adjusting scaling...

[List, Chris]

Troy - 

Ahhh, you had to go and ask that question :). You've forced me to work
my brain a little bit and figure out the math behind this thing, and
I've come to see that my method will work sometimes but not all the
time.

For my own sanity (because I never worked out the math before) and for
the sake of posterity, I've taken the time to write up an example...

Let's say, that for your VCO has the usual setup; 
Inverting summer -> voltage divider (v/oct trimmer) -> exp. converter

You need the output of the inverting summer + v/oct divider to scale
your input voltage by exactly -0.018 for correct tracking, and you start
out with it set to scale by -.016 (of course you don't know that). 

Now you play the low note, which sends 0v in through the CV, <<but>> to
get in tune, your tune knobs have to be adjusted, and let's say after
you get it in tune, they end up sending -5v into the summer. That means
your divider is outputting .08v to get you in tune. ** IF ** your
divider were set correctly (-.018 scale), those tune knobs be set to
output -4.445v to get the same .08v from the divider to create that same
pitch for your root note! Ya dig? So, because of your bad tracking, your
initial tune knob setting is "wrong" - it's too low - but you don't know
that. 

Now you play a note two octaves higher, you send 2v in through the CV,
your total summed voltage is now -3v, this gets scaled to .048v coming
out of the divider, but, if your scale were correct when you started
you'd now have; -4.445v coming in from the tuning knobs, and 2v from the
CV, and the output of your divider would be (-2.445 * -0.018) = .044.
Lower numbers = higher pitches, so the note generated by .048v sounds
too low. In this case, if lower your divider from -.016 to -.014, your
output voltage will go down, your pitch will go up and the two notes
will be in tune - but you're going in the wrong direction! In this case,
you want to make  the pitch go in the opposite direction when you turn
the v/oct knob and my method works.

Let's say, however, that when you played your low note, you set the tune
knobs so that they send 1v into the summer to get the pitches to match.
Your divider output is now -.016v. If your scale were correct the tune
knobs would need to output .888v to get the same pitch. Now when you
send in a 2v CV, your output is -0.048, but it should be -0.052. Again
your pitch is too low, but this time, **increasing** the divider to
-.0173 will get them closer to the proper tuning and your method works!

What does this mean? It means that 
a. If the sum of your input voltages for the higher note < 0 (i.e. the
output of your divider is positive):
	The v/oct trimmer must be turned so that the second notes gets
more out of tune
	ELSE
	The v/oct trimmer can be adjusted so that the notes get more in
tune
 
b. My VCOs all seem to require at least -2v or -3v to the initial tuning
to get the pitches to match, and so the first condition of point a. has
always been met for my tuning exercises .

c. There's probably a more foolproof way to set the v/oct. (and I've
just been lucky that I haven't needed it :)
  
- CList

> -----Original Message-----
> From:	Troy Sheets [SMTP:tsheets at saturn5.com]
> Sent:	Monday, October 20, 1997 7:45 PM
> To:	Chris.List at sc.siemens.com
> Cc:	tsheets at saturn5.com; synth-diy at horus.sara.nl
> Subject:	Re: adjusting scaling...
> 
> 
> > 
> > Here's what I do...
> > 1. Play a low note on my reference synth (ref-VCO) so that pitch CV
> = 0v
> > out for my midi->CV converter...
> > 2. Set the pitch of the modular VCO (mod-VCO) to match (using course
> /
> > fine tune)
> > 3. Play a note about three octaves up on the ref-VCO
> > 4. If the VCOs are in tune - or in tune enough that you can't notice
> a
> > difference, goto step (8).
> > 5. Tune the mod-VCO to match the pitch of the ref-VCO (using course
> /
> > fine tune) paying careful attention to whether you have to tune up
> or
> > down to get them together.
> > 6. Adjust the v/oct trimmer. Turn the trimmer so that it causes the
> > pitch of the mod-VCO to go in the <<opposite direction>> from the
> way
> > you tuned it in step (5). The amount to adjust it should be
> proportional
> 
> this puzzles me.  Why can't I just leave the mod-VCO and the ref-VCO
> out of tune, and adjust the v/oct trimmer until they are in tune?
> Is there something I am missing that makes this method not work?
> 
> -troy
> 
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