[Smt-talk] Early account of beats

JAY RAHN jayrahn at rogers.com
Thu Sep 16 10:46:03 PDT 2010

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: 


     to MGG 13, 216-17, Mersenne (1636-37) said a tempered 5th
     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.Subsequent
     to Werckmeister, but earlier than various 19th- and 20th-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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