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From what I understand,

  • Simple Meter -- divisible by twos
  • Compound Meter -- divisible by threes

Why do we choose 2 and 3? Why not n divisions?

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12

The difference between a simple meter and compound meter greatly affects the feel of the piece and the differences are bigger than you think. There are other types out there, but let's correct some definitions first. A simple meter is not defined by being divisible 2s and a compound meter is not defined by being divisible by 3s. It's much more about the subdivisions

A simple meter is a meter that has the beat assigned to a simple note duration represented by the lower number of a time signature. The subdivision of the beat of a simple meter are in two. So in 2/4, 3/4, and 4/4 you would count the following way:

X: 1
M: 2/4
K: Cmaj
L: 1/8
"1"G"+"G "2"G"+"G|

X: 1
M: 3/4
K: Cmaj
L: 1/8
"1"G"+"G "2"G"+"G "3"G"+"G|

X: 1
M: 4/4
K: Cmaj
L: 1/8
"1"G"+"G "2"G"+"G "3"G"+"G "4"G"+"G|

A compound meter is a meter that has the beat assigned to 3 of the note duration represented by the lower number of a time signature (so for 6/8 the beat is a dotted quarter note which is 3 eighth notes). The subdivision of the beat of a compound meter are in three. So in 6/8, 9/8, and 12/8 you would count the following way:

X: 1
M: 6/8
K: Cmaj
L: 1/8
"1"G"+"G"a"G "2"G"+"G"a"G|

X: 1
M: 9/8
K: Cmaj
L: 1/8
"1"G"+"G"a"G "2"G"+"G"a"G "3"G"+"G"a"G|

X: 1
M: 12/8
K: Cmaj
L: 1/8
"1"G"+"G"a"G "2"G"+"G"a"G "3"G"+"G"a"G "4"G"+"G"a"G|

You'll notice that both 6/8 and 3/4 contain the same number of eight notes as does 12/8 and 4/4, but the feel of the two are very different. If it helps you can think of compound meter as having a "triplet feel".

Now, let's get to the why not n. There are plenty of time signatures that are not simple or compound, but typically the are grouped in smaller subdivisions of 2 or 3 which is key. These are typically known as odd meters. For example 7/8 can be grouped as 1 group of 3 and two groups of 2. This helps stress accents and define the feel of the meter. Subdivisions of 2 and 3 are seen as the building blocks of any meter and bigger groups of them are just seen as combinations of the 2 and 3 subdivisions.

See also:

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  • Regarding the last paragraph, you ultimately conclude that a time signature such as 7/8 is seen as one group of 3 and two groups of 2. In that sense, 7/8 is not grouped into 7. This again is subdivision in terms of 2s and 3s. But why? Why do we see it as combinations of 2s and 3s? Could you address that issue specifically?
    – Stan Shunpike
    May 18, 2018 at 8:10
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    @StanShunpike, 2 and 3 are the first primary numbers after one. So we cannot get any more simple in our division than that. Ultimately, every number greater than one can be broken down into multiples of 2 and/or 3. I think the reason is simply math.
    – Heather S.
    May 18, 2018 at 11:27
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    @stanshunpike - 3+2+2 /is/ grouped into 7, especially if that pattern repeats! As others have mentioned, 2 and 3 are most commonly used because any number larger than 3 can be broken down into combinations of both of those numbers. “Yes but...WHY?” Well, I think the answer there is: cultural. As soon as you look at Carnatic music, for example, the rules change entirely. In Carnatic music tradition, that same 7/8 could also be divided into 3+4, 5+2, or 6+1. 2&3 are more relatable to our ears (since we know 8ths & triplets), so we use them more.
    – jjmusicnotes
    May 18, 2018 at 12:07
  • It seems to me that mention of the link between dance and human anatomy and music is worthwhile here. At least that explain all duple meters one way or the other. We have four limbs, but that's just two sets of two. But using three limbs or three fingers is very reasonable. Five is another number that might make sense but as mentioned here, it is generally treated as 2+3.
    – Todd Wilcox
    May 18, 2018 at 20:02
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The distinction is silly - and certainly not appropriate for african based rhythms. For example a bembe is both in 6/8 and in 3/4. According to the above these are supposedly rhythms have a very different feel - but in a bembe (or any other afro based 6/8 rhythm) you have to feel both - or you don't know the rhythm.

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    In @Dom's answer I think the point is simply to say 6/8 has two pulses and 3/4 has 3 pulses. I've only read a little about African rhythms, but isn't the composite of these two thought of as a meter? Meaning we have three meters 6/8, 3/4... and bembe. I don't think he meant to exclude polyrhythms.
    – Michael Curtis
    Dec 13, 2018 at 22:39

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