simple question

Does anybody know the approximate relative amplitudes of
the partials in a "typical" harmonic timbre (say, a vocal
"ah")? Are they inversely proportional to their position
in the series? Or do they drop off more quickly?

-Carl

In a piano tone, or other plucked string, the amplitude of the partials is
roughly inversely proportional to the harmonic number: the 2nd harmonic is
half as loud, the 7th harmonic 1/7th as loud, etc. So I've been led to
believe. In other timbres, this varies widely. In a clarinet tone, the
odd-numbered harmonics are louder, on a flute the even-numbered harmonics.
Don't know about voices.

Kyle

Carl Lumma wrote:

>
>
> Does anybody know the approximate relative amplitudes of
> the partials in a "typical" harmonic timbre (say, a vocal
> "ah")? Are they inversely proportional to their position
> in the series? Or do they drop off more quickly?
>
> Arthur H.Benade's 'Fundamentals of Musical Acoustics' discusses the voice as a musical
> instrument. I quote page 369 where he gives the recipe for a typical intermediate voice
> sound in ordinary speech " The amplitude An of the nth harmonic partial is primarily
> related to the fundamental amplitude A1 by the formula An = a1/n squared", with a few
> weakened partials.

> He then elaborates by explaining that the ears themselves have progressively greater
> sensitivities for high frequencies (up to about 3500 Hz ) than for lower frequencies and
> considers "the loudnesses of individual voice partials that someone would perceive if they
> came to his ear one by one, on the assumption that he is listening only a short distance
> away from the mouth of the singer." Interestingly, the 'loudness recipes' for two different
> sung pitches both show peaks of loudness at the 7th, 11th and 26th partials.

> I'm not qualified to offer further analysis. I found Benade's book at Amazon. I hope this
> helps.

>

--- In tuning@egroups.com, Carl Lumma <CLUMMA@N...>
wrote:
> Does anybody know the approximate relative amplitudes of
> the partials in a "typical" harmonic timbre (say, a vocal
> "ah")? Are they inversely proportional to their position
> in the series? Or do they drop off more quickly?

Carl, there is no such simple relation for vocal sounds.
For example, the loudest partial in vocal sounds is
governed by the absolute frequency of the formant
corresponding to the vowel in question. Accentuating
this effect leads to "overtone singing".

--- In tuning@egroups.com, kgann@e... wrote:
> In a piano tone, or other plucked string, the amplitude of the
partials is
> roughly inversely proportional to the harmonic number: the 2nd
harmonic is
> half as loud, the 7th harmonic 1/7th as loud, etc. So I've been led
to
> believe.

I'm afraid that's not correct. A better answer, a
relationship showing many dips and peaks along the
series depending on where the string is plucked, is to
be found in Helmholtz and/or Benade (I don't recall
which at the moment).
The timbre you describe is a sawtooth wave,
a very buzzy timbre with little resemblence to any real
acoustical timbres (a trumpet might be closest).

[Paul Erlich wrote...]
>Carl, there is no such simple relation for vocal sounds.
>For example, the loudest partial in vocal sounds is
>governed by the absolute frequency of the formant
>corresponding to the vowel in question.

Which is why I asked about "ah". But I understand that
resonant filtering does complicate the matter. So what
about a few idealized generators: reed, bowed string, we
already have Kyle Gann's input on plucked strings.

[Alison Monteith wrote...]
>I'm not qualified to offer further analysis. I found
>Benade's book at Amazon. I hope this helps.

Thanks for the reminder -- forgot I own the book!
Working. . .

-Carl

--- In tuning@egroups.com, "Paul Erlich" <PERLICH@A...> wrote:

http://www.egroups.com/message/tuning/13389

> --- In tuning@egroups.com, Carl Lumma <CLUMMA@N...>
> wrote:
> > Does anybody know the approximate relative amplitudes of
> > the partials in a "typical" harmonic timbre (say, a vocal
> > "ah")? Are they inversely proportional to their position
> > in the series? Or do they drop off more quickly?
>
> Carl, there is no such simple relation for vocal sounds.
> For example, the loudest partial in vocal sounds is
> governed by the absolute frequency of the formant
> corresponding to the vowel in question. Accentuating
> this effect leads to "overtone singing".

Yes... This we went over when the Tuvans came to town!
________ ___ __ __ _ _
Joseph Pehrson