History and theory of oscillator sync

The basic principle

Author: Rob Hordijk

Traditionally analog synthesizers use subtractive synthesis to generate sounds. The principle is that the following three basic parameters control a musical sound:

Ideally there would be a module to control the pitch, a module that controls the volume and a module that controls the timbre. With volume this is not a problem, a standard VCA-ADSR or VCA-LFO combination affects only the volume, but modules that control the pitch of a sound have a timbre of themselves. This is in practise not a drawback, but opens lot’s of possibilities instead, as the basic timbre can be controlled in the pitch controlling module(s) and additionally finished in the timbre-controlling module(s).

There are two basic types of sounds, pitched and unpitched. Actually there is a broad spectrum of sounds that fall somewhere between these categories, so it is best to qualify sounds in a spectrum with single-pitch sounds with pure harmonics on the one end and totally unpitched sounds on the other end. Chords, inharmonic sounds or the sounds generated by grainclouds would fall somewhere in between. Oscillator synchronisation only works predictably with single-pitched sounds.

The traditional module to control the basic pitch of a sound in subtractive synthesis is the voltage controlled oscillator or VCO. The idea is to use a type of vco that generates a periodic waveform with as many harmonics as possible. Most synthesizers offered two basic waveforms, the sawtooth wave and the square wave, named after the way they look when viewed on a oscilloscope screen. The reason to use these two is that a sawtooth waveform contains all harmonics of the fundamental pitch of the waveform, and the square waveform contains only the odd harmonics, lacking the even harmonics. When using flexible and good quality filters you can remove (subtract) unwanted harmonics from these waveforms and end up with the soundspectrum typical for some instrument.

Micromodulation

Theoretically this sounds fine but in practice it is a lot more complicated as musical instruments constantly change timbre in a very complex way, this is called micromodulation. The standard filters used to control the timbre are simply not sophisticated enough. This limits analog synthesizers in their potential to synthesize existing real-world musical instruments. This is not a problem as synthesizers are capable of generating complete different sounds, making analog synthesizers musical instruments in a class of their own. If our goal would be to accurately copy the sound of an existing musical instrument, it is better to use a sampler, or maybe even better to use the original instrument. Still though it is very well possible to apply several characteristics of an existing instrument and end up with very usable synthesized sounds. E.g. we can program the way an instrument is played, is it a windinstrument or a string instrument, is the string hammered, plucked or bowed, etc.

PWM, FM and Sync

Almost all analog synthesizers possess the possibility to control the pulsewidth of the square waveform. This changes the harmonic content of the waveform, the 50% pulse of a pure squarewave, as mentioned before, contains only odd harmonics, resulting in a ‘hollow’ timbre, the characteristic of some wooden windinstruments. But when changing the pulsewidth even harmonics start to appear in the soundspectrum, changing the perceived timbre. When modulating the pulsewidth all the separate harmonics increase or decrease their volume in their own way, resulting in a more lifelike sound. Modulating the pulsewidth with a lfo or a slow random signal mimics the effect of a small ensemble. And modulating the pulsewidth with an adsr, with slow decay and zero sustain settings, mimics the micromodulation of a hammered or plucked instrument. This is one example of what is meant by micromodulation, by changing the pulsewidth each single harmonic gets modulated in its own rhythm.

Micromodulation is a feature at the oscillator level, so to create more micromodulation possibilities on analog synthesizers the designers of these instuments started to explore the technical features of the oscillator modules. Two techniques where obvious, but both require at least two oscillator modules. These are ‘linear’ frequency modulation and waveform synchronisation.

Linear frequency modulation however doesn’t work very well on pure analog synthesizers for two reasons. First the oscillators are very temperature sensitive and constantly drifting, but FM requires rock-stable frequencies. Second selfmodulating or cross-modulation will increase or decrease the fundamental frequency in a complex curve. It is good to note that digital FM synths do not use linear frequency-modulation but linear phase-modulation, that does not have the mentioned drawbacks.

So with analog oscillators synchronizing the waveforms of two oscillators was the logical step to take.

To understand what synchronisation of waveforms actually does we have to look at the architecture of the traditional vco. Two types of vco’s were generally used, one generates only a sawtooth waveform that is later transformed in a squarewave with variable pulsewidth and sometimes a triangle- and sinewave as well. The other type generates both a squarewave and a trianglewave at the same time, that are later combined and transformed into a sawtooth waveform. The waveforms of these type of oscillators sound the same, only the synchronisation can be different. The sawtooth oscillator only features ‘hard’-sync, while the square-triangle oscillator features both ‘hard’ and ‘soft’-sync. To understand the difference we must look at how the oscillators internally work. The sawtooth oscillator consists of a capacitor that is slowly charged with a current, resulting in an increasing voltage. This is the ‘ramp up’-phase of the sawtooth. When the voltage reaches a certain maximum level the capacitor is shunted and immediately looses it’s charge. Then the charging starts again. The moment the capacitor is shunted is preferrably infinitely short, but in practice so short that it doesn’t influence pitch. The amount of charge current controls the frequency of the oscillator.

Now if we would have the possibility of shunting the capacitor on an outside signal we can force the oscillator to restart it’s waveform. Only this signal must be a pulsesignal of very, very short duration. So if we feed another waveform to the sync-input of an analog oscillator, when should it discharge the capacitor by momentarily shorting it? The designers choose to use the moment when the synchronizing oscillator’s waveform starts it’s own cycle. This is logical, now both oscillators start their cycles at the same time.

