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Night of the Living Pulse Widths

The following article is a reprint of a feature that first appeared in Transoniq Hacker, issue #85, July, 1992. 

This article is reprinted with the kind permission of both the author and the former publisher.

Kirk Slinkard

Once, in the distant past, in a time shrouded by the mists of antiquity, the SQ-80 had just come out into the world and was being fiercely challenged by some other beasts, one especially, called the M-1.

  The time had come for me to obtain a modern (at that time) synthesizer, so l explored the SQ-80 and found three oscillators per voice like the majestic Memorymoog, but with greater polyphony, and at less than half the cost, along with audio-frequency amplitude modulation and hard synchronization, and of course, many more waveforms than the Memorymoog had. Then, at the press of a button, it wielded an impressive eight-track sequencer.

I was quite astounded by all this power. And then I scrutinized the M-1. It basically just played samples and waves through effects with only the most rudimentary synthesis capability, and with a somewhat less impressive sequencer. It appeared to be little more than an organ and I puzzled how so many people could be raving about it (admittedly, a subjective viewpoint).

So I acquired the SQ-80 and experimented with features that I had never been able to use before. Among the armaments included in my new keyboard was a waveform labeled "PULSE."  I listened to it, expecting the sound of a narrow pulse wave that I had been hearing for years on other synthesizers, but that isn't exactly what I heard. I recall saying to myself "Gee, this waveform stinks!" I found that I could console myself by thinking of this particular waveform as one of the NOISE family of waves (which is where I believe it really belongs), but this left only the "SQUARE" wave in the pulse family of waves.

I also started to miss the pulse width modulation found in oscillators of most of the better synthesizers of the past, but then I conceived the idea that by using the SYNC feature on the "SQUARE" wave, I could get an impressive variable-width pulse wave with more modulation versatility than the older synths could get. There was a certain specific range of modulation that I had to formulate here, though. The ESQs and SQ-80 can effortlessly go way beyond this range for some nefarious sounds, but was just trying to duplicate the traditional P.W.M. available on the older analog oscillators.


So l worked out a reference patch, PULSEM, that uses the mod wheel to move oscillator 2 (with 1 and) turned off) through half of the pulse width range by diminishing its frequency as much as an octave while his SYNCed to the stationary oscillator 1. The chart shows what happens to oscillator 2 when you move the mod wheel. Since they are initially tuned to the same frequency, this ends up keeping oscillator 2's pitch constant while changing only the waveshape, or in this particular case, the pulse width.

When the wheel is all the way toward you, you get a 50% duly cycle, or a normal square wave (for information on duty cycles, see Clark Salisbury's transwave article in Issue #77).   As you move the wheel forward, the duty cycle increases to nearly 100% to give a really narrow pulse wave. Whenever it travels further away from 50% (in our particular case it only goes higher, up to 100%), the fundamental frequency and lower harmonics start to dwindle, and the upper harmonics increasingly dominate.

PULSE-M Audio Examples

Examples in HTML5 and Flash multimedia formats for maximum compatibility.

HTML5-Format Player

A very simple example of real PWM using ESQ/SQ80 synthesizer architecture.
PULSE-M patch by Kirk Slinkard.

    1) First, 2 notes played in succession, with pulse wave cycle entirely open to demonstrate simple square wave.
    2) Next, the same two notes demonstrating the PWM effect, as the Mod Wheel sweeps through the PWM duty Cycle.
    3) Finally, an open fifth harmony is held as the mod wheel sweeps through the entire duty cycle.

Flash-Format Player

I should mention here that the pulse width range of 50% to 100% sounds exactly the same as the 50% to 0% range, so by only having half of the full range to work with doesn't really take anything away from the sound at all. This P.W.M. setup has a wider modulation range and a more complete harmonic content (brighter) than the PULSE... transwaves on the more recent Ensoniq synthesizers (the VFXs, the SDs, and the newer SQs). On the negative side, the low-resolution digital nature of the waveforms makes the narrower pulse widths subject to digital distortions, especially on the higher notes and on pitch bends and modulations.

To give this patch a more static duty cycle, just turn off the mod wheel and tune oscillator two somewhere between zero and one octave below oscillator one. Where oscillator two is tuned will determine the pulse width. You should be warned that if you tune it more than an octave tower than oscillator 1, you will probably get the sound of silence whenever you try to play it.

This would actually give you a pulse wave that is trying to go higher than a 100% duty cycle, and you would end up with only the upper D.C. voltage of the original square wave, and D.C. voltages are really boring to listen to.



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