beats, of a different real time. That's sorted by the metronome mark. The reason for different time sigs is to give insight into DIVISIONS within bars. No divisions = no need for anything except a very simple time sig!
– Tim
Oct 8 '15 at 12:57
• To use the notation of the post below, I'm talking about something that goes X----- then repeats. It has no divisions, but how could that be written with something less than six beats per bar? Oct 8 '15 at 13:43

I start a list here, which is somewhat distributed in existing answers to other questions:

With "X" as a strong beat, "x" a weaker one and "-" unemphasized, we have

• 4/4: X-x-
• 3/4: X--
• 2/2 (also 4/4 alla breve): X-
• 6/8: X--x--, as commented this is typically counted X-

In any case the first beat of a bar is emphasized.

A lot of it comes down to convenience and convention. When the music is doing something normal, the composer should use the conventional time signature to avoid confusion. When the music is too exotic to fit a convention, the composer should strive to be clear and avoid writing something that could be misleading.

My first question is: why are these are taken to be the only types of meter? Might we not group a meter with 10 beats per bar into two pulses of 5 sub-divisions, for example?

This is about the ways that beats subdivide into smaller pieces, not the ways that measures break down into beats. I defy you to find a piece of music in the Western tradition that divides the beat into 5 parts. The measure, sure, but not the beat. Everything is 2s and 3s (or combinations of them).

Regarding 6/8 and 3/4: this is about convention. We don't have a bottom number to represent a dotted quarter, so we have to find the least-common-multiple and use eighth notes. 6/8 should generally be reserved for compound duple meter, 3/4 for simple triple.

Why shouldn't 6/8 represent one group of six beats (or six groups of one as they amount to the same thing)?

Because that would be weird. Firstly, very little music is legitimately "in six" as a rhythmic feel, and if we're talking about dividing a beat into six parts then it would be far simpler to just divide it into 2 or 3, and subdivide the rest of the way from there. Secondly, as previously mentioned, 6/8 should be reserved for the very common compound duple. If you really do have a piece in sextuple time, then use 6/4 which doesn't have the strong association with compound duple meter, or divide your measures further.

I was taught (because it really is a very vague topic) that it is all to do with your feet.

The time signature effectively dictates how you would most likely move your feet while dancing to the music.

For a march that's a definite left-right-left-right rhythm, which is basically two beats, so 2/4.

A waltz you move your feet in groups of three motions, so you get 3/4.

A Paso Doble could be danced in 6/8 time.

Etc - you get the idea I'm sure.

And of course that is all tied up with the overall rhythm of the music. So while the time signature can never tell you what the actual rhythm is, it can give clues as to how the overall feel of the music should be. Especially when coupled with other clues, such as the tempo and any style text above the staves.