What is an Oscillator?
The oscillator is arguably (OK we could say the keyboard, but let’s not get picky) the starting point for sound generation in a Synthesizer, after all it’s where almost all of the sounds are created.
The classic analogue Oscillator or VCO in a synthesizer had a choice of five basic waveforms: Sine Wave, Triangle wave, Sawtooth, Ramp (which is the reverse of a sawtooth), and Pulse.
Saw and pulse waves’ spectral content is very rich. For example, a saw wave with a base frequency of 500 Hz comprises harmonics spaced at equal intervals, with exponentially decaying amplitude as shown below.
However, many physical instruments harmonics are of lower amplitude at high frequencies, or may have resonances at particular frequencies. We can achieve this by filtering out, or boosting different frequencies with various types of filter.
The waveform affects the harmonics.
The exact relation between waveform and harmonic content is a very complex mathematical subject (Fourier analysis).
Sawtooth wave:
A sawtooth waveform contains all harmonics in inverse proportion to their number – with all these mathematical relationships you know something ‘natural’ is going on. So the 2nd harmonic is half the amplitude of the fundamental, the 5th harmonic is a fifth the amplitude and so on. Being so rich in harmonics, sawtooth waves are commonly used for brass, strings and some woodwind sounds.
Square or pulse wave:
The square wave contains only odd-numbered harmonics in the same proportion as in sawtooth waves. It produces a ‘hollow’ sound and is typically used for clarinets and reed instruments.
Triangle wave:
Triangle waves contain only odd harmonics, as with square waves, but at much lower amplitudes. In fact – yes, it’s more maths – the relationship is the square of the harmonic number. The 3rd harmonic has an amplitude one ninth (3×3) of the fundamental, the 5th has an amplitude of 1/25th (5×5) and so on. Although triangle waves do contain harmonics, they are not very dominant and triangle waves sound very sine-like. Some synthesisers dispense with a sine wave in favour of a triangle waveform.
Sine wave Harmonics:
A pure sine wave produces just the fundamental frequency, with no (or as close to as possible) Harmonics.
Complex Wave: Usually referred to as Noise, this is an almost random variation in audio voltage with no fixed frequency content. Useful for creating percussion sounds, and adding breath sounds when synthesising flutes or similar instruments.
We don’t need to get into the technicalities of how the shapes are created, just how to use, and control them.
Structure of a basic VCO module.
The Pitch plug: This controls the frequency or “Pitch” of the oscillator, the default voltage to frequency response is 1 octave per volt, the same as an analogue synthesizer.
We connect this to a Detuner Module so that the frequency can be set by octave, semitone, and fine tuned as an offset against any other oscillators if required.
The pitch of SynthEdit’s Oscillator modules are calibrated in Volts per Octave.
This means that signal of 5 Volts on the pitch plug sets the oscillator frequency to 440 Hertz or Middle A, (the note in the centre of a piano keyboard). Increasing the input by 1 Volt will cause the pitch to rise one octave- so the oscillator frequency doubles to 880 Hz .
Simplified: volts=1.442695041* Log(0.07272727273Hz)
To convert Volts to Frequency; Frequency = 440*2^(Volts-5)
To convert MIDI note number to Volts;
There are 128 midi notes. There are 12 semitones on an Octave. 5.0 Volts is middle-A (MIDI note 69)
Volts = 5.0+(MIDI note number-69)/12
The Pulse Width Plug: This controls the on and off times of the Pulse wave form- (see the diagram below) which in turn controls the sound of the tone due to the change in the number of harmonics in the waveform. Note: This control only varies the output when the pulse waveform is selected.
The waveform plug: Connects to a drop down list or similar selector control, so you can select the required waveform.
Sync: This plug allows you to synchronize the oscillator against another oscillator, which can produce some interesting (and outright ugly in some cases) harmonic changes dependent on the frequencies of the two Oscillators.
Phase Mod plug: allows you to phase shift the oscillator waveform by applying a voltage within the range of -5 Volts to +5Volts. By connecting this to the audio output of another Oscillator this allows you to create FM type effects from the two Oscillators.
PM Depth plug: This allows you to control the amount of the signal applied to The Phase Modulation plug that affects the Oscillator.
Properties Settings.
Smooth Peaks, or The Gibbs Effect.
In the oscillator’s Properties window you will see an advanced
option called Smooth Peaks (Gibbs Effect). Now compare the two oscillators’
waveform in a scope, and you will discover they are different. The top display is with Smooth Peaks turned off.
We can see a sharp peak with a ripple effect preceding the peak.
If we enable Smooth Peaks then the waveform will more closely resemble a saw wave. Disable smooth peaks, and a big ripple and spike appear at the edge.
Why is this? Without going into very complex maths and programming,
the waveform is band-limited, meaning that its frequencies
range no further than from 0 Hz to half the sampling rate.
The Fourier series tells us summing an infinite number of sine waves
creates a band-limited saw wave. Summing a limited number of sine
waves creates what programmers and mathematicians call the Gibbs effect; we call it ripples at the edges.
The same happens to other waveforms with sharp
edges—ramp and pulse come to mind. So, this rippling waveform is a
fixture in the digital domain. Smooth Peaks curtails the effect, but also
noticeably diminishes high frequency content above 4 kHz.
Sync X-Fade (Anti Alias):-
Reduces Aliasing noise when Syncing Oscillators at Audio rates. This can be disabled to provide precise note-on phase sync (useful for phase modulation patches) at the expense of introducing aliasing artefacts into the audio output.
Oscillator Sync:
When we Synchronise two oscillators in Synthedit, we ensure that the both start in phase (at the 0 volts part of the cycle) here we have two oscillators which are running at different frequencies, but are Synchronised.
With the Sync connection removed they are no longer starting at the 0 volts/0 degrees point as they did when synchronised.
When the first oscillator in the chain is higher in pitch than the following oscillator, this sync trick causes it to sound as if the following oscillator is tracking the leading oscillator’s pitch: any changes to the leading oscillator’s pitch will also cause a change in the following oscillator’s pitch. This works because you’re forcing the follower to reset in sync with the natural resets on the leading oscillator, locking them to the same frequency.
This crude form of pitch tracking can be used in a pinch to cause multiple oscillators to track together—but it’s a bit crude and has a noticeable side effect. The higher the frequency of the first oscillator, the more truncated the following oscillator’s shape will become—ultimately changing both its timbre and its amplitude. As such, this method of oscillator synchronization isn’t typically used for pitch tracking—after all, in most situations, you could just use the same keyboard, sequencer, or pitch control voltage to control both oscillators simultaneously anyway. So … what does this form of oscillator sync achieve?
Well it does produce some harmonically richer sounds by syncing even a simple sine wave, and once we get to a sawtooth the harmonics can become really wild especially when the first oscillator is lower in frequency than the second.
Oscillator 1 has a lower frequency than Oscillator 2
Oscillator 1 has a higher frequency than Oscillator 2 (Note that as Oscillator 1 rises in frequency the amplitude of Oscillator 2 will decrease)
Oscillator sync becomes very interesting once you start affecting the follower’s frequency independently from the leader. By modulating the follower’s frequency (with LFOs, envelopes, random voltages, etc.), you can achieve a crazy range of sounds some usable others- well a noise. Many of these sounds can be heard in synth lines from the 1980s (Cars, Keith Emerson to name but a few).
This is something that it’s better to try out for yourself than to hear and see the results than for me to attempt to describe
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