The History of the Harmonic Series
The story of the harmonic series starts nearly 2700 years ago back in the 6th century BC with a Greek philosopher and
mathematician named Pythagoras... Professor George Gibson from the University of Connecticut wrote an article entitled "Pythagorean Intervals" and in it it
discusses Pythagoras's great fascination with music. During part of the article Gibson shares that "Pythagoras was interested in understanding the notes and
scales used in Greek music. In particular, he studied the Greek stringed instrument, called the lyre"
(Gibson) 3 .
For those of you who don't know what that is, it is a u-shaped harp with strings, and you can sometimes see them in
pictures of Greek Gods. Anyways, Pythagoras noticed "that if you have two strings with the same length, tension and thickness, they sound the same when you
pluck them. This means they have the same pitch and sound good (or consonant) when played together.
The second observation was that if the strings have different lengths [but] keeping the tension and thickness the same,
the strings have different pitches and generally sound bad (or dissonant) when played together. Finally, he noticed that for certain lengths, the two strings
still had different pitches, but now sounded consonant rather than dissonant" (Gibson) 3 .
So the real question is: Is there a way can we figure out which string lengths sound consonant with other string lengths?
Surprisingly, the answer is quite simple, and can be found using the harmonic series. In the Encyclopedia Britannica it states that "the best-known harmonic
sequence, and the one typically meant when the harmonic series is mentioned, is 1, 1/2, 1/3, 1/4,... and so on" and this is the sequence which helped
Pythagoras discover which string lengths would sound consonant with other string lengths (Hosch) 4 .
So how do they relate? Well, when a string is plucked it starts to vibrate. This vibration has a specific frequency that
is called the fundamental frequency. Well, if we pluck another string that is exactly half the length of the first (with the same thickness, tension, etc.)
then it will vibrate at a frequency double that of the fundamental frequency. In other words, half the string length results in twice the frequency, and the
same goes for a string that is 1/3 the length, it will then vibrate at three times the frequency of the fundamental. This pattern continues on and on
resulting in a set of strings that when played together all sound consonant.
Pythagoras believed that numbers were the underlying principle that ruled the universe. So to discover that our mathematics
can predict what sounds sound good to the ear was quite the discovery.
And thanks for listening.
