[sdiy] Unstability of oscillators and psychoacoustic qualities

[Magnus Danielson]

From: Dave Krooshof <synthos at xs4all.nl>
Subject: Re: [sdiy] Unstability of oscillators and psychoacoustic qualities
Date: Sun, 22 Sep 2002 20:29:35 +0200

Hi Dave!

> >>It is interesting to note that certain
> >>filters is also claimed to be "cold" or "warm", such that a "cold"
> >>oscillator can be compensated with a "warm" filter.
> >
> >Then in that case, I would analyze waveforms and waveform stability, as
> >filters have no effect on frequency stability.
> Incorrect conclusion to a correct analysis.
> Waveform instablitilty *is* frequency instablility.

... or rather... can be. You can have waveform instabilities which do not
affect the phase relationships and thus do not introduce phasenoise.

> If not so much for the fundamentals - though you could prove
> mathematically the fundamentals are affected as well - it's
> very true for the overtones. And since a filter, even an
> LPF*, is mostly used to bring out certain overtones and is judged
> by it's behavior in doing so, warmness/coldness is bound
> to be decribed in the same terms as used for a VCO.

Right.

Also, the use of filters makes me look more at the phase noise aspect then at
the higher end of the overtone spectra.

> The way waveform instability affects pitch instabilty, is
> the same as Jurgen Haible described VCO instability:
> >>Phase noise comes into a classic saw VCO core at two points:
> >>a) the comparator (or whatever reset-) threshold (affects phase directly) and
> >>b) the ordinary CV path that controls VCO frequency (d_phi = d_f * d_t)
> >>I think (b) is the more important part.
> >>JH.
> Imagine ways to detect pitch:
> - Time the zero crossings: it will be unstable after passing a warm filter
> - Time the peaks: dito
> - FFT: you will notice pitches differ from frame to frame.
> 
> Pity: frequency is quite hard to measure, as you need a time frame
> to do your measurement in. The instablities discussed here happen
> to be smaller then a waveform, let alone a timeframe. So you
> will need good math, I'm afraid.

There is many ways to approach this. Frequency measurements as such is not a
problem. Modern frequency counters measure time intervals by counters. The one
I have just above my computer screen measure the time interval between the
trigger events to within 1 ns. If you relate this to a 1 kHz tone you can view
it as 1000000 +/- 1 counts for a single cycle. Measure for a gate time of 2 ms
and you've got yourself 6 digits for sure. The more sofisticated box I intended
to use for these exercises have a resolution of 200 ps per "tick" so a 1 kHz
tone would have 5000000 +/- 1 counts per cycle if being at accurate frequency.
The trick then is to measure the cycles back-to-back, which this counter on
steroids can do. This is actually rather old equipment, much more extreme gear
exists, but I think this is more than sufficient for these needs. I've measured
phase noise down to the level of a few ps(RMS) on a 125 MHz crystal
oscillator...

Since I suspects mostly frequencies below 10 Hz to be in there... we gain two
digits. The phase noise levels we then can measure is pretty good.

The absolute frequency is not as much of interest, but I can ensure pretty good
readings if I need to.

One issue is naturally the interplay of different overtones. One way to handle
this is to filter out only one overtone. The inherent phase noise of the setup
can be measured separately since I have a pretty quite oscillator for
reference.

> One way is to do correlation on the overtones for filter warmness.
> Or principal components / factor analysis on FT or even capstrum
> analysis. Buy a good book on social statistics to get the neck of
> factor analysis. (I did that before studying sonology).

Interesting twist! ;O)

> Clint Davis wrote:
> >I have to imagine that three strings
> >resonating together in such close proximity have a definite effect on each
> >other as the pressure waves interact with each other, since each is tuned
> >slightly apart.  I believe this would act completely different than just
> >having three oscillators tuned slightly apart.  I wonder if anybody has done
> >any research on that?
> 
> There's a lot of research done in voice analysis. The medical dept of
> the university of Utrecht (.nl) is doing a lot of research.

I've been to Utrecht once... but I guess that's beside the issue (I visited
Surfnet's office at the trainwaystation back in '95).

> Your ear happens to be a special thing: It manages to ignore
> the beating of natural sources, and do some correlation analysis
> to figure out it's actually 3 strings that are sounding.
> With singers the ear's/brain's analysis works even better.
> VCO's are in some respects too short of information to give
> the same psycho-acoustic effect as three strings. Beating
> will be more severe. With three synths running the same patch
> including FM, filters, whatevers and etc the results might
> be *very* pleasing.

Indeed. My approach is to learn what makes a single oscillator sound "warm" to
better be able to understand which of the complex aspects of multi-oscillator
setups that makes them "warm". Once the right properties is understood, the
rest should fall out by propper analysis, guided by the new knowledge. I think
this mailthread allready showed that pretty well.

Cheers,
Magnus