Subject: Re: Frequency response was Re: [linux-audio-user] Audiophile CD's
From: Jörn Nettingsmeier (nettings_AT_folkwang-hochschule.de)
Date: Tue Jan 29 2002 - 01:48:14 EET
Jason wrote:
>
> On Mon, 28 Jan 2002, [iso-8859-1] Jörn Nettingsmeier wrote:
>
> > Jason wrote:
> > > Timbre however, is a function of waveshape not frequency; the
> > > closer a signal
> > > gets to the Nyquist cutoff, the more generic it's shape becomes.
> >
> > true, but you needn't care. any "wave shape" other than plain sine
> > means "additional overtones above the fundamental", because each and
> > every shape can be expressed in terms of a sum of sine waves with
> > different frequencies.
> >
> > a sawtooth wave for example is nothing else than a mix of f + 2f +
> > 3f + 4f + 5f ... (where the amplitudes decrease as the factor gets
> > higher. when you draw the graph, it will gradually begin to resemble
> > a sawtooth, and it becomes less wobbly the more higher components
> > you add.
> >
> > thus, their frequency is higher. you'll get all relevant overtones
> > up to the 20something khz rolloff, but nothing higher, which you
> > couldn't hear anyway.
> >
> >
> hmmm. I'm really not convinced that hearing works by picking apart complex
> waveforms into fundamentals. Can anyone recommend any good books on
> psycho-acoustics that aren't *too* heavy on the calculus? If my thinking
> is wrong on this, I really want to correct it.
since you have little resonators in your ear that pretty much tune
in to one particular frequency, it really *is* picking it apart. not
in the sense of an fft, but in the sense of thousands of tuned
pitchforks resonating, and then "measuring" their amplitudes.
btw, an infinite sum of sine waves is absolutely equivalent to an
(idealized) sawtooth as you would find it on a bowed string
instrument. it's not merely a way of coming close to it in additive
synthesis, but it is in fact a valid, watertight description of what
happens. any waveform can be expressed thus. it is by no means a
reduction or loss of information.
although of course a bow does not think, yuck, i'll have to do about
30 sine waves simultaneously to get my job done.
instead it just elongates the string as much as the friction can
hold, then the string snaps back (not to zero, but into a negative
elongation due to its momentum), the friction takes over again, and
so on.
so yes, in nature you'd have a "direct" sawtooth wave, but as i
said, viewing it as a sum of sine waves is just convenient, and it
*does* model how we hear pretty closely.
-- Jörn Nettingsmeier home://Kurfürstenstr.49.45138.Essen.Germany phone://+49.201.491621 http://spunk.dnsalias.org http://www.linuxdj.com/audio/lad/
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