# Compound Meters



## Festus

Why is the top number in a compound meter divided by 3?


----------



## EdwardBast

How else could it be? If the beat level had duple divisions one would have 2/4, 3/4, or 4/4 instead of 6/8, 9/8, and 12/8 respectively.


----------



## mbhaub

I thought the definition of compound meter was that the beat is divisible by three. Just the way it is.


----------



## NoCoPilot




----------



## Festus

Well, I guess I have a basic misunderstanding of compound meters and must return to the book for further study.


----------



## Roger Knox

Festus said:


> Well, I guess I have a basic misunderstanding of compound meters and must return to the book for further study.


Let me give it a try. It has to do partly with music notation. You likely know these things already, I'm just trying to explain the "why" of your original question. To do that I need to go back a ways.

*The Beat*
The bottom number of the time signature gives the _beat_ that we count. For example, the quarter(1/4)-note.

*The Bar (or Measure)*

Beats are grouped by _accent_ (shown here as bolded numbers). In a _bar_ the first beat in the group has the accent. The top number of the time signature gives the number of _beats_ that we count.
- 2/4 time has 2 quarter notes -- *1* 2. Any time signature with 2 at the top is a _duple_ meter.
- 3/4 time has 3 quarter notes -- *1* 2 3. Any time signature with 3 at the top is a _triple_ meter.
- 4/4 time has 4 quarter notes -- *1* 2 *3* 4. Any time signature with 4 at the top is a _quadruple_ meter.*
We may say that in terms of notation, the beats are divisions of the meter as represented by the time signature.

*Subdivision of the Beat*

While beats are _divisions_ of the meter. dividing the beat is called _subdivision_.

*Simple Meter*
Beats can be sub-divided by 2 in our notation system. For example, 1 quarter(1/4)-note can be sub-divided into 2 eighth(1/8)-notes. Meters where the beat can be subdivided by 2 are called _simple meters_. In piano lessons, for example, I leaned to count them as follows: 
- (2/4) *1*-and 2-and. Simple duple meter;
- (3/4) *1*-and 2-and 3-and. Simple triple meter;**
- (4/4) *1*-and-2-and-*3*-and-4-and. Simple quadruple meter.*

*Compound Meter*
Beats can be sub-divided by 3 in our notation system. *This is done when the beat is a dotted note.* For example, if a dot is put on the right side of a quarter-note, it becomes a dotted quarter-note. The dot adds half the time value of the beat to the note. To a quarter note, the dot adds the time value of an eighth note. The sub-division of the dotted quarter note equals 3 eighth notes:
- (6/8) *1*-and-a 2-and-a. Compound duple meter;
- (9/8) *1*-and-a 2-and-a 3-and-a. Compound triple meter;
- (12/8) *1*-and-a 2-and-a *3*-and-a 4-and-a. Compound quadruple meter.*

*Some of the rules for simple meter change with compound meter.* The bottom number of the time signature now represents the _subdivision_ of the beat, and the top number the _number of beats_. For example in 6/8 the beat is a dotted quarter note subdividing into 3 eighth notes, which is where the bottom numeral 8 comes from. The number of beats is 2, subdividing into 3+3=6 eighth notes, which is where the top numeral 6 comes from.

The reason compound meter uses different rules than simple meter is that with the beat divisible by three we would have to use the fraction 1.5 (quarter plus eight note or dotted quarter note) to represent the beat, which would be confusing.

* in 4/4, a simple quadruple meter, there is a secondary accent on *3*, shown in bold-italic. The same principle holds for 12/8, a compound quadruple meter, where there is is a secondary accent on the third beat or dotted quarter note (also the 7th subdivision -- eight note -- of the beat) in this bar.
** unlike the other meters given here with 8 as the bottom number, 3/8 is considered a simple meter because the top number is 3, the number of eight-note beats, and the bottom number is 8, the _beat_. This is different than in compound meters such as 6/8 where the bottom number gives the _subdivision of the beat_, the eighth note.


----------

