Fractions and Music for the CSET

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Excerpt from the CSET study guide

Teacher candidates studying for the CSET subtest III Visual and Performing Arts section, should understand the time signature and the duration of a note when reading sheet music.

Question: What math form relates most to music?

Answer: Fractions

The first person to make the connection between math and music was Pythagoras. The Greek octave had five notes. Pythagoras pointed out that each note was a fraction of a string. If you had a string that played an A, the next note is 4/5 the length (or 5/4 the frequency) which is approximately a C. The rest of the octave has the fractions 3/4 (approximately D), 2/3 (approximately E), and 3/5 (approximately F), before you run into 1/2 which is the octave.

In the modern day key of C, these are the fractions (ratios) in relation to C:

C – 1
D – 9/8
E – 5/4
F – 4/3
G – 3/2
A – 5/3
B – 17/9

Fractions are also involved in the time signature of music. When you look at a particular note in a measure, one thing you can ask is “What fraction of a whole measure is that note?”

The most common time is “four-four,” which is written as the fraction 4 over 4 (4/4): 4 beats to a measure with a quarter note (1/4 note) getting one beat. Another example is “six-eight,” (6/8) which means 6 beats to a measure with an eighth note (1/8 note) getting one beat.

With six-eight (6/8) time the question is “What fraction of the measure is an eighth note?” This is the same kind of fraction problem where you cut a pie up into 6 equal slices. One slice is 1/6 of the whole pie, and 2 slices make 2/6 or 1/3 of the pie. If you take one slice away, 5/6 of the pie is left. It’s the same with the measures of 6/8 music. An eighth note is 1/6 of the

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