By the end of the nineteenth century, the Pythagorean quest might have seemed played
out. With Newtonian and Maxwellian physics securely in place, the metaphorical language
of harmony, not to mention the details of music theory, might appear to be only a historical
vestige, a transitional scaffolding that by then could be left behind. But facing the puzzles
and paradoxes of the nature of matter first raised by the study of spectra, physicists again
resorted to the precise kinds of numerological-musical theorizing that had many precedents
in the Pythagorean episodes discussed above. At such moments of trial and disorientation,
it was as if the scaffolding reemerged from the buildings into which it had seemed
absorbed, ready once again to help us scale what appeared to be unsurmountable obstacles.
The story that unfolded was epitomized in “ the bible of spectroscopists, ” Arnold Som-
merfeld ’ s Atomic Structure and Spectral Lines (1919), which begins by asserting that
“ what we are nowadays hearing of the language of spectra is a true ‘ music of the spheres ’
within the atom, chords of integral relationships, an order and harmony that becomes ever
more perfect in spite of the manifold variety. ”^1 How, then, did the music of the spheres
come to the atoms?
Because these developments were the work of many hands, assembling several indi-
vidual portraits may elucidate the different musical facets of the emergence of quantum
theory. After Helmholtz and Lord Rayleigh had brought the theory of sound and music
to such a high degree of development, experimentally and mathematically, it stood
ready, in its new formal generality, to address kinds of problems no one had anticipated
might by informed by harmonic considerations. Given the universal success of con-
tinuum mechanics in the theory of light and sound, the discovery of discrete spectral
lines characteristic of each chemical element was a shock. Such dark, discrete lines
were observed in the sun ’ s spectrum, first by William Wollaston (in 1802), who attrib-
uted them to the boundaries between Newtonian colors, and then by Joseph von Fraun-
hofer (in 1814), who began cataloging them using his newly invented spectrograph
( figure 16.1 ).
The problem was how such discrete lines could be consistent with the continuous wash
of spectral colors Newton observed in sunlight. When Anders Jonas Å ngstr ö m measured
barré
(Barré)
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