Musical Theory IX

Time Signatures - a brief introduction

I don't want to alarm anyone, but there is some math involved in time signatures. This is probably the most clear example of the connection between math and music. Music is a division of time into smaller portions, and what better way to convey this division of time than through basic fractions. If the idea of time signatures in music was taught alongside the concept of fractions in mathematics in our schools, our children would have a much clearer understanding of both. In my experience, I found that students of mine that spoke a second language or were strong in mathematics were much quicker to pick up musical concepts. Similarly, some of my younger students who started with me prior to starting school, once they were in school were much stronger at math and languages. I don't think this connection is a coincidence.

In order to make keeping track of your location in a piece of music easier, the music is divided up into "bars". (Seperated by vertical lines, or bars, hence the name.) Within the bar, there can be a combination of several different kinds of notes

Whole notes
Half notes
Quarter notes
Eigth notes
Sixteenth notes

...and the list continues.

At this point you may notice that the names of the knows corrispond to fractions, and in particular, the negative powers of two. (1/2, 1/4, 1/8, 1/16, 1/32...) This is because the system is build upon dividing notes in half. Two half notes are equivalent in time to a whole note. Two quarter notes are equivalent in time to a half note. The pattern continues. Dots and ties can be used to get time values that are not equal to negative powers of two, but these will be discussed next week.

How do we know how many notes we are able to fit into a bar, and which kind of note gets the beat? (Yup, it's important to know which note gets the beat. If you have a conductor standing over you, banging his baton on your stand, red-faced, you REALLY don't want to be guessing.)

This information is indicated by the time signature. The time signature is composed of two numbers, and closely resembles a fraction. Time signatures such as 2/4, 3/4, 4/4, and 6/8 are very common. In fact, the time signature of 4/4 is call "common time", and may sometimes be represented by a C.

The top number in the time signature is a count of how many. Break apart those common time signatures in your mind into 2*1/4, 3*1/4, 4*1/4, and 6*1/8. Mathematically, this makes sense as 4*1/4 is equivalent to 4/4. But what can this tell us? Well, the bottom number indicated the type of note that gets the beat. In the case of the first three, the quarter note gets the beat. Translated into english, as time signature such as 2/4 would be "Two quarter notes to the bar". The last time signature listed above, 6/8, would have have the eighth note as the beat, and be translated to "Six eighth notes to a bar".

Bars don't have to hold less than one, either. In the case of 5/4 time, there are 5 quarter notes to a bar. This leads us to the Quiz Question that was carried over from last week:

Quiz Question:

Name one song (other than Take Five) that is in 5/4 time.
(*Hint* There is a very well-known movie theme in 5/4 time...)