You have already gotten acquainted with it in the previous articles. You have learned, for example, that this type of waveform is the simplest of all ─ it's a basic and isolated sound, involving no harmonic nor inharmonic sounds ─ and its frequency determines the pitch of the sound in question. As you will see, the sine wave is at the origin of all the other waveforms listed in this chapter.
The square wave differs from the sine wave in that, besides the fundamental frequency, it also contains odd harmonics.The sum of these harmonics and the fundamental give it its square shape. As you can see, its cycle is equally divided into two alternating constant amplitudes above and below the baseline. That's why it's called a symmetrical wave and, thus, a true square wave. Otherwise, if the time the wave is above the baseline differs form the time below the baseline, the wave is not symmetrical and it's called a "rectangular" wave.
The pulse wave is derived directly from the square wave. It's a wave where the second part of the cycle is replaced by absolute silence. So it's not a symmetrical square wave. The time it spends above the baseline is called "duty cycle."
In an upcoming article you'll see what happens when you modify the duty cycle in real time by means of Pulse Width Modulation (PWM) ─ a pretty severe term that hides lots of interesting sound manipulation possibilities!
The triangle wave is comparable to the square wave in that it contains a fundamental sound plus odd harmonics. However, the power of each harmonic in the triangle wave is twice as low as their counterparts in the square wave. Thus, the power of the harmonics in the triangle wave is reduced twice as fast as in the square wave.
A triangle wave can be more or less symmetrical.
The sawtooth is the most extreme asymmetrical triangle wave. It can adopt two shapes: A progressively increasing ramp followed by an abrupt drop, or a sharp rise followed by a progressive descent.
When it comes to frequency, the sawtooth is the richest in terms of harmonics ─ it has them all! This richness make it particularly interesting for subtractive synthesis, as you'll see in a future article.
They are the foundations of granular synthesis, which ─ guess what? ─ we'll address in a forthcoming article.
We're dealing here with a complex sound wave that is well beyond a simple waveform. This type of element ─ and the resulting synthesis ─ only exists in the digital realm, there is no single analog device that can produce it.
A grain not only contains a given waveform, but also a start point and an envelope (we'll see what all that is...in a future article). Grains also contain frequency information in digital format, like the period of the waveform itself and even its spectrum. This information can be obviously accessed and modified with a computer.
The waveform contained in the grain can be "synthetic" or "sampled." In the first case, they are classic waveforms, "synthesized" in a traditional way by summing basic sine waves. In the second case, they are digitally recorded sounds – sampled ─ classified in what's called a wavetable – a table in which each cell containing a sound is identified by a pair of coordinates that give you access to the cell in order to read or write to it. Wavetable synthesis will also be studied in a more detailed manner in an upcoming article. Do note, however, that granular and wavetable synthesis do not necessarily overlap.
The following audio example shows a sound before and after extreme "granularization."