Quick Guide To Oscillators

Quick Guide To Oscillators

Oscillators form the core of many synthesis systems. We get good vibrations as we explain how they work and what they do…

Virtually every form of synthesis (with the possible exception of physical modelling popularised in Yamaha’s range of VL synths) follows three main stages: tone generation > tone shaping > volume shaping. The tone generation section can take several forms but the most common is the oscillator which is the main sound source in analogue synthesisers and software emulations.

Oscillators generate sound by, er, oscillating. That is, their circuitry basically changes or oscillates between two states very quickly, and just as a vibrating string produces a sound, so the oscillating electronic circuit generates a waveform that can be amplified and used as a sound source. And that’s as technical as we’re going to get here!

The output of an oscillator has three parameters – frequency or pitch, amplitude or volume and waveform or tone. We can see how they relate to a sound by looking at the simplest of all waveforms, a sine wave.

Give me a sine

Oscillators produce repetitive or cyclic waveforms which are usually measured in Hertz (abbreviated to Hz). The faster the oscillator vibrates, the more cycles there will be in a given time and the higher the frequency or pitch will be.

Here we have one full cycle of a sine wave. The distance from the highest to lowest points (technically, the peaks) is its amplitude and the greater the amplitude, the louder it will be.One full cycle of a sine wave. The greater the amplitude, the louder the sound.In the following illustration, you can see the differences between waveforms of different amplitudes and frequencies in. The top two waveforms have exactly the same number of cycles but the peak-to-peak range – the amplitude – of the top one is greater so it will be louder. The bottom waveform has the same amplitude as the top one so they will have the same volume, but it has more cycles so its pitch will be higher.The top two sine waves have the same frequency but different amplitudes so the sound the same pitch but the lower one is quieter. The bottom sine wave has the same amplitude as the top one but more cycles so it has the same volume but a higher pitch.

In control

One of the main features of analogue synthesisers is the way the various modules pass messages to each other. It’s all done with voltages. When you press a key on an analogue synth it sends a specific voltage to the oscillator which generates a particular pitch. Higher and lower keys produce higher and lower voltages and correspondingly higher and lower notes. Analogue oscillators, therefore, are commonly known as VCOs or Voltage Controlled Oscillators.

Voltage control was used with synth modules such as oscillators, filters, amplifiers and envelope generators. It became such a natural and relatively intuitive method of control that even now, many digital synthesisers emulate the VCO routing concept sometimes quite specifically as in Reason’s Control Voltage cabling. Even though digital oscillators don’t generate waveforms in the same way as analogue synths, many soft synths adopt analogue synth methods and terminology.

Nice tone

The tone of a waveform is determined by the harmonics it contains. Harmonics are additional frequencies higher than the fundamental and usually at a lower volume  Harmonics have a natural mathematical relationship to each other – the 2nd harmonic is twice the frequency of the fundamental, the 3rd harmonic is three times the fundamental frequency, the 6th harmonic is six times the frequency and so on. The science of sound doesn’t get much easier than this!

The harmonics in a waveform determines its shape. We can easily see the amplitude and frequency of a wave by looking at it. However, each waveform has its own harmonic content and its own tone, and it’s virtually impossible to know what it will sound like by looking at it. The best approximation we can do is to say that the more complex a waveform is, the more likely it is to have lots of harmonics and sound richer, certainly in comparison to a sine wave.

Look at that wave

A handful of waveforms are commonly used in synthesis, each with a distinctive wave shape and sound.

The simplest is the sine wave which we’ve already looked at which consists only of a single fundamental frequency.It is often used for flute and drawbar organ sounds.
 A sine wave has only one harmonic and that's the fundamental.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.
A sawtooth waveform contains every harmonic with amplitudes in inverse proportion to their harmonic number.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.
A square wave contains only odd harmonics with amplitudes in inverse proportion to their harmonic number.Triangle waves contain only odd harmonics, as with square waves, but at much smaller 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.
A triangle waveform contains only odd-numbered harmonics with very low amplitudes.

