Fast VCOs/V->F converters

[Douglas R. Kraul]

More on accuracy, some comments on digital waveform generation, and
expectations...

When evaluating pitch accuracy in musical applications there are two
important factors: absolute (isolated note) pitch accuracy and relative
error (two or more notes).  Of the two, relative is hardest to hit because
of the small error required but in many ways easiest to implement because
all that is really important is that all of the VCOs do the same thing -
this is referred to "tracking".

In the area of absolute accuracy the old rule of thumb used to be no more
the 5 cents error (A cent is one hundredth of a semitone ).  Expressed as a
percent error one needs this formula: 2^(5/1200).

At A440 this is 1.837Hz, at A up four octaves (x 16) this is 29Hz.

This rule of thumb is based on tests that were done with pro musicians who
could gauge pitch errors *of isolated tones*.

Relative errors between two or more simultaneous pitches are much more
stringent simply because the ear is extremely good at detecting beat
frequencies.  Chorus effects will be detected at sub 1Hz errors,
Vibrato/Tremolo like effects at around 6Hz.  When I used to do this stuff
almost 25 years ago we worked darn hard to get near perfect (much less then
1 Hz) tracking over five octaves that would hold for long periods of time
(after thermo warm-up).  It wasn't easy but it was doable.  The reason for
all this attention to accuracy between VCOs was simple.  If I wanted
chorusing/flanging I'd patch it, I didn't want it on its own initiative!

When doing the math of "is it good enough" you need to factor both of these
issues if high performance is a requirement.

When one flirts with the digital domain as in this application another area
needs to be looked at: short-term phase jitter.  Like it or not, playing
back a waveform from memory with a VCO still is subjected to all of the
realities of sampling.  What you are creating is a variable sample rate
system where the VCO frequency sets the sampling rate.  All of the Nyquist
nasties apply, but one of the worse and most subtle is what happens when the
sample rate jitters.  Small, fast changes in the phase of the sampling clock
cause the modulation of the spectrum of the sampled waveworm and as a result
produce all sorts of sideband frequencies, most of which are inharmonic -
digital grunge in other words.  Grudged that our hears really, really hate
(and probably why any of you are making analog synths in the first place).
Unfortunately it doesn't take much for this to become noticeable.  Without
doing the math a rule of thumb is that the amplitude of the grunge is
influenced by the amount of phase jitter.  If you think about how many dB
down an inharmonic must be before your ear will ignore it you will see that
these things need to be rock stable in the short term.

This affects all schemes that use some type of clock multipliers, be they
waveshappers or PLL.  PLL are particularly bad hear because they are by
there nature (If the have any reasonable loop response time) always hunting
for the perfect frequency match but never quite getting there.  Waveform
multipliers produce edge jitter effects because the comparators never fire
quite the same twice (the edge uncertainty is roughly less then their time
delay)  and clock pulse stretchers be they all digital or dirty old one
shots never produce the same delay twice running.

I think you can see why DCOs became the norm!

Since I bopped into this thread a bit late I'd like to ask a question about
the end goal here for the waveform table lookup VCO.  What is the
expectation that this design will produce in the way of sonic diversity?
The practical answer may be startling!  How many table locations are being
considered?  Will waveform sequencing be possible?  Are we trying to
reinvent the PPG?

Douglas Kraul
-----Original Message-----
From: Martin Czech <martin.czech at intermetall.de>
To: synth-diy at mailhost.bpa.nl <synth-diy at mailhost.bpa.nl>;
theremin1 at worldnet.att.net <theremin1 at worldnet.att.net>
Cc: dkraul at mindspring.com <dkraul at mindspring.com>
Date: Monday, November 23, 1998 5:14 AM
Subject: Re: Fast VCOs/V->F converters


>> I did the math, and perhaps its even correct! (; :
>>
>SNIPPED A NICE ERROR ESTIMATION.
>
>Perhaps the pll approach could work without too much artefacts.  If you
>make a decent hf-vco that has only an error of about some semitones, you
>could compare that to a dco with the exact frequency. Assuming 0.083V per
>semitone, the corrective voltage has only to be , say , 200mV maximum.
>Ie. there is a closed loop regulation, but a very weak one, just enough
>to pull the hf-vco to the exact value. The normal sproiiiing artefact
>comes from wide range plls, with strong feedback. This is not neccessary
>if the hf-vco is allmost correct.
>
>m.c.
>