Pythagoras linked musical consonance to small-number string ratios by 600 BCE.

Evidence

The connection between length proportions on a string and pleasing musical intervals is attributed to Pythagoras. According to the legend, Pythagoras as early as 600 BCE used a monochord, a stretched string over a resonator, to connect intervals like the octave and the fifth with length ratios of 2:1 and 3:2, respectively. This reinforced deep mysticism about the fundamental connection between small whole numbers and the clockwork of the heavens. It is said that Pythagoras’ followers believed only he could hear the music of the spheres, the divine harmonies of small integers governing the motion of the planets and the heavens. In 1618, English physician and mystic Robert Fludd wrote De Musica Mundana, which included a compelling illustration of the divine monochord (figure P.1), elevating the monochord to the governing engine of the universe. — Eric J. Heller, Why You Hear What You Hear- An…, 18

Categorization

• DEFINE: Introduces the monochord and the 2:1 octave / 3:2 fifth length ratios as foundational to hearing theory.
• XREF: Connects to the music-of-the-spheres tradition and to Kepler’s harmonies, plus to numerological readings of acoustics.