Practice question · Numerical answer
A string of length 60 cm sounds a note. What length, in centimetres, sounds the octave above it?
Hints
- The octave corresponds to the ratio 2:1.
- Halve the length.
Show the answer
30
Why
30 cm: halving the string raises the pitch by an octave, the 2:1 ratio. This is directly demonstrable on any stringed instrument, which is part of why the Pythagorean claim was so persuasive.
Practise Pythagoras and Early Pythagoreanism
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