Pythagoras and the mathematics of music
This page delivers no verdict; it presents claims and evidence with their sources. No theory in science is absolute. Method
For everyone
The Pythagoreans noticed that consonant musical intervals correspond to simple number ratios: the octave 2:1, the fifth 3:2, the fourth 4:3. Halving a string raises its pitch by an octave. The story that Pythagoras discovered this while listening to a blacksmith's hammers is physically incorrect and is regarded as a later legend.
For specialists
The relation valid for string-length ratios does not hold for hammer weights; the sound of a hammer does not stand in a simple ratio to its weight. Pythagorean tuning is built from pure fifths; twelve fifths exceed seven octaves by about 23.5 cents (the Pythagorean comma). Equal temperament distributes this difference evenly across the octave.
Claims
- Consonant musical intervals correspond to ratios of small whole numbers.[1]
Evidence
Supporting
Dividing a monochord string at ratios 2:1, 3:2 and 4:3 produces the octave, fifth and fourth.[1]
Challenging
It was shown that the blacksmith's-hammers story is physically invalid and that most discoveries attributed to Pythagoras come from later Pythagoreans.[2]
Connections
Sources
- Book (1989). Greek Musical Writings, Vol. II: Harmonic and Acoustic Theory. Cambridge University Press
- Book (1972). Lore and Science in Ancient Pythagoreanism. Harvard University Press
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Cite this page
Athena contributors. (2026). Pythagoras and the mathematics of music. Athena: The tree of human knowledge. Retrieved November 1, 2026, from https://latifkedi.github.io/athena/en/d/pisagor-muzik/
@misc{athena_pisagor_muzik,
title = {Pythagoras and the mathematics of music},
author = {{Athena contributors}},
year = {2026},
howpublished = {\url{https://latifkedi.github.io/athena/en/d/pisagor-muzik/}},
note = {Athena: The tree of human knowledge. Accessed: 2026-11-01}
}Added: September 27, 2026 · Last changed: September 27, 2026 · Page history