Music- How Fractions and Rhythms Work Together

If you remember from an earlier post, rhythm is the way that sound is organized through time. A lot of people get the idea of beat and rhythm confused and often think they are synonyms. 

Once you get the idea of the difference, they are easy to tell apart. Beat is the strongest pulse in a piece of music. Often, they are felt in groups of 2, 3, or 4. How do we know how many are in a group? If you listen very carefully you will hear one beat that is the strongest and one or more slightly weaker beats. A great example of this is a waltz. Waltzes are in 3 with beat 1 being the strongest and 2 and 3 being weaker. The Viennese style of Waltz especially emphasizes this feeling, as the entire foot only touches the ground on 1 and it is just the toes touching the ground on 2 and 3.

If that is the beat, then what is the rhythm? It is how we organize the beat and the space between the beats. It is very rare for a waltz to only have 3 notes all on the beat over and over. We may have longer notes that last longer than 2 beats or shorter notes that move in between the larger beats.

It sounds confusing but looking at rhythms and hearing the difference between the beat and the rhythm makes it a natural process.

Rhythms are completely mathematical. Every way that we organize the rhythms is measured. Splitting the overall beat into rhythms is the work of division. For an example, we will start with music based around 4 beats. If one note takes up all four beats, it is called a whole note. To help students remember its name I remind them that it takes up the whole measure. When we split the whole note in two equal parts, the result is two half notes. Again, we notice that these take up half a measure of 4, each getting 2 beats. Splitting the whole note further into 4 parts or 1 note for each beat, the name is quarter note and notice that it takes up ¼ of the measure. Further dividing the whole note into smaller parts, we end up with 8 eighth notes in a measure, 16 sixteenth notes and so forth. 

If the number of beats in a measure is constant, then we can use addition or subtraction to figure out which beat we are on. If we are looking at a measure of 4 quarter notes, the third beat is the third quarter note. Either we count to three from the left or we can subtract 1 from the right. In combinations of eighth notes and quarters we simply count each eighth note as half of one beat, so that it takes two eighth notes to fill one beat. It is the opposite for a 2 beat note or half note, there would only be two remaining beats when one half note is present.

I’m going to stop here before you get overwhelmed, but be comforted by the fact that rhythms work in an organized system with rules and definite answers. Simple knowledge of fractions and division can go a long way to understanding and organizing rhythms.