[Smt-talk] Early account of beats

Nicolas Meeùs nicolas.meeus at paris-sorbonne.fr
Sun Sep 12 13:02:49 PDT 2010

  Is there any account of beats in Schlick? The German word he uses is 
/schweben/, often taken to mean "to beat" because we know better, but 
that is not the German sense: /schweben/ means "to float".

What Schlich says, really, is this:
... /mach /[/die quint/] /dazu nitt hoch genug, oder ganz gerade in. 
sonder etwas in die niederer schweben, so vil das das gehor leyden mag.../
... make its fifth not high enough nor exactly, but somewhat floating in 
the low, as much as the ear may suffer...

We know that this probably refers to a sensation (not a consciousness!) 
of beating. But to deduce that Schlick accounted for beats (or, even 
more, for an interference between harmonic partials) would be 
farfetched, to say the least.

To answer the question otherwise: there is no mention of temperament, 
that I know (or that is known, I'd dare say), before Schlick. The tuning 
of Pythagorean diminished fourths (e.g. /d-g/b) as approximations of 
perfect major thirds (/d-f/#), as described in several 14th- and 
15th-century texts (and earlier in Safi al-Din) cannot be considered 
temperaments, as they involve pure intervals (pure fifths, in this case) 
exclusively. The difference between a Pythagorean diminished fourth and 
a major third is so little (2 cents) that it hardly could have been 
considered /schwebend/.

Nicolas Meeùs
nicolas.meeus at paris-sorbonne.fr

Le 10/09/2010 16:09, JAY RAHN a écrit :
> Does anyone know of an account of beats (i.e., interference between 
> the two tones of an interval) prior to Schlick (1511)?
> Jay Rahn, York University (Toronto)
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