[Smt-talk] Early account of beats

[Daniel Wolf]

On Wed, 15 Sep 2010 01:38:15 +0200, Ildar Khannanov <solfeggio7 at yahoo.com>  
wrote:

> 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.

I don't believe that Nicolas was drawing that conclusion. The phenomenon  
of beating has always been perceived, and it has always been possible for  
musicians to tune by reducing (or increasing, as the case may be) the rate  
beating but the description has changed, for example through the  
possibility of measuring the rate of beating with use of a metronome or  
watch.

>  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.

The chorus effect of courses of piano wires being slightly mistuned from  
one another is well-known.

>  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.

While the non-linear effects of imperfect piano wire can, indeed, change  
the proportions of the spectra, even in instruments with the highest  
quality the stiffness of the wire stretches the spectra considerably from  
a simple harmonic structure.  It is typical for the stretching to be such  
that the 15th partial has a frequency of ca. 16 times the frequency of the  
fundamental. The consequences of this for setting a temperament on a piano  
are obvious and piano tuners have developed several strategies for  
compensating for this; this contributes, perhaps, an element  to the  
aesthetic design of the piano, which is a greater attenuation of upper  
partials when compared, for example, with the harpsichord.  (Robert  
Escot's discussions of the trend to attenuation in modern instrument  
design are relevant here.)

I
> have (sic) 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).

"Dirty" is a coarse and relative term.  "Dirty" can mean a collateral  
sound, not considered part of the music proper, but associated with its  
production; I know Javanese musicians who find the bowing sounds of  
western strings to be almost intolerably ugly, I personally dislike the  
sound of saxophone keywork, many people dislike the sound of page turning  
or chairs creaking.  "Dirty" can also indicate a preferred element of  
timbre in a particular performance practice, for example the constant  
vibrato in much western string or flute playing, or all of the nuances  
between breath, pitch, and timbre found in shakuhachi or all of the  
effects of gu-qin playing.  While you may have worked in particular  
traditions where you find the sound to be dirty — whether through  
commission or omission — making such a statement for "folk music" in  
general would be grossly inaccurate; it is certainly not true of Irish or  
German or Scandinavian folk musics, for example.

>  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!

That is confusing the possibilities of an instrument with the actual  
selection of those possibilities used in a particular performance practice  
tradition. It is perfectly possible, for example, to play a Javanese rebab  
in beatless unison (_pleng_ is the Javanese term) with any of the  
metallophones in the gamelan.  One of the most esteemed performance  
practices, however, involves playing higher tones slightly sharp to the  
ensemble;  this is useful as the rebab frequently cues the solo female  
vocalists, who are also supposed to sing sharp, and in both cases, the  
higher pitch is perceived to be more audible over the rest of the ensemble.

Having played in ensembles of shawms, cortholts, and crumhorns for 35  
years, as well as having more than 30 years experience in tuning  
harpsichords, I have never found this to be the case.  Indeed, in early  
music, excepting the
plucked gut-strung instruments, with short and rapidly attentuating  
durations (and even so, these are longer than modern synthetic strings!),  
one is always working with instruments with bright spectra requiring that  
one tune by
reduction of beating.  ( The frequently heard complaints about the  
intonation of early music groups are often attributable to the fact that  
the quality of intonation, in terms of simple spectra, is more obvious  
than on modern instruments (like the piano) or in contemporary performance  
practice, where, for example, a constant use of vibrato may compensate for  
intonational impurity.

>  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.
>

I don't subscribe to the view that western classical music is dead or  
dying, whether by murder or suicide; western art music, its makers, its  
means of delivery, and its audience simply continues to change, as it  
always has changed.  The more relevant dissertation would be written on  
"how changes in instrument design are or are not parallel to changes in  
compositional and performance aesthetics."

Dr. Daniel Wolf
composer
Frankfurt am Main