All sound is made up of a repeating vibration. This vibration's shape, of course, is known as a waveform. Most electronic music instruments offer some basic waveform shapes, then have filters, distortions, etc to modify the existing waveform. I wanted to write about another type of waveform modification called chaining or replacement modulation. A waveform usually refers to a single cycle or period of the repeated pattern. This first figure shows a couple of typical waveforms found in most synthesizers. The top waveform is usually called a sawtooth wave, and the lower one is usually called a square wave.
Chaining is very similar to replacement modulation, except that chaining occurs when you have complete cycles of waveforms chained together. Replacement modulation, in contrast, is when you have partial waveforms substituted within a single cycle of a waveform.
Let's consider the length of a waveform. Normally, we would think about a waveform as a single cycle, but what happens if you consider the repeated pattern to be 2 or more cycles? Your ear would certainly hear the same sound, but you could say that the fundamental frequency was different, with a different emphasis on the harmonic spectrum. If the 2 cycle pattern in the figure on the right consisted of 2 different waveforms but the time that it took to oscillate the blue portion was the same, then you would hear the quality of each of these waves being the same, but the top one would be an octave higher than the bottom waveform.
Now, we can take the two different waveforms from the first figure and switch between them either within the same cycle or every other cycle.
On the left we see an example of replacement modulation on top, and chaining on the bottom. There are not many commercial non-modular synthesizers that do this - Casio CZ and SC Prophet VS come to mind, but typically this has to be patched on a modular synthesizer. There are several options when it comes to ways to patch this idea. Most options revolve around a sequential switch or voltage controlled switch or fader module.
Using an analog sequencer to control the switching, one could easily have long chains of different waveforms repeating as one cycle. The following figure shows 2 cycles:
It is also interesting to use a fader module instead of a switch because you can have varying degrees of mixes between 2 separate waveforms instead of either one or the other.
As a final note, I want to mention that if you create a patch like this where you are switching between 2 waveforms, say a sawtooth and inverted sawtooth, then used a pulse waveform with variable pulse width to control a voltage controlled switch, you can vary the point of switching between the two waveforms within the same cycle. The following figure illustrates this idea:
Here, the black waveform on top would be the output, the red waveform shows a non-switched saw wave, and the pulse wave at the bottom shows the switching control. This can be a powerful alternative to the typical PWM (pulse width modulation) that so many synthesizers offer and any 2 waveforms can be used (or even a high pass output and low pass output of a multimode filter).