Newton and the Mystery of the Major Sixth 127
reflection ” — sudden seizures in the behavior of light — as a way to incorporate certain
aspects of wave theory into a predominantly particle view.^18
Newton ’ s musical analogy, however, has an unexpected relation to the wave theory.
Already in a 1672 manuscript, he supposed that “ the vibrations causing the deepest scarlet
to be to those causing the deepest violet as two to one; for so there would be all that variety
in colours which within the compass of an eight [octave] is found in sounds, & the reason
why the extremes of colours Purple & scarlet resemble one another would be the same
that causes Octaves (the extremes of sounds) to have in some measure the nature of
unisons. ”^19 Here Newton seems to assume that the “ resemblance ” of purple and scarlet
parallels the “ resemblance ” of octaves.
In this manuscript, Newton tried to find empirical support for the 2:1 ratio of the “ vibra-
tions ” of purple and scarlet in the ratios between spaces of colored rings from illuminated
lenses (first described by Hooke, though usually known as “ Newton ’ s rings, ” figure 8.4 ).
Yet in Newton ’ s rings the ratio of the extreme colors was “ greater than 3 to 2 & less than
5 to 3. By the most of my observations it was as 9 to 14. ”^20 In his Opticks (1704), Newton
stated that rings “ are to one another very nearly as the sixth lengths of a Chord which
found the Notes in a sixth Major, ” such as from D to the b above it, compared to the octave
D – d.^21 Here Newton reduces the number of his “ principal colours ” from seven to
five, which probably stemmed from his observations of the rings, in which it is hard
to observe minute color nuances. Thus, he was open to altering his musical enumeration
of spectral colors.
Newton ’ s hesitation between octave and major sixth shows the difficulty and importance
of the point. He had initially assumed an octave, based on his prior ideas about the perfec-
tion and completeness of that interval, whereas a major sixth clearly comes from empirical
observation and seems to indicate some quality inherent in light itself. Indeed, a wave
theory can far more naturally explain this ratio than can a particle theory, which lacks a
concept of wavelength (whose place Newton tried to supply with his “ fits ” ). In terms of
wavelength, visible light spans roughly only a major sixth, about a ratio of 700:400, cor-
responding to the modern conventions for violet at 400 nm and red at 700 nm, noticeably
short of an octave. In short, the human eye has never experienced an octave relation,
whereas the human ear recognizes many octaves.^22 Newton ’ s analogy is therefore in
tension with this fundamental inconsistency. Clearly troubled by the discrepancy between
octave and sixth, in order to agree “ something better with the Observation ” Newton then
reinterpreted his measurements through a rather intricate stratagem. He suggests that the
rings ’ major sixth could be understood “ as the Cube Roots of the Squares of the eight
lengths of a Chord ” in an octave, thus rather tortuously reinterpreting the musical interval
of a sixth in terms of an octave.
This connection between cube roots and squares resembles Kepler ’ s third law connect-
ing the cube of the distance of a planet from the sun and the square of its period.^23 Newton
considered that relation crucial to establishing the inverse square law of gravitation; in the