[Smt-talk] Early account of beats

JAY RAHN jayrahn at rogers.com
Mon Sep 13 17:29:13 PDT 2010

Nicholas Meeus claims that between two tones with harmonic
spectra many fluctuation rates can be perceived at the same moment but that most
people would remain unable to concentrate on a specified one. To be sure,
various rates would be present acoustically as, in principle, they are within a single tone. However, hearing interference between two tones is quite a different task than hearing out the partials within a single tone. Nonetheless, as among the partials of a
single tone with a harmonic spectrum, the slowest rate of interference between two tones would tend to predominate perceptually, especially if the lowest
partials were most intense, which they would tend to be on plucked strings and
particular organ stops. In contrast, hearing a difference of, e.g., a quarter
comma between successive tones as a quarter of a comma seems much more demanding than
Schlick’s somewhat vague prescription to listen for the undulation produced by
a flattened A sounded simultaneously with D a 5th below ‘as much as it can endure.’


In any event, I find it remarkable that nobody prior to
Schlick seems to have drawn attention to audible interference between pairs of
tones, especially as harmonics (in the sense of flageolet tones) and resonance
(in the sense of sympathetic vibration) appear to have been observed at least
as early as, respectively, ancient Greece and China. In principle,
interference, harmonics, and resonance would have been semi-objective ways of verifying
whether particular numerical (or geometrical) entities had been transferred more or less precisely to a monochord
or other instrument.

Jay Rahn, York University (Toronto)

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