Newton and the Mystery of the Major Sixth 123
In this passage, Newton independently puts forward an analogy between optics and
music years earlier than Robert Hooke, who communicated this analogy to Henry Old-
enburg in a 1672 letter later forwarded to Newton.^6 In his notebook, Newton extends
this analogy from sound to light to heat: “ Thus a little heat is least perceptible to one
newly come from a greater. ” In framing this analogy, Newton might well have recalled
several ancient texts he had studied: a famous passage in Plato ’ s Republic described
the inability of the eye to deal with sudden passage from light to darkness, but there
is no precedent in Plato for the comparison with sound, though Aristotle does discuss
such a comparison. Thus, Newton may have synthesized Aristotle ’ s comparison of light
and sound with Plato ’ s description of the physical (almost visceral) effect of abrupt
transitions in light.^7
Returning to enumerate the parts of an octave, Newton begins a new thought in square
brackets, which he used to set off speculative or interpretative comments: whole tones
might be divided into semitones and quarter tones, “ but they would be of no use ” because
“ the number of discords twixt each concord would much more bee harsh than the concord
would be pleasant. ”^8 Here, as with Vicentino before him, quarter tones open new theoretical
possibilities. Though Newton initially reverts to the conventional view that semitones and
quarter tones are “ unpleasant ” discords, he then strikes out his closing bracket in order to
open a new thought: “ Yet perhaps ½ or ¼ notes passed over very hastily with a larger stay
upon the concords twixt which they are, might be delightful. ” This shows a certain curios-
ity about new musical possibilities; there is no evidence that he ever read Vicentino, though
he studied Kepler closely. Newton closes off this line of thought by noting that “ since they
are such discords, inserted as ’ twere by accident only to graduate concords, & so quickly
slipped over, the sense cannot perceive any error or exactness in them, & therefore be they
useful yet to treat of them would be lost labor. ” Even the way he decides to end his brack-
eted digression shows his preoccupation with “ the sense, ” here meaning the experimental
judgment of the ear, rather than any prior theoretical considerations. This experiential
orientation accords with his earlier optical/musical analogy, which emphasized the physi-
cal response of eye and ear.
Newton limits himself to the diatonic order in his following discussion of how the modes
“ much limit the parts of the tune from discord sounds of one with another, particularly
because tunes framed by divers of them differ in their airs or Modes. ” He enumerates all
the possibilities of ordering tones and semitones and reconstructs the conventional modes,
presented in tabular form. Newton several times refers to “ sweetness, ” “ grace, ” or what is
“ grateful to the ear, ” rather than numerical theory, as his criteria in setting out “ the 12
Modes in their order of elegancy, ” again seeming to prefer empirical, physical criteria of
satisfaction to pure numerology. This represents an important divergence from Boethius ’ s
preference for rational judgment over the evidence of the ears; Newton too followed Aris-
toxenes ’ empiricism, whether knowingly or not.^9 Likewise, in his “ Questiones quaedam
Philosophiae ” (composed in the early 1660s), Newton had noted that “ the senses of divers