Synth Waveforms

One of the fundamental components of synthesizers is the oscillator, which is just a term for a repeating pattern of values that you might be able to configure. In music, oscillators are mostly used as the generation or manipulation of sound. This article covers the application of oscillators in generating sound.

The first step toward recreating the sounds you want to use in your music, whether you gained inspiration from your favorite musician or a new concept for a sound has arrived in your head, the first step (in subtractive design, anyway) is to become familiar with the different waveform oscillators, who are differentiated by waveforms that produce unique sounds.

Basic Waveforms of Synthesizers
Most synthesizers will involve the employment of one or more of these waveform types.


 * Sine waves are smooth and clean. They are most frequently used in additive synthesizers for their purity. Any waveform can be created by combining sine waves until the harmonics match your intended result. You'll notice later that adopting this as a design principle has a name.
 * Triangle waves are a compromise between the pulse waveforms's computery timbre with the smoothness of the sine. Triangle waveforms are the smoothest one can get while preserving the computery nature. The next waveforms will have a perceived "edge" to them, in the form of buzziness or upper-frequency sizzle, because their waveform involves a sharp slope (or no slope) to the other vertical half of the audio track.
 * Square waves make "beepy" and "boopy" computery noises but generally lack fuzz like the triangle. Squares are a step away from smoothness and more toward buzziness. Square waveforms drone at low frequencies, and by the nature of their upper and lower envelopes are the loudest waveform.
 * Sawtooth waves are aggressive and buzzy. They are buzzy at nearly any frequency. Sawtooths can have a ramp width, which stretches out the waveform and makes the sound bassier.
 * Pulse waveforms have a slight tinny quality at the higher frequencies. At lower frequencies, they buzz and drone. They are like square waves, except that the balance of staying on one vertical half vs staying on the other vertical half can be uneven. A square wave will be 50/50, whereas a pulse will be 25/75, or some other duty cycle ratio. Smaller duty cycles (15/85) or larger duty cycles (60/40) will sound like a reed instrument, while middle duty cycles (50/50) will become a square wave.

Other Waveform Types

 * Exponential waves are the compromise between the sawtooth and the sine.

The Fundamental Sine Wave
At this point, it is important to go into detail about waveforms and their relation to the sine wave, because to understand synthesis, you must understand the relationship between the waveforms and actual sound.

Remembering from earlier pages, sound is essentially a speaker taking in and pushing out air to jostle sound waves around us. Thus there are only two motions a speaker can make in order to produce sound. If you recall the waveform diagram showing the compression (take in air) and refraction (push out air) of an audio waveform, you'll note that this is how we see our music as it is processed by the speaker. If you had a stereo track of a mono sound and inverted the left track against the right track (and centered the panning for each), the waves would cancel each other out. By adding two unique sine waves of the same frequency but one is inverted (you may also see it as it being in a different phase aka sine( pi + x) ), we have created what effectively is sine(x) + ( -1 * sine(x) ) = silence. In Additive Synthesis (which may get its own article later), it is believed that we can make any instantaneous timbre by combining enough sine waves together. To demonstrate this, we will need another observation. Let's say we want to create a triangle wave.

By the third image, the three sine waves begin to create this trending shape that a perfect computer can eventually turn into what resembles a triangle wave. The same process, just with different sine waves, will generate all of the other waveforms.

You can observe the result of this synthesis, which is known as Additive Synthesis, in utilizing the frequency analyzer (also known as a spectrum analyzer, etc). In short terms, this frequency analyzer is a tool that scans our sound, pieces at a time, and tries to tell us what oscillations (looping patterns) it sees. It reports these patterns as a frequency and its amplitude, or loudness, in said frequency. The sine wave is exactly one harmonic, as shown in the picture, because you can only determine one frequency in said waveform. The sine wave is considered to be the "atom" that can be combined to create new waveforms. Each of the harmonics that you see can be considered to be one sine wave that is added to create the desired waveform.

Noise
Noise is what we call a waveform that has a very high distribution of frequencies across the spectrum, or to put it in another way, has a ton of harmonics that render the sound far more complex that the human ear can perceive very well. Noise can be the presence of natural acoustics in a recording or it can be a generated waveform. Generated noise waveforms are periodic (they loop like how a sine wave loops) and are made out of sine waves just like the other waveforms. They can be manipulated until they have a perceived pitch (the fundamental harmonic is recognizable) and with other things like envelopes can be turned into useful things, especially in percussion.

Periodic Waveforms vs Quasi-Periodic Waveforms
Periodic is a term used to describe a wave whose base harmonics are exact, whereas quasi-periodic synth sounds will use detuning, white noise sculpting, or other harmonic-adding tricks to create wide "bands" of frequencies to add to the sound, helping to help timbre sound fuller.

For example, quasi-periodic synths can help simulations of real instruments feel less mechanical and cold by adding imperfections that help it feel more human. You may also notice that each higher harmonic is given a wider bandwidth. This is a rule-of-thumb tip for synthesis with these "natural synthesizer" designs, as opposed to synthesis of other kinds of sounds.

Harmonic Randomness
While we are still on the subject of waveforms and timbre, it is helpful to note that tiny adjustments of your softsynth's harmonics will typically only result in a slightly different sound. Synthesizers like ZynAddSubFX have Harmonic Randomizer dials that can help keep the sound of your synthesized instrument from sounding exactly the same on every hit. Some musicians may pursue exactly similar results every time while others may want the nature of randomness to help shape their music. Analog synthesizers, especially old ones with imperfect parts, were incapable of reproducing the exact same sound, which gives them their more raw and human feel. Softsynths of today will use complex mathematics to emulate these imperfections. You'll note in the synth design breakdown that this is called component modelling synthesis.