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This is exactly the kind of translation that begs the answer. So far
as I can tell, the German <i>schweben </i>has no connotation of
fluctuation, wavering, or beating, outside the context of music.
Schlick's usage of the term to describe a tempered fifth may well
have been its first usage in a musical context (there are not that
many texts about music in German before 1511). To say today that
when Schlick said that tempered fifths produce a 'floating' effect,
he meant a 'beating' effect, because we know today that the effect
results from beating, merely reverses the argument.<br>
<br>
The expression <i>gleichsschwebend</i>, as applied to equal
temperament, is puzzling because the beating rate for two identical
intervals is never the same. As Reinhart Frosh rightly describes,
the beat rate is proportional the the frequencies involved. This
also is what Werckmeister already stated (albeit implicitly) in 1707
(<i>Musikalische Paradoxal Discourse</i>): "equal temperament is
when all the fifths 'float' (<i>schweben</i>) by 1/12 of a comma" :
it is the size of the tempering interval that remains constant, not
the beating rate. <br>
<br>
When Werckmeister speaks of <i>schweben</i>, he usually refers to
the tempering or the tempered interval. In <i>Musikalische
Temperatur</i> (1691), for instance, he writes:<br>
<blockquote><i>Einige bringen es vor/es mussen alle Quinten ein
Viertel eines commatis herunter schweben</i> (p. 1)<br>
Some claim that all the fifths must 'float' a quarter of a comma
lower<br>
<i>Etliche lassen alle Quinten theils auffwarts / theils
unterwarts schweben </i>(p. 2)<br>
Some let all fifths 'float' partly upwards, partly downwards<br>
...<i>und das D soll wieder 1/4 Commat. schweben mit dem G. </i>(p.
53)<br>
...and D shall again 'float' by 1/4 comma with respect to G<br>
etc.<br>
</blockquote>
In other words, for Werckmeister, <i>schweben </i>cannot have
meant 'to beat'; it may have meant 'to temper'.<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>
Le 13/09/2010 14:02, <a class="moz-txt-link-abbreviated" href="mailto:reinifrosch@bluewin.ch">reinifrosch@bluewin.ch</a> a écrit :
<blockquote
cite="mid:30983380.90791284379338887.JavaMail.webmail@ps10zhh.bluewin.ch"
type="cite">
<div class="bwmail">
According to the "Dictionary of Terms in Music, English-German,
German-English" by Horst Leuchtmann (Metzler, Stuttgart, 1998),
the first translation of "Schwebung" is "beat, beating", and
"equal temperament" translates into "gleichschwebende
Temperatur", because the beat rates of ET harmonic-complex-tone
fifths divided by the frequency of the lower of the two tones of
the fifth are equal in all cases, namely (3 - 2^(19/12)) =
0.003386. For instance, the ET-fifth A3(220 Hz)-E4 generates
0.003386 x 220 = 0.745 beats per second.
</div>
</blockquote>
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