# Fractions and the Musical Meter

Fractions and the Music Meter

In western music, we use something all a meter to define a piece’s rhythmic structure. On staff paper, the meter is placed before the whole piece but after the clef (the clef is used for finding notes, to learn more about clefs click here). The music meter is essential for understanding the rhythmic ‘feel’ of a piece. This article will discuss the use of the music meter and its parallels with fractions.

What Makes up a Meter?

Here is a diagram of the musical meter: The meter is made up of two numbers that describe the rhythm. The top number designates how many beats occur in a measure (a 4 designates 4 beats per measure), while the bottom number designates what note represents the beat (4 = quarter note, 2 = half note, 8 = eighth note, etc.).

[It is important to note that if one is determining the number of beats per measure from a compound meter, they must divide the top number by 3. We will expand on this later.]

If you want to understand the concept of note values and measures click here.
Therefore, if we decide to use a meter that looked like this: The ‘3’ (above) would designate that each measure would contain three beats, while the ‘4’ (below) designates that the quarter note represents one beat. We can look at the musical meter as a fraction with the denominator determining the base note value for a beat and the numerator defining the number of beats used per measure.

Meters Classified by Their Number of Beats per Measure
In music, we would define this ‘¾’ meter as a triple meter because it uses three beats per measure. This is how to classify meters by their number of beats. Again, this is found from the top number.
For example,
A meter with two beats per measure would be a duple meter.
A ” ” with three beats per measure would be a triple ” “.
A ” ” with three beats per measure would be a quadruple ” “.
Though it is possible to have meters classified as quintuple, sextuple, septuple, etc. these are uncommon but they are still based on the number of beats per measure.

Meters Classified by Their Division of the Beat

This may seem simple enough but there are more complexities to meters. These complexities show themselves in the differences between the simple and compound meters. The difference between simple and compound has to do with the first division of the designated beat. If you do not understand note divisions I would suggest clicking on the link above.

The simple meter is one where each beat of the measure is naturally divided into two, thus all the rules discussed previously apply to the simple meter.

Contrary to this, the compound meter is one where each beat of the measure is naturally divided into three.
For example, look at this diagram of the compound meter 6/8 below: One can see that the beat is clearly represented by the dotted quarter note. Yet, why is there an ‘8’ as the bottom number of the meter? This is because it is a compound meter that is designating the division of the beat in three.
When the dotted quarter note is divided into three we find three eighth notes. The eighth notes are represented by the ‘8’ as the bottom meter number.
Here is another example.

Let’s say we want to have three sixteenth notes make up the beat, and I we want to have three beats per measure. The main beat would be a dotted eighth note which is divided into three sixteenth notes.

Thus, our compound meter would look like this: Our compound meter is 9/16. Notice how the main beat is a dotted eight note and that each eighth note can be divided into three sixteenth notes.

Finally, there is another type of meter worth mentioning that I will not go into great detail. This meter is referred to as the complex meter. It has very special properties and differs a lot from simple and compound.