Planck’s Cosmic Harmonium 263
years and generations. For before Johann Sebastian Bach, the tempered scale had not been
at all universally known. ”^21
In his autobiography, Planck immediately turns from this description back to his involve-
ment in thermodynamic issues, especially those that emerged the following year (1894)
concerning black-body radiation, leading to his famous postulation of the quantum of
action in 1899 – 1900. Though outwardly Planck ’ s musical investigations seem unrelated
to the culmination of his work in thermodynamics, he treats both as part of his ongoing
stream of scientific activity. The connections and contrasts that emerge shed a new light
onto Planck ’ s development, helping us understand how this immensely cautious man found
himself advancing the most controversial and consequential innovation of modern physics.
Until his musical work of 1893 – 94, Planck had been an unalloyed conservative, a
devotee of absolute laws who (against the powerful arguments of Boltzmann) resolutely
maintained the absolute validity of the second law of thermodynamics, upholding entropy
alongside energy as mainstays of deterministic (as opposed to statistical) mechanics. His
work on the battle between tempered and natural tuning was the first place in which his
sense of the absolute was truly challenged. Initially prepared to believe in the absoluteness
of natural tuning, at least for cultivated musicians, his own musical experiments led him
to the opposite conclusion: the prevalent conventions of tempered tuning, however recent
in the long view of music history, outweighed the claim of the “ natural. ” His results were
nuanced: though natural tuning does, in fact, have some sway over music, he realized that
musicians gravitate toward tempered tuning out of habit, and (more surprising still) he
himself found those “ unnatural ” tempered intervals more expressive. This moment of self-
realization was mirrored in his experiences with others. Not only did he observe his singers
sink into tempered triads, he realized that he himself was not immune, but had been formed
by the conventions of tempering he too had grown up with.
For someone as devoted to the absolute as Planck, these musical results were disquiet-
ingly relativistic. Though he does not use that precise term, in fact he tested the absolutistic
claims of the advocates of natural tuning and concluded that, far more than he or they ever
expected, the conventional “ frame of reference ” of tempered tuning conditions our expec-
tations and our felt experience. To put the matter provocatively, Planck ’ s musical trials
were a kind of Michelson – Morley experiment with respect to absolute versus relative
tuning; he, like they, derived a null result, namely that musicians do not perceive absolute
natural tuning any more than optical experimenters can observe absolute motion with
respect to the ether.^22 On the other hand, though the claims of natural tuning had now been
rebuked by experiment, he does not altogether disavow its power in musical experience,
even though he showed that natural tuning was overshadowed by the greater practical force
of habitual tempered tuning.
Planck ’ s musical realization resonated through his work as he sought a unified concep-
tion of the forces of nature, in accord with more general Wilhelmian views about the unity
of knowledge.^23 As Hui put it, his