Mark this space

One of the most interesting waveforms is the pulse wave because the wave can be changed to alter its harmonic content. It looks like an offset square wave. Whereas in a square wave the upper and lower sections of a cycle are the same – square – in a pulse wave these can be varied. Technically, the upper part is called the ‘mark’ and the lower part the ‘space’. Synth controls for adjusting them are called ‘pulse width’ or ‘mark/space ratio’ controls.
This is a pulse wave with a 1:3 mark/space ratio and it has, therefore, no harmonics that are a multiple of 3.
The term ‘pulse width’ is more intuitive but ‘mark/space ratio’ helps us understand what harmonics are in the wave. The mark/space ratio isn’t actually a ratio between the mark and space widths but a ratio between the mark and the complete cycle. So, a square wave has a mark/space ratio of 1:2 and the mark is half of the cycle. A ratio of 1:4 means the mark width is 1/4 of the cycle, a ratio of 3/4 means it is 3/4 of the cycle and so on.

Now, a feature of pulse waves is that harmonics that are multiples of the right-hand ratio number are absent. The square wave with a 1:2 ratio has no even harmonics – harmonics 2, 4, 6, 8, 10 and so on are absent. A mark/space ratio of 1:3 would have no harmonics that are multiples of 3 – 3, 6, 9, 12 and so on.

As a pulse wave becomes narrower it becomes thinner and takes on a nasal quality. It is commonly used for oboe and harpsichord sounds.

What’s that noise

The final waveform we’ll look at is noise. This is a hissing, rushing sound similar to what you hear when a TV signal is lost or you tune between radio stations.
White noise contains all frequencies in the audio spectrum in equal amounts.

Noise comes in several colourful varieties. The most common is white noise which contains all audio frequencies in equal proportions. Pink noise is the next most popular. It contains fewer high frequencies, sounds less hissy and has a rushing sound. You can create an approximation of pink noise by running white noise through a low pass filter (see The Quick Guide To EQ And Filters).

Take away

Tech terms
Hertz
The tech term for ‘cycles per second’, named after Heinrich Rudolph Hertz (1857-1894). If a sound source vibrates at 100 cycles per second it has a frequency of 100Hz.

Modulator
A synth module whose output is used to change another.

A
So that instruments can play in tune with each other, they must sound the same pitch when they play the same note. In 1939 it was agreed that the A above Middle C should be 440Hz (in the 19th century is had been as low as 435Hz) so use this when setting an oscillator’s or synth’s pitch.

Analogue synths use a process called subtractive synthesis. You start with one of the waveforms just described and run it through a filter to remove some harmonics – hence subtractive synthesis. Most forms of synthesis are subtractive to some degree – as soon as you add a filter to the process you are going to remove something!

One alternative to subtractive synthesis is additive synthesis which is simply adding waveforms together. If you have enough oscillators – and time and patience! – you can try this by adding sine waves together. Create a sawtooth wave, for example, by mixing sine waves at the frequency and proportion of the harmonics as described above.

Home in on the range

As well as generating waveforms, most oscillators have range and tuning controls. Range sets the octave and traditionally this was calibrated in ‘feet’, a throwback to the days of organs when the length of an organ pipe determined its pitch. Options will typically be 2′, 4′, 8′, 16′ and 32′. Each foot is an octave and 8′ is the octave starting at Middle C. Many modern synths calibrate their oscillators in octaves.

Tuning controls fine tune an oscillator to a specific pitch. Many oscillators have coarse and fine tuning controls. In the early days of analogue synths, oscillators were notoriously unstable and kept drifting out of tune. They were often switched on hours before a performance to let them stabilise but the musician would often be playing it with one hand and tuning it with another.

Modern instruments are far more stable and digital synths and software should never have tuning problems. However, it’s common to run two oscillators together and to detune one slightly against the other to thicken the sound.

How low can you go?

We’ve been talking about oscillators as sound sources but they can be used as modulators, too. The LFO (Low Frequency Oscillator) is simply an oscillator that oscillates at a low frequency. It could be so low that it takes several seconds or even minutes to complete a cycle.

LFOs are typically used to add vibrato to a sound by applying a sine wave at a frequency of around 5-8Hz to the pitch. Applying it to volume produces tremolo and applying it to a filter to produce variations in tone.

When selecting an oscillator, it’s important to pick one that generates the type of sound you want for your raw material. This overview of oscillators will help you do that..

For more info…

Synthesiser documentation should contain information about the oscillators it contains and may we modestly suggest the Quick Guide to Analogue Synthesis.