[Smt-talk] Early account of beats

[JAY RAHN]

I don't think it is too overreaching to regard Schlick's use of schwebend (wavering) as referring to beats. Schlick contrasts schweben with gerade (straight)--actually a pretty good pair of metaphors for what 'in-' and 'slightly-out-of-tune' perfect 5ths sound like. 

At A 440, the rate of interference for a perfect 5th in quarter-comma tuning, which is what he seems to be trying to  prescribe, would be about 1.4 Hz, i.e., audible as undulation, especially if the tones were played on an organ, which is Schlick's immediate concern, and if the tones were held for a long time, as he stipulates. (The undulation at A 440 would arise between a D (~146.7 Hz) in the middle of the bass-clef staff and the A (220) on the top line. For D and A an octave higher, the undulation rate would be ~2.8 Hz.)

Since at least as early as the 4th to 2nd centuries BCE in
 Greece and China, theorists would have occasion to describe interference effects between the tones of, e.g., a Pythagorean major-3rd interval. In the 14th century, Marchetto's tuning of sharpened degrees would result in quite pronounced interference. But did anyone describe such interference before Schlick?

Jay Rahn, York University (Toronto)


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