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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.<br>
<br>
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.<br>
<br>
The word Schweben describes the effect, but it says nothing of the
cause.<br>
<br>
Nicolas Meeùs<br>
<a class="moz-txt-link-abbreviated" href="mailto:nicolas.meeus@paris-sorbonne.fr">nicolas.meeus@paris-sorbonne.fr</a><br>
<br>
<br>
<br>
<br>
Le 16/09/2010 19:46, JAY RAHN a écrit :
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<p class="MsoNormal">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.<o:p></o:p></p>
<p class="MsoNormal"><!--[if !supportEmptyParas]--> <!--[endif]--><o:p></o:p></p>
<p class="MsoNormal">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.</p>
<p class="MsoNormal"><!--[if !supportEmptyParas]--> <!--[endif]--><o:p></o:p></p>
<p class="MsoNormal">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.</p>
<p class="MsoNormal"><!--[if !supportEmptyParas]--> <!--[endif]--><o:p></o:p></p>
<p class="MsoNormal">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.’<o:p></o:p></p>
<p class="MsoNormal"><span style=""> </span></p>
<p class="MsoNormal">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: </p>
<p class="MsoNormal"><!--[if !supportEmptyParas]--> <!--[endif]--><o:p></o:p></p>
<ol style="margin-top: 0in;" start="1" type="a">
<li class="MsoNormal" style="">According to MGG 13,
216-17, Mersenne (1636-37) said a tempered 5<sup>th</sup>
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.</li>
<li class="MsoNormal" style="">Subsequent to
Werckmeister, but earlier than various 19<sup>th</sup>-
and 20<sup>th</sup>-century general and technical
music dictionaries, Johann Christoph Adelung’s
Grammatisch-kritisches Wörterbuch (1793-1801) 3,
1617-18, gives the following for Schocken:<o:p></o:p></li>
</ol>
<p class="MsoNormal" style="margin-left: 0.5in;">1)
Stoßen, Franz.<i> chocquer,</i><span style="font-style:
normal;"> <span style="background: none repeat scroll
0% 0% yellow;">Engl.
</span></span><span style="background: none repeat
scroll 0% 0% yellow;"><i>to shock</i></span><i>;</i><span
style="font-style: normal;"> in welcher Bedeutung es
noch in einigen gemeinen
Sprecharten, besonders am Nieder-Rheine, gangbar ist.
2) <span style="background: none repeat scroll 0% 0%
yellow;">Hin und her bewegen, schweben</span>;
schaukeln, welches das Intensivum oder Diminutivum
davon ist. <span style="background: none repeat
scroll 0% 0% yellow;">Ein Schiff schocket, sagt man
in
Nieder-Deutschland, wenn es von einer Seite zur
andern wankt</span>, 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. <o:p></o:p></span></p>
<p class="MsoNormal">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.</p>
<p class="MsoNormal"><!--[if !supportEmptyParas]--> <!--[endif]--><o:p></o:p></p>
<p class="MsoNormal">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.</p>
<p class="MsoNormal"><!--[if !supportEmptyParas]--> <!--[endif]--><o:p></o:p></p>
<p class="MsoNormal">Jay Rahn, York University (Toronto)</p>
<p class="MsoNormal"><!--[if !supportEmptyParas]--> <!--[endif]--><o:p></o:p></p>
<p class="MsoNormal"><!--[if !supportEmptyParas]--> <!--[endif]--><o:p></o:p></p>
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