[sdiy] Analysis of frequency variation in analogue synths

[Ian Fritz]

Tom --

Irregularity or "analog "feel" in acoustic instruments has been a topic of 
great interest in the musical acoustics community.  If you want to see what 
has been done, you need access to a technology library and a couple of days 
of free time to go through the literature.  The Journal of the Acoustical 
Society of America would be a good starting place.

I have copies of some older papers.  For example, the paper "Characterizing 
the clarinet tone: Measurements of Lyapunov exponents, correlation 
dimension, and unsteadiness" by Wilson and Keefe (JASA v.104, p550, 1998) 
gives details of a careful time-series analysis on data from real 
players.  They find a small positive Lyapunov exponent, indicating a 
possible chaotic component stemming from the nonlinear behavior of the 
instrument.  But further analysis of period-synchronous amplitude indicated 
that unsteadiness of the player was the dominant contributor to the data, 
and that AM not FM was the dominant mechanism.  Fascinating that they were 
able to pull that out.

Other people have found that period-synchronous noise can produce a 
reasonably natural sounding signal.  For example noise bursts gated at the 
period of the signal and mixed in are supposedly useful. This is in 
agreement with the Wilson and Keefe paper, so that would probably be a good 
place to start, if you are looking for an acoustic instrument analog 
feel.  The irregularities in a VCO might very well be different, though.

You can read a good summary of time series analysis techniques in JC 
Sprott's book on the subject.

   Ian





At 05:56 PM 4/30/2007, Tom Wiltshire wrote:
>Hello all,
>
>I've just spent an interesting but rather confusing evening trying to
>analyse the minor variations in frequency that are supposed to
>account for the 'analogue character' of VCOs. I'm hoping to design a
>digital oscillator for my monosynth project, and had wondered about
>trying to include an 'analogue feel' parameter. As a precursor to
>this, I thought I'd better find out what 'analogue feel' really looks
>like.
>
>Given that I haven't got a full suite of fancy equipment at my
>disposal, I sampled some tones from my Pro-One and SH101 into the
>computer and then looked at the results with software I wrote to
>analyse sound files. This has its limitations, chief among which is
>the 44.1KHz (or maybe 48KHz) input sampling of the computer's audio
>input.
>
>The method I used to find frequency variations was to count the
>samples between zero crossings, so I'm really counting the time each
>half-wavecycle takes. I also used interpolation to try and make the
>results more accurate than simply rounding to the nearest sample as a
>simple count would do.
>
>I would have expected some fairly slow, smooth variations, but in
>fact I saw fairly spikey variations, every few wavecycles. Many
>wavecycles are at constant frequency, then one half-cycle will be
>particularly short. Sometimes these short cycles seem to occur
>regularly, but not so regularly that it's a dead giveaway. Both
>synths I used are based on the CEM3340 oscillator, so these effects
>may be a characteristic of that oscillator. Even if that is the case,
>this is a highly regarded oscillator chip, and it would be
>interesting to know if that was a part of its sound. The Pro-One has
>two oscs, but I was only using Osc B's triangle wave for the
>analysis. On the SH101, I used the ramp wave, since it gave a more
>reliable result than the square, which isn't terribly symmetrical and
>makes a mess of half-wavecycle timings (one long pulse, one short
>space each time, you see).
>
>As I said, it was a very confusing evening and I'm still not
>convinced that the results I got aren't a side effect of the
>experimental set-up, so I'm going to look into it some more. If I get
>some decent results I feel I can trust, I'll put them up online. What
>I wanted to know from the list is:
>
>Does anyone know how 'analogue feel' has been implemented in the past?
>
>Has anyone attempted the sort of analysis I was trying not entirely
>successfully to do this evening?
>
>
>Thanks,
>Tom
>
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