Planck’s Cosmic Harmonium 261
To test this surprising result, Planck wrote a short composition (though he modestly
does not use this term for what he calls his “ series of chord progressions ” ) specifically
devised to test whether, when singing without accompaniment, a chorus would gravitate
toward natural or tempered tuning ( figure 17.3 ; ♪ sound examples 17.2, 17.3).
Planck constructed his first example so that, if the chorus allows every triad to adjust
itself to natural tuning, then by the end, the final C would be five syntonic commas lower
than the initial C, a bit more than a half step flat.^19 Planck assembled a chorus of “ friendly
musical ladies and gentlemen ” who sang this passage to him many times, beginning with
a normal-tempered piano chord at the beginning. He found, indeed, that the pitch sank
about a half step, as he expected, showing that natural tuning is a significant effect on
choral singing. But then he arranged a second “ counter-experiment, ” as he called it, an
inversion of the melodic motions of the first example that would, by symmetry, evoke
a rise of five syntonic commas (about a half step) above the starting pitch ( figure 17.4 ;
♪ sound examples 17.4, 17.5), were the chorus constantly to adjust according to
natural tuning.
Using this inverted test-composition, Planck ’ s results seemed contradictory; the pitch
rise did not materialize as would have been anticipated had the singers always reverted to
natural tuning. He reasoned that singers tend, when prolonging a note, to go flat, which
would have canceled out the expected rise in pitch here, though it would have assisted the
fall in pitch in the previous example ( figure 17.3 ). From his observations, Planck concludedFigure 17.3
Planck ’ s first test composition, devised to check whether an unaccompanied chorus would gravitate toward
natural or tempered tuning; using natural tuning, the tonic C should fall about five syntonic commas (about a
half step) ( ♪ sound examples 17.2, 17.3).