[Smt-talk] Early account of beats

[Nicolas Meeùs]

  Specialists agree today, I think, that Mersenne was among the very 
firsts to have described beating (and, for that matter, harmonic 
partials). His knowledge in this respect did not spread widely at first 
and even Sauveur's early 18th-century experiments puzzled many a 
musician, including Rameau who believed that the production of harmonic 
partials was caused by resonance. It is not sure that Werckmeister knew 
much about harmonic partials and beating either.

It goes almost without saying that musicians (Schlick included) had 
found long before Mersenne that tempered intervals produce a wavering or 
trembling effect. But the question is whether they realized that the 
wavering was caused by an interference between the partials. I certainly 
never claimed that interference may not describe what Schlick 
experienced. I only claim that we cannot be sure (and I believe that it 
is improbable) that he knew that the cause of the fluctuation was 
interference.

The word Schweben describes the effect, but it says nothing of the cause.

Nicolas Meeùs
nicolas.meeus at paris-sorbonne.fr




Le 16/09/2010 19:46, JAY RAHN a écrit :
>
> Returning to my original query, namely, whether Schlick (1511) is the 
> earliest account of interference (i.e., slow undulation or faster, 
> phenomenally fused beating), I would emphasize that my (and others’) 
> understanding was premised on the contrast between schwebend and 
> gerade as between wavering and straight.
>
> On the basis of an entry in a contemporary online German-English 
> dictionary, Nicolas Meeus originally claimed that schweben means “to 
> float.” However, the dictionary he cited is a general dictionary, not 
> a dictionary of music, and it lists the following additional 
> translations for schwebend: floating, hovering, pending, soaring, 
> suspended, wavering, breezing, poising, impending, unadjusted, 
> undetermined. All the same, he insisted that to claim that Schlick was 
> referring to beats (or, even more, to an interference between harmonic 
> partials) would be farfetched.
>
> Subsequently, Nicolas admitted that schwebend/gerade may correspond to 
> wavering/straight but suggested that the most neutral translation 
> would be something like unstable/stable, which, he felt, may or may 
> not connote beats and went on to say that interference may or may not 
> describe what Schlick experienced.
>
> Thereupon, Reinhart Frosch pointed out that in a contemporary 
> German-English music dictionary the first translation of Schwebung is 
> “beat, beating” and Martin Braun emphasized that in a context of 
> musical acoustics Schwebung and schweben exclusively mean “beat” and 
> “to beat.” Contrary to Nicolas, Martin went on to say that ‘if one 
> wants to understand why the Germans called this oscillation 
> “Schwebung,” one has to look into the history of the word. The meaning 
> “deviation” [which Nicolas suggested as a substitute] is not part of 
> this history, but, for example, “flying” and “hovering” are.’
>
> Since Nicolas regards Werckmeister’s 1691 account of tuning as 
> relevant to Schlick, I think it is worthwhile to point out the 
> following, to which a colleague has drawn my attention:
>
>    1. According to MGG 13, 216-17, Mersenne (1636-37) said a tempered
>       5^th should schweben once per second. His terms in the Harmonie
>       universelle are trembler (to tremble, to vibrate) and battre (to
>       beat). Leaving aside the question of just how quickly tempered
>       5ths would tremble, vibrate or beat throughout the entire gamut,
>       Mersenne’s specification of a rate would seem to indicate a rate
>       of interference.
>    2. Subsequent to Werckmeister, but earlier than various 19^th - and
>       20^th -century general and technical music dictionaries, Johann
>       Christoph Adelung’s Grammatisch-kritisches Wörterbuch
>       (1793-1801) 3, 1617-18, gives the following for Schocken:
>
> 1) Stoßen, Franz./ chocquer,/ Engl. /to shock//;/ in welcher Bedeutung 
> es noch in einigen gemeinen Sprecharten, besonders am Nieder-Rheine, 
> gangbar ist. 2) Hin und her bewegen, schweben; schaukeln, welches das 
> Intensivum oder Diminutivum davon ist. Ein Schiff schocket, sagt man 
> in Nieder-Deutschland, wenn es von einer Seite zur andern wankt, wovon 
> man im Hochdeutschen schaukeln oder schwanken gebrauchen würde. 
> Jemanden schocken oder schockeln, ihn schaukeln, daher in einigen 
> Gegenden die Schaukel auch Schockel genannt wird.
>
> Adelung’s understanding of schwebend seems more like wavering or 
> hovering than like floating, suspended, etc. To be sure, in 
> contemporary English, hovering can mean hanging suspended in the air 
> or remaining in an uncertain or irresolute state, but it can also mean 
> wavering, fluctuating, or remaining in one place in the air by beating 
> the wings.
>
> In any event, deviating does not seem to have occupied a place in the 
> history of musical schwebend. Granted, instability overlaps some of 
> its uses, but this instability is consistent with motion in general, 
> and in particular with repeated change of position, albeit within a 
> larger region, as in Mersenne’s trembling/vibrating and beating.
>
> Jay Rahn, York University (Toronto)
>
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