[Smt-talk] Early account of beats

[Ildar Khannanov]

Dear Colleagues,
 
I agree with Nicolas that hearing the effect of beating, as we can hear it today, was impossible in the earlier stages of western music history, but I propose a different explanation. 
 
Of course, Jay may have come with this interesting question sitting at the D-model Steinway and touching slightly detuned fifth. Indeed, the interference of the  overtonal spectra produces beating. The formant of the  higher note in a fifth interferes with the second harmonic of the lower. When the two strings are tuned to each other perfectly (Perfect Fifth) the second harmonic of the lower comes into resonance with the formant of the higher tone and the amplitude)s of both waves are multiplied evenly  throughout all the wavelengths.  If the two waves are not congruent (vary in frequency) and not in phase (do not start at the same time) the resonance will be very unevently distributed throughout the sinusoid and instead of steady increase of the amplitude, we will hear irreguarly placed peaks of loudness, or beatings.  
 
But this can happen only if both sounds come from a perfect instrument, that is, the instrument, which is capable of distinguishing and emphasizing the formant and  harmonic partials, generated only by this formant. Physically, in order to have this, the string quality must be very high, because it has to vibrate with its halves, its thirds, its foruths exactly. If the string is of poor quality (has variations in thikness and viscosity of metal), and the soundborad is not precisely cut, your instrument will produce a cloud of non-harmonic partials, that is, noises, or what in contemporary acoustics is called distortions. I have worked as a musical folklorist in Russia for several years and noticed that most folk instruments produce dirty sound (clean sound is aesthetically unacceptable in folk music).
 
Now, to the point. Before the Cremona violin, instruments in Europe were very imperfect. Yes, we have some old organs and harpsichords, but they have been restored. Try to hear a beating of a detuned fifth on two Shaums, or on two Kurais (Bashkirian national instrument, a kind of flute traverse). The kurai is a phantastic solo instrument, but the sound of  an ensemble of kuraists is hilarious!
 
There is a dissertation, entitled How equal temperament has killed western music. I could add to it How acoustically perfect instruments have killed western music.
 
 
Best,
 
Ildar Khannanov
Peabody Conservatory
 
-- On Tue, 9/14/10, Martin Braun <nombraun at telia.com> wrote:


From: Martin Braun <nombraun at telia.com>
Subject: Re: [Smt-talk] Early account of beats
To: smt-talk at societymusictheory.org
Date: Tuesday, September 14, 2010, 1:49 PM


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.

Reply:

"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."

Reply:
"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

---------------------------------------------------------------------
Martin Braun
Neuroscience of Music
S-671 95 Klässbol
Sweden
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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