Technically, at the sync-input of the oscillator, the signal of the synchronizing oscillator goes into what is called a ‘transient detector’. A transient in a waveform is the moment when a waveform changes from it’s maximum to it’s minimum or from it’s minimum to it’s maximum value, actually the moment when the capacitor is shunted in the case of the sawtooth oscillator. The transient detector regenerates the shunt-signal of the synchronizing oscillator in the synchronized oscillator.

Transients in a waveform are actually quite important in the timbre. They are moments of very high energy, they must have this energy, as in practice the transients in a squarewave use this energy to very quickly pull the conus of the loudspeaker into or out of the loudspeakerbox. Not only the mass of the conus must be moved in as short a time as possible but also the airpressure inside and outside the box must be overcome. It is easy to see that at this moment all the harmonics must be at their maximum volume to add together all their energy to accomplish this move of the conus. So, as Spock would say, logic predicts that strong transients influence the brightness of the sound.

To summarize, in a traditional analog oscillators waveform, if there is some ‘corner’ in the waveform, that point is called the transient. In a sound this influences the brightness, but this point is also used to synchronize another oscillator. This means that sounds without transients, like sinewaves are not able to synchronize another analog oscillator that use only a transient-detector. Normally the sync-input is hardwired through a simple switch to the sawtooth output of the other oscillator.

On the Nord Modular the sync-input signal doesn’t go into a transient detector but into a zero-crossing detector. This detects if the synchronising waveform crosses the zero voltage line in an upwards direction to generate the internal "syncpulse". This is a big advantage over analog oscillators as now the oscillator can synchronise to any type of signal.

The other type of oscillator mentioned, the one that generates square-triangle waveforms at the same time also uses a capacitor, but this capacitor is not shunted. After the charging reaches a maximum level the charging current is reversed and the capacitor is discharged in the same rate as that it is charged, resulting in the triangle waveform. The charge/discharge signal results in the square waveform. Now we have two possibilities. We can still shunt the capacitor with an extra shuntcircuit, enabling hardsync. But we can also force the oscillator to toggle the charge/discharge state. This forces the triangle waveform to reverse it’s direction. This is called ‘soft’-sync and sounds distincly different from hard-sync. E.g. hardsync can generate a strong transient in a synced trianglewave on the syncing moment, but softsync will by itself not add such a strong transient. So it sounds smoother.

The sonic effect of synchronising one oscillator with another is, that the synchronised oscillator inherites the pitch of the synchronizing oscillator, but the waveform of the synchronized oscillator consists of several cycles of the original waveform and a ‘broken’ cycle at the end, broken at the moment when the sync-moment occures. That is, when the pitch of the synchronized oscillator is set several times higher that the pitch of the synchronizing oscillator. It is not very useful to set the frequency of the synchronized oscillator to a lower value than the synchronizing oscillator, as the extra transients that are so characteristic of the sync sound only occur when the frequency of the synchronized oscillator is set higher. You can check this by recording a sample of a sync sweep in your PC and examine it with a wave editor. Recording the output of the synchronizing oscillator into the left input and the other oscillator into the right input of your soundcard will reveal everything.

From this it may be obvious that self-synchronization of a single oscillator, and cross-synchronizing where one oscillator syncs another, whose output syncs the first, do not work. In both cases the waveforms simply stop, so if you try this and you hear no sound, that is correct, these are ‘forbidden’ connections.

Sound characteristics of oscillator synchronization

When synchronizing two analog sawtooth oscillators and sweeping the frequency of the synced oscillator, the sound is a bit similar to the sound of a square oscillator with a sweeped pulsewidth, only the sweeping is more pronounced and harsh. This is due to the fact that a pulse waveform always has two transients in one period, but the synced sawtooth gets more and more transients when it sweeps up. The appearance of these transients in the period of the waveform produces this chracteristic harsh but still pleasing result. The more transients appear the more energy the sound gets in it’s very high harmonics. Due to the fact that soft-sync does not generate such strong transients, it sounds a lot softer, hence it’s name. There are no Nord Modular oscillator modules that have a softsync input, but by manipulation of the grey slave signal we can easily create the traditional softsync where the direction of the waveform of the synced oscillator is reversed by the syncing oscillator. We will see that with this method we can even go beyond and create softsync types that are not present on traditional pure analog oscillators, but are some hybrid form between traditional softsync and FM.

Workshop

In the workshop you will learn step by step how to patch the basics of several oscillator synchronisation patches and what the connections do. The patches are designed to demonstrate the principles and to test them yourself. Most of them are kept deliberately very simple and so might not be directly usefull musically. This way you will quickly and easily become a master of sync in a very pleasant way. Hopefully the workshops will be inspiring and help you look and hear beyond the obvious and you can turn the discussed matter into something musically useful to you. Nothing prevents you from changing and adding to the patches. Au contraire you are invited to.

If you didn't know already, you will find that the Modulars are incredibly versatile synths and you can do a lot of things simply not possible on other synths, as none will allow you the freedom of connections and programming potential they do. Hat's of for Clavia.

 

To learn more about the following subjects go to one of the following workshops

Hardsync on the Modulars

Hardsync workshop

VOSIM, an application of hardsync

VOSIM workshop

Softsync and FM sync on the Modulars

Softsync and FM-Sync workshop