Math in Music

A detailed Summary of Math in Music

Math and Music. In thinking of these concepts, many people do not see any relation

between the two. In reality, however, mathematics has a tremendous effect on music and they are

closely intertwined. The relationship between these two arts, though it might be hard to connect

at first, is, after a bit of study, unmistakable.

Pythagoras was the first to discover the mathematical basis for music. He discovered that

there was a connection between the length of a string (such as on a guitar) and the pitch of its

vibrating note. By conducting experiments with a musical instrument called a monochord, a

stretched string with a movable bridge, Pythagoras found that the shorter the string, the higher the

pitch (frequency). He then moved the bridge to shorten the string to half of its original length. He

found that the frequency of the second note (shorter string) divided by the frequency of the first

note (longer string) equaled a ratio of 2:1, and that string-length of the second note divided by the

string-length of the first note the equaled a ratio of 1:2. Thus, he found that an octave (a note

eight full tones above a given note) is obtained by shortening the strin

notes, the ratio of new length to original length should be 2:3 for a fifth and 3:4 for a fourth.

fifth and fourth notes of the octave produce harmony, or are pleasing to the ear. To obtain these

from French mathematician Joseph Fourier who proved that musical sounds, both instrumental

musical harmony which was the ruler of everything in nature.

and most harmony singing involves octaves and fifths. Another way to look at this is if you blow

music. From the knowledge that whole numbers determine musical intervals, the Pythagoreans

Plucking a string at different points creates sound waves which display various sine and cosine

One of the more practical and modern-day applications of math in music involves the use

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