ProPulse: the Backstory

To understand the ProPulse, we need to understand the ARP Pro-Solist.

Madness

The ARP Pro-Soloist is a fascinating synthesizer: its facilities are totally over-engineered for the limited numbers of presets it provides. I have long been interested in its crazy circuits, and indeed posses a couple of circuit boards from one. It has been out of production for 38 years.

To understand the Pro-Soloist, first imagine a fairly conventional synthesizer halfway between an ARP Solus and an ARP Oddysey: single VCO to VCF (4034= 24db/8ve) to VCA audio path, with an ADSR and an AR envelope generators, an LFO. Now we add the extra features that make it utterly unique:

• First, a pressure sensitive keyboard allows vibrato to be played in. Players of use this to get a quite wobbly sound.
• Second, the VCO is replaced by one running at about 512 times the audio rate. Octave up and down controls select a different division of the clock, allowing very stable linearity at the top and bottom ranges (the Roland SH-3A and Arp Explorer used this same method, though only 64 and 32 times the audio rate). The saw waveshape is made by adding up the various divisions available: this only will have a minor audible effect on quite low notes.
• Third, a complex waveshaper impemented in logic allows a variety of pulse wave of different widths and phases, which it cryptically calls 1/7, 1/9, 14, 2/11. This is the primary function of the ProSoloist. The Pro-Soloist also has a saw, square and envelope-modulated dynamic pulse waves as well as the fractional pulses.
• Fourth, a very complex bank of 3 resonators with selectable characteristics allows formant-like characteristics. The resonators are fed by the pulses only and the resonator output usually goes direct to the VCA output. (The main and last other synth to take up this idea complex preset resonators was the Polymoog.)
• Fifth, a system of routing allows the pulse waves to be variously routed to the VCF and or to the resonators. And the output of the resonators can be split, with one formant going to the VCF and the others going to the VCA. And a lower-level pulse can be selected. A beast!

We get an architecture like this:

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Now some sounds just use the vanilla synth chain: the Flute preset for example. But most use the resonators in various configuration. These resonators exhibit quite strong phase changes, so the result of mixing the resonated pulse with the parallel signal (typically a saw through the VCF) results in a much more complex waveshape than, for example, a “phase linear” equalizer would cause. Indeed, because the waveshaping also changes the phase of the pulses, we could think of the Pro-Soloist as a patch designed to cause maximum phase disruption, making different notes and filter sweeps more interesting: the so-called superposition synthesis.

Sanity

I think the reason no-one has offered the Pro-soloist waveshaper is two-fold: first because it would seem to require a supersonic VCO and complex logic circuits, and second because the Service Manual does a little misdirection that will add to the confusion in trying to understand it. I mean, what is a 1/14 pulse wave? And what is a 2/11 pulse waves? I set about trying to find out.

So I simulated the logic gates on computer: here is a screenshot:

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What I found was that the logic circuit produces a single pulse per wave, not multiple ones. And this pulse was delayed by almost the same amount as its width.

Why would they do this? First, because it means you can simply add two different of these preset pulse outputs: their 1 states never overlap. And second, because it gives a different set of harmonic cancellations when summed with the “saw” signal of the Pro-soloist: thinning the harmonics rather than thickening them.

Furthermore, the names like 1/9 and 1/14 seemed to indicate a design ideal: the actual circuit produces something different, limited to the clock rate (of 64 clocks per cycle). For example, 1/14 should 4.5/64 clocks; you cannot have half clocks, so it is 5 clocks and starts at the fourth clock. And the 2/11? 64/11 * 2= 11.6 which rounds down to 11/64 clocks.

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Looking at this, it struck me that you could generalize this with a very straightforward analog circuit, as a waveshaper that converts a saw to one of these “phase pulses” which is what the ProPulse does. It just needed to range from the 1/64 pulse to the 11/64 to capture the functionality.

But here I struck a snag: every VCO produced a different output level. The Eurorack specification give 5V PP as the typical wave level, but reality complicates it. So I have built in a calabration mechanism, so that the range can be reliable. See the Theory of Operation for how to calibarate it: you would calibrate it each time you plug a new VCO in.

As well, I noticed that for most of the presets, the level drop only occured on the wider pulses. So I generalized this: as the pulse/phase decreases, the level of the pulse increases: this kind of power compensation is a feature of high-end VCOs.

Finally, it seemed to me that if I wanted to support the Pro-Soloist architecture well, in a modular environment, I needed to provide the multiple outputs that make it easy to feed parallel chains: rather than having to mult the saw firt, it was easy to provide a replicated “Saw Though” output.

And, also, a mix output with a 50/50 mix. This again prevents the need for a subsequent mult.

