← Fractions for Grown-ups · Lesson 1 of 3
A string that sings
An old tradition credits Pythagoras with noticing that musical intervals are fractions of a string. Stop a vibrating string halfway along, and the half sings an octave higher. Stop it at two-thirds of its length, and you hear a fifth; at three-quarters, a fourth.
Fractions began as lengths you could hear. That is still a good way in: a fraction is a part of a whole, measured.
Which length of string sings an octave above the whole string?
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