[Smt-talk] Early account of beats

Martin Braun nombraun at telia.com
Tue Sep 14 11:49:48 PDT 2010

Nicolas Meeùs writes:

"Schweben may mean 'deviate' (downwards of upwards): I fully agree and I 
think this is the best translation proposed up to now. But it certainly is 
NOT the precisely defined meaning of 'to beat' as it is used today.


"Schweben" never meant "to deviate", in no possible context throughout the 
history of the German language.

"Eine Schwebung" arises, if the simultaneous second vibration deviates in 
frequency, either upwards or downwards. A correct translation of a 
Werckmeister line would be this:

German original:
"Einige bringen es vor/es muessen alle Quinten ein Viertel eines commatis 
herunter schweben."

Correct English translation:
"Some suggest that all fifths must beat downwards by a quarter of a comma".

The image that the writer had is that a pitch oscillates (beats) between 
zero and a quarter comma down. [This is physically wrong, because loudness 
not pitch oscillates. But it is a common error, even today.]

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" is not part of this history, but, for example, "flying" and 
"hovering" are.

Nicolas Meeùs writes:

"Equal temperament is characterized neither by equal beating, nor by equal 
acceptability of its intervals. It is characterized by the equal size of its 
intervals, even although this cannot easily be perceptually evaluated."

"Equal size" of tempered intervals is a white elephant for a biological ear. 
Andreas Werckmeister had nothing but biological ears. For his ears it was 
important what he could hear. He did not hear mathematical purity but 
pleasantness of sound.


Martin Braun
Neuroscience of Music
S-671 95 Klässbol
email: nombraun at telia.com
web site: http://www.neuroscience-of-music.se/index.htm

----- Original Message ----- 
From: "Nicolas Meeùs" <nicolas.meeus at paris-sorbonne.fr>
To: "JAY RAHN" <jayrahn at rogers.com>
Cc: <smt-talk at societymusictheory.org>
Sent: Tuesday, September 14, 2010 6:17 PM
Subject: Re: [Smt-talk] Early account of beats 

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