Pythagoras & the Music of the Spheres

28 May 2019

‘There is geometry in the humming of the strings. There is music in the spacing of the spheres.’

                                                                           – Pythagoras (569–490 BCE)


Philosopher, lute player and ‘father of numbers’, Pythagoras of Samos remains something of a mystery. None of his writings survive today and his accomplishments are available to us only through the work of historians and his many devout followers. But we do know Pythagoras was, in a sense, the very first mathematical physicist: without recourse to mystic theories, he endeavoured to explain the cosmos through his wave theory of the string in a system that came to be known as musica universalis or the ‘music of the spheres’.


A colourful (if almost certainly apocryphal) tale tells that Pythagoras’ grand theory was sparked by his happening upon four blacksmith’s hammers. According to the second-century Enchiridion Harmonices by Syrian mathematician Nicomachus of Gerasa, Pythagoras discovered the principles of consonance and dissonance on comparing the tones sounded by these four hammers and investigating each hammer’s relative weight. The sounds of the first and second hammers seemed to be ‘singing the same note’ – an octave – and when Pythagoras observed that their weights of 12lb and 6lb formed an exact ratio of 2:1, he sensed there was a pattern afoot. The third hammer he heard sounded a perfect fourth with the lowest of the hammers, while the fourth hammer sounded a perfect fifth, and their corresponding weights of 9lb and 8lb (which formed ratios of 4:3 and 3:2 when placed alongside the large 12lb hammer) extended the pattern further. Pythagoras returned home to test out his theory using strings, exploring these same ratios of 2:1, 4:3 and 3:2, but now comparing the length of strings and the tone they produced when made to vibrate. He found his theory worked perfectly: the principles of musical harmony were based on the mathematical foundations of the natural world.

But Pythagoras did not stop here. He was certain that such a theory must extend beyond the earth and into the heavens:

‘If earthly objects such as strings or pieces of metal make sounds when put in motion, so too must the Moon, the planets, the Sun and even the highest stars. As these heavenly objects are forever in motion, orbiting the Earth, surely they must be forever producing sound.’

Pythagoras concluded that each of the planets, through their orbits, must produce a particular note according to its distance from an immovable centre (Earth). Just as differing the length of a string adjusts its pitch when the string vibrates, so these varying distances must produce different tones: the ‘music of spheres’, no less.

‘The Intervals and Harmonies of the Spheres’ from Thomas Stanley’s The History of Philosophy (1655)


Pythagoras’ theory rippled on through the ages. Philo of Alexandria declared that it was surely the ‘music of the spheres’ that Moses heard as he received the Tablets on Mount Sinai, while Saint Augustine claimed that men could only hear these sounds at the point of death, when the secrets of the cosmos were suddenly unlocked. Music was included in the Quadrivium, the medieval curriculum that included arithmetic, geometry, music, and astronomy, along with the Trivium (grammar, logic, and rhetoric), and the seventeenth-century astronomer, astrologer and mathematician Johannes Kepler remained convinced that ‘that the geometrical things have provided the Creator with the model for decorating the whole world’. Drawing closely on Pythagoras’ work, Kepler’s Harmonices Mundi (1619) attempted to explain the proportions of the natural world – particularly its astronomical and astrological aspects – in relation to music.





Pythagoras’ theory is of course now wholly discredited, but space exploration has nonetheless uncovered a number of ‘sounds’ in space – all essentially inaudible but with scope to be ‘converted’ into familiar noises: plasma waves ripple between Saturn and its icy moon Enceladus, the gas giant Jupiter cracks and booms constantly with lightning bolts and thunder, and in 1967 ‘pulsing’ radio signals were detected from a star and first thought to resemble an extra-terrestrial beacon (leading the source to be nicknamed LGM-1 for ‘little green men’) before its discoverers happened upon a similar signal from another part of the sky. And for some, powerful links between theories of sound and the cosmos remain. If, as the Nobel Physics Laureate George Smoot III has said: ‘the universe is, at some level, music, then it seems only natural that we should study it with musical tools of thinking.’

An image of Jupiter’s storms, assembled from three separate images acquired
by Nasa’s Juno spacecraft. Image produced by Kevin M. Gill.

Kate Wakeling, Aurora Writer-in-Residence


We explore Pythagoras’ ancient concept of a ‘music of the spheres’ in our latest Orchestral Theatre production that tours this week (1–5 June) to Canterbury, Birmingham and London.