Detuning again (was: AW: Wavetables and a load of bull)

[Haible Juergen]

> >On a different tangent - had some private mails with JH about
> >cloning the Taurus I pedals. Has anyone done this ? How integral
> >to their sound are linear oscillators to give a fixed beat rate ?
> 
Just to avoid confusion, I don't think that a *fixed* beat rate
is very desirable. This would be similar to the effect we
know from PWM with the same LFO rate across the
keyboard - rather boring.

And the usual detuning of a V/Oct system has the problem
that the beat frequency (B) rises with the frequency of the
note that is played (f), resulting in either very detuned sound
in the upper range, or almost no beating in the bass range.

Either extreme is not perfect, but there will be a certain 
"optimal detuning function"
B = OptDet (f), 
which might be different according to personal taste and
the special application of this sound.
Now you can write down any OptDet (f) as a series of
OptDet(f) = k0 + k1 * f + k2 * f**2 + k3 * f**3 + ... .

The Detune knob of an exponential VCO changes k1.
Hmm, have to think which k's are affected by the Scale
and HFT trimmers ... 
I have found thru experiments that k0 can make a great
difference if you want to create a "warm" sound without
sounding out of tune. So it's really not *constant* beat rate
that sounds good (it does not), but the extra degree of
freedom to shape your beat rate across the keyboard
range.
Now k0 corresponds to an offset voltage in a linear VCO,
and to an offset current in an exponential VCO. So with
a linear VCO, and with some cheap opamps in the
control path, you are likely to get just the right amount of
k1 for a "warm" sounding instrument.
This does *not* meant that you don't need to control k1
anymore - and like Joachim pointed out, the Beat 
Pot in the Taurus does exactly this, ordinary Detune,
changing k1.
Speaking of the Taurus, I really don't know if the k0 really
matters at all. If you just play bass notes you can detune
as much as you like, you won't notice an out of tune sound
in the upper range when you only play low notes (;->).
I never played a Taurus myself, so I cannot decide.

But I can tell from my JH-4 module, with a slightly modified
SEM-style VCO, that switching k0 between (almost) zero
and a tiny value like 0.3Hz makes an enormous difference.
It's like switching "warmth" on and off. Think of a slow
chorus, but without the side effects of modulated delay
lines like noise and blurred attack phase. People who 
hear it are always impressed (blush).
I have made a redesign of the JH-4 front panel, but I won't
include a Lin Detune pot, like I intended - just a 3-way switch 
with off and two different values of k0. Experiments over
the last months have shown that this is enough. The rest
will be done with the ordinary Detune knob. This confirms
my assumption that the unintentional offset voltage of 
a not perfectly trimmed linear VCO does the trick, but
I can't be sure of course.

Finally, I'd like to add a little example from the OB-8's 
PWM keyboard tracking. As you might now, the OB-8 has
this clever feature to change the LFO rate over the keyboard,
not with 1 Oct (LFO) / 1 Oct (key), but rather with 
1 Oct (LFO) / 4 Oct (key). (This corresponds to a 1/4 Oct / V
LFO tracking, but it's not a hardware LFO).
It turns out to be a very good compromise for PWM, and while
PWM is not exactly the same as detuning, I have calculated
the coresponding k0 and k1. If we have two A's that are 4
octaves apart, we could get 0.5 Hz PWM rate at 55 Hz,
and 1 Hz PWM rate at 880 Hz, for example. This makes
0.5 = k0 + k1 * 55    and
1    = k0 + k1 * 880 .
This would mean (if I haven't made a mistake) 
k0 = 0.47Hz   and
k1 = 6e-4 Hz / Hz.
I don't say this is the optimum for detuning; it just shows
what is possible.

BTW, I highly appreciate the work of Ian, Terry and Magnus
to make VCOs even more precise - you guys are 
truely brilliant ! - but I also recommend to add this little circuit
that introduces a tiny offset current to the integrator. Try it,
and see if you like it !

JH.