Isaac Newton and the mystery of the major sixth: a transcription of his manuscript ‘Of Musick’ with commentary

Abstract

Isaac Newton's only extended manuscript ‘Of Musick’ is here transcribed with commentary, especially concerning his analogy between music and colour. This manuscript shows that Newton's musical judgements relied more on experiential qualities, on ‘sweetness’ or ‘gratefulness’, than on purely theoretical preconceptions. The manuscript also shows that he formulated the music/colour analogy years before he could have read suggestions of it in Robert Hooke's 1672 letters, leaving open the possibility of alternative classical or alchemical sources. Newton later used this analogy in his optical writings to define seven spectral colours analogous to the seven tones of the diatonic scale, implicitly presuming that the spectrum, like the scale, spans an octave. His experiments with ‘Newton's rings’ in thin transparent bodies, however, led him to note that a major sixth, rather than an octave, describes the recurrent air thickness leading to the same colour. In his Opticks, Newton argued that this major sixth could be reinterpreted as giving an octave ratio by taking the cube roots of the squares of the air thickness. By finding an optical analogue to Kepler's Third Law of planetary motion, Newton also restored the primacy of the octave in his analogy by arguing away the major sixth. Though he did not recognise it as such, this major sixth can be interpreted in terms of the wave theory of light as the ratio of the extreme wavelengths of visible light. Newton's musical analogy, followed more strictly, could have revealed a hallmark of the wave nature of light.