WebFacts 1
Why are these intervals called "perfect"? From the time of the earliest writings
about musical intervals (fifth century B.C.), the unison, fourth, fifth, and octave were considered
the purest intervals because of their acoustic properties-hence, our term "perfect." These
intervals were also considered beautiful because of their mathematical ratios. The octave
described the relationship between a plucked full length of string and a plucked string divided in
half (ratio 2:1). The fifth described the relationship between the whole string and a string twothirds
the original length (ratio 3:2). The fourth resulted when sound of the whole string was
compared with that of a string three-fourths its length (ratio 4:3). The difference between the
ratio numbers in each case is 1: 2 - 1 = 1, 3 - 2 = 1, and 4 - 3 = 1. Mathematicians call these
"superparticular" ratios. If you have access to a violin, guitar, or other string instrument, try it
out!
Many writers from the Middle Ages (c. 500 -1430) and Renaissance (c. 1430-1600)
attribute the discovery of the perfect intervals to the famous Greek mathematician Pythagoras,
who was said to have discovered the ratios of numbers (in the sixth century B.C.) by listening to
smiths striking anvils with hammers in a blacksmith shop and noticing that when the sizes of the
hammers were in a ratio of 2:1, an octave sounded. (This legend, although often repeated, is not
true because the sounds produced would be determined by the size of the anvils, not the
hammers. Like many legends, it may hold a grain of truth, though-the earliest written sources
we have describing the interval ratios are from Pythagoras's followers.)
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