Linear Detuning Modification for SEM VCOs

Schematic
Circuit Description
Original Idea

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For builders of Modular Synthesizer equipment, Jürgen Haible has generously shared a VCO feature he has developed. It generates "Constant Beat Rate Detuning". So that the reader can fully appreciate this modification, I have attached the message announcing the availability of this circuit and the original message where this idea was being developed. If you would like to examine the Synth-DIY archives, look for "fundamental problem" and "linear detuning".

A schematic of the SEM board, including the VCO, is on Kevin Lightner's Synth Fool web site.

If you'd like, check out the pictures and schematics from Jürgen's Modular Synthesizer on Synth Fool.

Circuit Description

From: Jürgen Haible
To: "Synth DIY mailing list"
Date: Mon, 11 Aug 1997 17:46:31 +0200
Subject: linear detuning works !

For those who followed the thread about linear (constant rate)
detuning in exponential VCOs:

*** Proudly presenting: ***

The capacitive divider thing works very well.
I modified a SEM VCO (clone) with a 150n / 1n divider, and injected a 0 ... 1.5uA constant current (manually controlled by a potentiometer and a 10Meg resistor).
It fullfills all my expectations: Precise detuning from 0 to 1Hz with constant beat rate over the keyboard. Combine this with the normal detune knob, and you get everything from constant rate to a rate increasing with factor 2 per octave.
Only a few components involved, worth less that one dollar.
Believe me, once you have heard this, you want it all the time!
I have drawn a little schematic. Mail me if you want it, or if you want to put it to some archive.
Though I have tried it on a SEM VCO, it should work on almost every sawtooth-based VCO, so it's a possible modification for many synths.

JH.

Original Idea

From: Jürgen Haible
To: "Synth DIY mailing list"
Subject: A fundamental problem of exponential VCOs?
Date: Thu, 10 Jul 1997 17:30:35 +0100

Hi!

I spent some thoughts on beating between a pair of exponential (V/Octave) VCOs.

I found that I run into one problem quite often: When I detune the VCOs so much that I get a decent beat rate of 0.2 to 1 Hz (which I find very pleasant), the VCOs sound very detuned in higher octaves, *regardless* of the scale adjustment of each VCO. I thought that a fairly constant (or only slightly changing) beat rate over the whole frequency range would be a good start for experiments. Then I did some simple calculations and found that this is impossible with exponential VCOs.

On an exponential VCO we usually have 2 trimmers (I omit the HFT here), detune and scale. If you have perfect matching of scales of the two VCOs, you can produce some beating with the Detune trimmer. Then you'll *always* have a certain beat rate at a certain note *and* the double beat rate one octave higher. And so on. So you can only choose between too much detuning in ithe upper range or almost non-existing beating in the lower range.

Then I thought of compensating this by slightly changing the Scale trimmer of one VCO. I start with some arbitrary amount of mistracking, then I use the Detune trimmer to get the VCOs in tune at some note in the upper range of the keyboard, and watch how the beating increases if I go up or down the keyboard. Going down, it sounds quite pleasant - basically the effect I wanted to accomplish. But going up, things become unpleasant very fast. No much use of notes above your chosen "reference note".
Maybe in that range the HFT trimmer would already have some effect and you could slightly compensate for this (making the Scale of one VCO slightly flat, and over-compensating with HFT), but I have not really analyzed this, and probably it will not work good enough.

To me, it looks like this: Most of us use exponential VCOs to get rid of the offset voltage adjustments you need in linear (V/Hz) VCOs. But exactly this (offset misadjustment) would be the means to get a constant beat rate term over the whole keyboard !!

To be more precise: The offset must be introduced *after* the exponential converter. We get *rid* of this by generating an exponential current which charges some capacitor directly. The only way to *introduce* an offset here would be an offset *current*. Maybe some leakage current has some (positive) effect, but it's really hard to control such small amounts of current. (If 1kHz corresponds to some uA, then a 0.2 Hz difference would correspond to some nA ... ) (Method A)

Another way to introduce an offset is using an exponential voltage-to-voltage converter (just drive the collector current into a resistor instead of the VCO capacitor), and use this voltage to drive a linear VCO. Some Korg Synths did this (Polysix, Trident), and as far as I know the first Moog Modular VCOs as well. Problem here: You must take care that the offset voltage doesn't grow too *large*, which reduces the usable range to approx. 5 or 6 octaves. (To cover a larger range with linear VCOs, you have to switch resistors, or do some waveshaping/dividing tricks.) (Method B)

So we have two possibillities to make controlled use of a constant term in beat rate:
Either use method A and find a way to control very small amounts of current (a linear current sorce in parallel of your exponential one, adjustable from 0 to a few nanoamperes), or use Method B and extend the usable range with an opamp that has extremely low offset voltage drift.

I encourage you to make experiments, if this sounds reasonable to you.
If not, please tell me - comments invited (;->)

Before I close, I'd like to take a look at some typical commercial synths. Maybe there is some connection between their VCO architecture and the "richness" of their sound:

Category 1 - Linear VCOs (with or without expo converter in front of the VCO core)

Korg Trident, Polysix
Moog Taurus 1, some Modular VCOs (the ones with driver + VCO modules)
Yamaha CS-50/60/80

Category 2 - Expo VCOs with cheap expo converter (maybe some leakage, or other aberration from perfect V/Oct curve ?)

Old-style Minimoog,
Oberheim SEM

Category 3 - Expo VCO with perfect expo converter (by autotune that includes a table to correct scale imperfections)

OB-8

These are just examples, of course. And most analogue synths would be somewhere in between category 2 and 3, as they don't have scale correction, but a pretty precise straight forward expo converter. (later Minimoogs, Roland SH-synths, OB-Xa, and many, many more). I just wanted to show that there might be some *tendency*, some *trend* from very rich sounding synths at one end to very precice sounding instruments on the other end. And that the reason for this is not black magic, but of some physical nature. And, that this may have something to do with a linear term in VCO detuning.
I am quite sure about the extremes (category 1 and 3), but not of the things between. Maybe temperature drift has more effect than the basic architecture in some synths.

Please tell me what you think.

JH.