The science of Synthesis - Part 5 Waveshapes and it's properties

Oscillators generate a consistent, repeating signal. Signals from oscillators and other sources are used to control the movement of the cones in our speakers, which make real sound waves which travel to our ears.

Oscillators generate a consistent, repeating signal. Signals from oscillators and other sources are used to control the movement of the cones in our speakers, which make real sound waves which travel to our ears. If you tie one end of a rope to a doorknob, stand back a few feet, and wiggle the other end of the rope up and down really fast, you're doing roughly the same thing as an oscillator. The difference is that you're wiggling a rope, whereas the oscillator is wiggling an audio signal.

Audio signals are often represented on a graph where the horizontal x-axis represents time and the vertical y-axis represents the pressure of the signal. This is called a time domain representation of audio.

The Sine Wave

A sine wave is the simplest wave shape and is based on the mathematical sine function. A sine wave consists of the fundamental frequency alone and does not contain harmonics. This means that they are not suitable for sole use in a subtractive sense, because if the fundamental is removed no sound is produced (and there are no harmonics upon which the modifiers could act). Consequently, the sine wave is used independently to created sub-basses or whistling timbres or is mixed with other waveforms to add extra body or bottom end to a sound.

The Square Wave 

A square wave is the simplest waveform for an electrical circuit to generate because it exists only in two states: high and low (Figure 1.7). This wave produces only odd harmonics resulting in a mellow, hollow sound. This makes it particularly suitable for emulating wind instruments, adding width to strings and pads, or for the creation of deep, wide bass sounds.

The Pulse Wave

Although pulse waves are often confused with square waves, there is a significant difference between the two. Unlike a square wave, a pulse wave allows the width of the high and low states to be adjusted, thereby varying the harmonic content of the sound.

Today it is unusual to see both square and pulse waves featured in a synthesizer. Rather the square wave offers an additional control allowing you to vary the width of the pulses.

The benefit of this is that reductions in the width allow you to produce thin reed-like timbres along with the wide, hollow sounds created by a square wave.

The Sawtooth Wave

A sawtooth wave produces even and odd harmonics in series and therefore produces a bright sounds that is an excellent starting point for brassy, raspy sounds. It's also suitable for creating the gritty, bright sounds needed for leads and raspy basses. Because of it's harmonic richness, it is often employed in sounds that will be filter swept.

The Triangle Wave

The triangle wave shape features two linear slopes and is not as harmonically rich as a sawtooth wave since it only contains odd harmonics (partials) ideally this time of waveform is mixed with a sine square or pulse wave to add a sparkling or bright effect to a sound and is often emptied on pads to give them a glittery feel.

The Noise Wave

Noise waveforms are unlike the other five waveforms because they create a random mixture of frequencies rather than actual tones (Figure 1.11). Noise waveforms can be 'pink' or 'white' depending on the energy of the mixed frequencies they contain. White noise contains equal amounts of energy at every frequency and is comparable to radio, static, while pink noise contains equal amounts of energy in every musical octave and therefore we perceive it to produce a heavier, deeper hiss.

Noise is useful for generating percussive sounds and was commonly used in early drum machines to create snares and hand claps. Although this remains it's main use, it can also be used for simulating wind or sea effects, for producing breath effects in wind instrument timbres or for producing the typical trance leads.

Creating more complex waveforms

Whether oscillators are created by analogue or DSP circuitry, listening to individual oscillators in isolation can be a mind numbing experience. To create interesting sounds, a number of oscillators should be mixed together and used with the available modulation options.

This is achieved by first mixing different oscillator waveforms together and then detuning them all or just those that share the same waveforms so that they are out of phase from one another, resulting in a beating effect. Detuning is accomplished using the detune parameter on the synthesizer, usually by odd rather than even numbers. This is because detuning by an even number introduces further harmonic content that may mirror the harmonics already provided by the oscillators, causing the already present harmonics to be summed together.

It should be noted here that there is a limit to the level that oscillators can be detuned from one another. As previously discussed, oscillators should be detuned so that they beat, but if the speed of these beats is increased by any more than 20 Hz the oscillators separate, resulting in two noticeably different sounds. This can be sometimes be used to good effect if the two oscillators are to be mixed with a timbre from another synthesizer because the additional timbre can help to fuse the two separate oscillators. As a general rule of thumb, it is unusual to detune an oscillator by more than an octave.

Additional frequencies can also be added into a signal using ring modulation and sync controls. Oscillator sync, usually found within the oscillator section of a synthesizer, allows a number of oscillators' cycles to be synced to one another. Usually all oscillators are synced to the first oscillators' cycle; hence, no matter where in the cycle any other oscillator is, when the first starts it's cycle again the others are forced to begin again too.

For example, if the two oscillators are used, with both set to a sawtooth wave and detuned by -5 cents (one-hundredth of a tone), every time the first oscillator restarts it's cycle so too will the second, regardless of the position in it's own cycle. This tends to produce a timbre with no harmonics and can be ideal for creating big, bold leads. Furthermore, if the first oscillator is unchanged and pitch bend is applied to the second to speed up or slow it's cycle, screaming lead sounds typical of the Chemical Brothers are created as a consequence of the second oscillator fighting against the syncing with the first.

After the signals have left the oscillators, they enter the mixer section where the volume of each oscillator can be adjusted and features such as ring modulation can be applied to introduce further harmonics. (The ring modulation feature can sometimes be found within the oscillator section but is more commonly located in the mixer section, directly after the oscillators). Ring modulation works by providing a signal that is the sum and difference compound of two signals (while also removing the original tones). Essentially, this means that both signals from a two-oscillator synthesizer enter the ring modulator and come out from the other end as one combined signal with no evidence of the original timbre remaining.

As an example, if one oscillator produces a signal frequency of 440 Hz (A4 on a keyboard) and the second produces a frequency of 660Hz (E5 on a keyboard), the frequency of the first oscillator is subtracted from the second.

660Hz - 440Hz = 220Hz(A3)

Then the first oscillator's frequency is added to that of the second.

660Hz + 440Hz = 11000Hz(C#6)

Based on this example, the difference of 220Hz provides the fundamental frequency while the sum of the two signals, 11000Hz, results in a fifth harmonic overtone. When working with synthesizers, though, this calculation is rarely performed. This result is commonly achieved by ring modulating the oscillators together at any frequency and then tuning the oscillator. Ring modulation is typically used in the production of metallic-type effect (ring modulators were used to create the Dalek voice from Dr Who) and bell-like sounds. If ring modulation is used to create actual pitched sounds, a large number of in-harmonic overtones are introduced into the signal creating dissonant, unpitched results.

The option to add noise may also be included in the oscillator's mix section to introduce additional harmonics, making the signal leaving the oscillator/mix section full of frequencies that can then be shaped further using the options available.

Here concludes the fifth part of this post, if you want to know more about acoustic science, please read Rick Snoman's Dance Music Manual (Second Edition) Toys, Tools and Techniques.