wave multiplier

[Dan Slater]

Scot Gresham Lancaster wrote:
> 
> At 09:14 AM 3/19/98 -0800, John Speth wrote:
> >Is the Serge Wave Multiplier schematic to be found anywhere on the Web?
> (If so where?)
> 
> I worked with Serge for several years and he remains a good friend. He was
> not really into freely distributing his designs, except in the case of the
> now long departed "Synapse" magazine, in which he released the ASR (or
> analog shift register schematic) under the nom de' plume of Arpad Benares.
> (I have that issue and could post the schematic if anyone was intrested.) I
> think the patent with Frank Eventoff for what was called the rainmaker or
> rainstick (as I remember it was called ) is not quite the same as the wave
> multiplier, but rather more like the triple waveshaper, which had a more
> subtle effect, like the one described in the patent, the wave multiplier
> used more of a hardware timbre map like what was later described by Daniel
> Arfib and Marc LeBrun in early issues of the Computer Music Journal as Timbe
> Modulation using linear transformation remapping. This form of synthesis was
> used to a great extent in the digital synthesizers the Touche' and 400
> series instruments by Buchla in the mid 80's. Serge's Wave Multiplier is a
> precursor to all that. It should be noted that each section of the three
> sections of the module modifies the wave in specific and unique ways.
> Basically the reverse biasing of the rectifier in each section by the
> voltage control remapped the input voltages second derivative or the rate of
> change of the signal across the voltage range. Subtle changes in the bias of
> the initial state of that diode array yielded completely different behaviour
> for each of the sections. A totally brilliant and unique design....
> 

	The second Serge wave multiplier section appears to be a form of a non
monotonic (waveform can reverse) non-linear function generator. It could
be implemented as a variation of a diode function generator as was often
used in analog computers from that era, although Scot suggests that
maybe the implementation was somewhat more clever.

	Donald Buchla used somewhat similar non monotonic non-linear function
generators in a variety of his products prior to the Serge design. The
Buchla designs were always hardwired to a specific oscillator. One of
the first designs was a 100 series module, the 148 Harmonic Generator.
The 148 is a VCO that outputs 10 sinewaves, all harmonically related
(harmonics 1-10), phase locked and capable of very wide band FM
modulation. The design used a triangle wave master oscillator and a
series of diode wave shapers to produce the necessary harmonics as
triangle waves followed by sine shapers. For example, the 2nd harmonic
was formed by full wave rectifying the fundamental, level shifting and
then applying a sine shaper. The 3rd harmonic was formed by a more
complex diode function generator that synthesized a 3X triangle wave
that then drove a sine shaper. With various combinations of diode
function generators, the first 10 harmonics could be formed. I think
that it is likely that Serge was inspired by a combination of this unit
and maybe even more, by the voltage controlled oscillator waveshapes of
the early Buchla instruments. Serge was clever in making the unit
independent of the oscillator and probably in keeping the implementation
very simple. This and the DSG appear to be the most clever of the Serge
designs.

	The Serge wave multiplier (2nd element) is probably the most
interesting of the Serge wave multiplier designs. As I have not seen
one, the following is somewhat speculative. It apparently can accept an
input signal and cause it to fold over a few times. The output is non
monotonically related to the input signal, ie., it can reverse at
certain voltage levels. The amount of fold over is voltage controlled.
The implementation would be fairly straight forward if done with a diode
function generator design. The number of folds  is a function of the
number of stages in the diode function generator. This type of circuitry
is well documented in books on analog computing.

	Later Buchla synthesizers used another type of non-monotonic function
generation that Buchla called Timbre Modulation (TM). The TM here may be
a specific analog implementation of the TM described in the CMJ journal.
The output of a Buchla oscillator could be caused to fold over on top of
itself many times. The Buchla 208 module (often seen as part of the
Music Easel) and the 259 complex oscillator both included this
capability. The timbre modulation level is voltage controllable. An
abbreviated explanation follows: As the TM control voltage is increased
the oscillator wave shape changes from a sine wave into a more complex
wave in that the waveform starts folding over onto itself again and
again, maybe 10 or more foldovers in the same wave period at the maximum
CV. The acoustic effect is somewhat like a combination of filtering and
phasing. The TM circuitry is physically implemented as a master VCO with
a hard synchronized slave VCO. As I recall, the TM is voltage controlled
by adding the control voltage to the slave oscillator so that it
produces more cycles per master oscillator cycle. As a further
implementation detail, the slave VCO is implemented as a through zero FM
design.

	As Scot has indicated, later Buchla instruments have also included non
monotonic waveshaping capabilities, generally implemented as digital
table lookups.

Dan Slater (dslater at ix.netcom.com)