The “Out HPF Mix” also has a fixed 6db/8ve high-pass filter, because in the ARP Pro-Soloist presents, the saw+pulse input is almost always high-pass filtered.

Having the idea, simulating the logic, designing the circuit, simulating the circuit in TINA-TI, recapturing it in Kicad, laying out a board and sending off the order to the PCB fab took less than 48 hours. After fixing a couple of power issues (see the Release Notes) the Rev 0 PCB worked as expected, and is suited as the first release. (A revision fixing the minor issues will come shortly, if demand warrants.)

Armchair Analysis

What is the harmonic effect of mixing a delayed pulse with the saw?

First, lets recall that a saw wave has every harmonic aligned in phase so that they all start at the zero crossing, while a pulse of 1/n ratio has gaps in its harmonics every n harmonics (a “cyclical spectrum”. Adding a 0 degree aligned pulse to a saw adds harmonics that are not integer multiples of the ratio denominator.

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Now when you mix a saw with pulse of 1/n delayed by about 1/n there will be no effect at the n harmonics regardless of the phase: the pulse has nothing there. So the output will just have the n harmonics contributed from the saw.

Instead, the action happens at the non-n harmonics. These are delayed by some amount that is more or less out of phase: because in both the pulse and the saw all harmonics are phase-aligned at their leading edges, therefore when the pulse of width 1/n starts at 1/n the effect is to cancel out (and shift the phase of) harmonics that are furthest away from being a multiple of n.

So lets say we have a pulse wave of 1/7 the cycle time, that a starts 1/7 in. That pulse wave has minima around every 7th harmonic (7, 14, 21 etc), and maxima around every 7 harmonic – 3.5 (3,4, 10, 11, 17, 18, etc). Mixing the saw and the pulse together means will not change the harmonics of saw around 7, 14, 21, but it will decrease those around 3,4, 10, 11, 17, 18. And the other harmonics will also have some decrease, and a phase effect.

Now if we put the saw though a magic low pass filter with no phase effect, then well above the cutoff point we will get the non-n harmonics of the pulse, but below the cutoff-point we will get the cancellation effect of and those non-n harmonics will be decreased. So changing the filter frequency will actually result in a kind of spectrum inversion!

• If we consider the simple case where we are simply adding to a saw wave a pulse of n=2. So this is a 50% square wave, 1/n. If we delay it by 180 degrees, i.e. by 1/n, we get a square wave all of whose harmonics are at 50% to the harmonics in the saw. This cancels out all the odd harmonics, and we get an output wave containing only even harmonics: in effect a sawtooth at twice the original frequency. This is a well-known effect, and can be easily demonstrated by geometry (by drawing them and drawing their sum.)
• Now if we reduce this to n=4, say. So the pulse is 25% and delayed by 25%. The pulse has a cyclical spectrum with dips every 4n harmonics. Added to the saw, this increases the level of the first harmonic, and all the harmonics at 4n will be unchanged. But the harmonics in between (at every 3n (?) will be reduced because they are not (I need to check this) aligned at 0 degrees in the two input waves. (Whenever you add two sines not at the same phase, you get a relative decrease in their level.) So the effect may be that you get a different alignment of formants, with dips tending in the opposite harmonics to the dips of the raw pulse.

But the reality is even more complex. Not only do real low-pass filters have changes of phase around the the cutoff, which may cause an extra boost or an extra cut of harmonics, but if we send the pulse through a resonator, these too may cause phase effects. In our example, for some note, the resonator may change the phase of harmonic 5 by 30 degrees but the phase of harmonic 10 by 180 degrees, resulting in a different spectrum than just simple cancellation/enhancement.

So perhaps we can say that the ARP ProSoloist architecture’s key characteristic is that is causes very complex boosts and cuts to different harmonics from the interaction of the delayed pulses and the VCF, and this volitity will occur in the intersection of the passbands of the VCF and the resonators, which is primarily the “vocal formant” area that the human ear is so adjusted for.

Superimposition Synthesis

Superposition synthesis adds and subtracts different waveforms to get unique mixes of the different harmonics: depending on their relative phase some harmonics will be augmented, some will be attenuated. However, the classic analog VCO waveforms (produced by standard saw-core VCOs) have a key limitation: their waveforms are all locked to the same phase. So superposing the waves will give you just simple mixing of the harmonics: predictable but underwhelming. The ProPulse waveshaper changes both pulse width and pulse phase at the same time: when used in superimposition each shared harmonic will act differently (some louder, softer, some with changed phase).
This module is an original design and provides the multiple outputs useful for superposition synthesis, including a fixed HPF output like its inspiration, the cryptic pulse waveshaping of the amazing ARP Pro-Soloist: run ProPulse in parallel to your normal patch through a resonator for that Pro-Soloist buzz!