Bartok research

Just listening to Bartok this morning, and got to thinking...he did a
lot of research into Hungarian, Eastern European, and Middle Eastern folk
music, cataloging thousands of tunes...are the results of this research
published? Is it available for purchase? Did he talk about the tunings in
any depth? Of course, he used "microtones" occasionally, so he was
obviously hip to the concept...I would like to know more about this area
of his life, so if anyone has any info, let me know...also, the forum CD
master DAT is done, I'll pick it up real soon...Hstick

On Wed, 22 Jul 1998 23:48:07 +0100 (BST) tuning@eartha.mills.edu wrote:

>
> Can somebody in this forum help me understand the concepts of overtones and
> tone color? For example, A440 produced by a tuning fork consists of
> vibrations having frequencies of mostly A440. But A440 played on a piano or a
> tuba will have more overtones, frequencies that are multiples of 440 - 880,
> 1320 etc. This is were I lose it. Are overtones different frequencies
> produced by different aspects of whatever materials are producing the sound?
> So if the sound is being created by simpler materials such as a tuning fork,
> the will be fewer other frequencies involved, whereas if the sound is created
> by a piano, the hammer and string are more complex materials and therefore
> have more frequencies or overtones?

It's not the materials, it's the way that things vibrate. Here's an
oversimplified description. A pure vibration like that of a tuning
fork is a simple smooth "sine wave" of frequency 440, say. A more
"jerky" vibration of frequency 440 is mathematically equivalent to the
combination of smooth sine waves of frequencies 440, 880 etc., the
bigger the component of the overtones, the more complicated is the
resulting waveform and the "richer" is the sound. The way that the
vibration is set up determines what sort of waveform it gives, and
hence determines the timbre.

Basic books on musical acoustics will explain this with diagrams, much
better. perhaps the Just Intonation web site has book references?

David Griffel
-------------
School of Mathematics, email d.griffel@bris.ac.uk
University Walk, Tel. 0117 928 7983
Bristol, BS8 1TW, Fax 0117 928 7999
England.

> wrote:
>
> Can somebody in this forum help me understand the concepts of overtones and
> tone color? For example, A440 produced by a tuning fork consists of
> vibrations having frequencies of mostly A440. But A440 played on a piano or a
> tuba will have more overtones, frequencies that are multiples of 440 - 880,
> 1320 etc. This is were I lose it. Are overtones different frequencies
> produced by different aspects of whatever materials are producing the sound?
> So if the sound is being created by simpler materials such as a tuning fork,
> the will be fewer other frequencies involved, whereas if the sound is created
> by a piano, the hammer and string are more complex materials and therefore
> have more frequencies or overtones?

You're on the right track. The simplest acoustic timbre (to my knowledge) is that
of the flute, which approaches a pure sine wave (fundamental). A vibrating
string, on the other hand, vibrates along its entire length (1/1, the fundamental
pitch), half its length (1/2, giving the octave), a third of its length (1/3, an
octave and a fifth), a fourth (1/4, two octaves), and so on (Pythagoras had some
very nice discussions on this subject). Different string materials, means of
excitation (such as a bow or the hammers of a piano), tension, and other factors
(such as the presence or absence of a mute on a viola, or bray pins on a harp,
for example) influence how loud (roughly speaking, how great the amplitude) any
given overtone will be in relation to the others. It is the balance or proportion
of loudnesses of all the individual overtones that determines the timbre of a
sound, whatever the source or medium of that sound might be  it might be a
vibrating string, a column of air, a speaker set in motion by an electronic
signal, etc. Incidentally, it is because the ratios of vibration of overtones
get progressively more complex the higher up the overtone series one goes that we
have the eternal invention of different systems of tuning and their resultant
aesthetic and scientific debates (like many that are found in this very digest!).
Some of the more theoretically learned contributors can clarify these points
better than I (I'm certain I detected a more than a few cringes at my
over-simplifications), but hopefully this can begin to help.
All The Best,
Dr_Orient

Dr_Orient wrote:

> You're on the right track. The simplest acoustic timbre (to my knowledge) is that
> of the flute, which approaches a pure sine wave (fundamental).

That is a widely-held misconception. Almost all flute tones have a LOT of
overtone content. As with most winds, they have more overtone content in their
lower register, and less in higher registers. I'll attempt to ftp to where anybody
who's interested can find it, a GIF file of a spectral decomposition of a flute
tone.

A tuning fork is however, indeed pretty much a sinewave, which means that a
"Rhodes"-style electric piano should be too. After the attack transient, a
vibraphone and glockenspiel have almost all of their energy in just two or three
overtones, but they have a huge amount of wildly nonharmonic overtone content during
the attack transient.

On Wed, 22 Jul 1998, John Starrett wrote:
> It is not so much that rich tones are composed of a fundamental
> frequency and its overtones as that they can be decomposed this way.
[snip]
> Joseph Fourier figured out how to add up cosine and sine
> waves, which are mathematical representations of the the simplest kinds of
> sounds, to obtain any type of periodic function whatsoever, [snip]
> Describing a complex waveform in terms of its decomposition into a
> sum of sine and cosine waves whose frequencies are simple multiples of
> the fundamental (such as A 440) is useful, but not necessary, for
> describing a tone and understanding why a waveform looks and sounds as it
> does.

There's been much excellent discussion on this topic already; I'd just
like to interject that the reason Fourier-type decomposition of periodic
waveforms is useful is because we believe that the inner ear does
something very similar, therefore it tells us something significant
(_pace_ Brian, not _everything_) about how we would hear such a sound.

--pH http://library.wustl.edu/~manynote
O
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