In this article we will demonstrate how to (as shown in this video, below):
- Create a Pulse Wave (wavetable) with Saw waves
- Create a Staircase Wave (wavetable) with Saw waves.
- Modulate Pulse Width (PWM)
What if we have no Pulse-width Oscillator? Intuitively, we may think that a pulse wave can be created by combining 2 square waves. It sounds similar to the technique of summing two identical oscillators together. But by the law of superimposition, it will not introduce any asymmetry; it will modify both positive and negative phases equally.
The value of the pulse wave comes from the so called pulse-width, which is chiefly in the horizontal axis, or the duty cycle of the waveform. When modulated, the wave may seemingly take on the characteristic of two waves, or a chorus-type effect. But, as we'll demonstrate, it is a lot more than that.
Typically, when we can synthesize pulse waves, we can achieve it by modulating the width of a square wave. You may know of this as Pulse Width Modulation (PWM).
We can achieve similar results with any other waveform by the same principle we demonstrate here, and we'll look at this in a second video; Part 2. The principle technique here will offer PW and PW Modulation with any other wave shapes, more or less, but no other sound will be as rich as the traditional rectangular pulse.
An interesting alternative to a PW option, is to mix two Sawtooth waves together (Fig.1), and invert and offset the phase of the second waveform. I.e. Mix a saw and ramp wave.
Fig.1 - Pulse-wave (Yellow) result of Mixing Saw (Blue) & Ramp (Red) waves.
1. Create a Pulse Wave (wavetable) with Saw waves
In Absynth there is no go-to PW option, as many of you might know, but we can still create it. So well start by opening up the wavetables,
As you go to the spectrum tab, you'll see that the Saw wave has a consistent series of all harmonics. This offers a lot of options for using filters and subtractive synthesis, because we have a lot to work with. But in this case we will remove harmonics by superimposing another wave, by going to the Transform menu and selecting Mix.
The default is a Sine wave. We'll load up another Saw wave (Saw_real) and invert the phase. As you can see the wave, has disappeared by superimposition.
We can now offset the mix to reveal either of the Saw waves. But in this case we'll leave the mix ratio in neutral position and instead offset the phase offset to introduce the pulse wave itself (Fig.2).
Fig.2 - Creating a Pulse Wavetable in Absynth's Wave window.
By cycling the phase we can adjust the pulse width; through a square wave up to the narrowest of pulse widths. But if we leave it symmetrical at 50%, the result is a Square wave. In other words, we are left with only the odd harmonics here. If you can't see the wave shape you can identify the square, by listening for the second octave harmonic to detect whether it is present or not. If it is not there it is a square wave; well, this is generally true because all the octave harmonics are even numbers.
Having only odd harmonics, the square wave is a particularly hollow sound, whereas a pulse is regarded as a richer sound. In the spectrogram here, you can see the odd harmonics present in a square wave, being enriched as the pulse width decreases (Fig.3). I'll demonstrate how to do this in real-time, in a moment.
Fig.3 - Spectrum of Pulse Wave (approx 49% PW).
2. Create a Staircase Wave (wavetable) with Saw waves.
But while we're manipulating saw waves in the wave window, I'll show you how to add a staircase-like wave, which is basically achieved the same way as a square wave, except we leave the phase unchanged.
In this window, we simply alter the Frequency ratio. For example lets choose ten steps. The steps themselves are actually a high frequency saw wave, and what we need to do is decrease the mix ratio, so we a mixing more of the original gradient, or the original staircase, back in. This is more useful as a modulation source (Fig.4).
Fig.4 - Creating a Staircase Wavetable in Absynth's Wave window.
3. Modulate Pulse Width (PWM)
To do the PWM in real-time, we'll load up Absynth (and a Blue Cat Audio Oscilloscope, for demo purposes). And we'll go to New Sound, and start with a filtered Saw wave (Saw_filt2) this time. It's a lot more rounded than the digital saw wave (Saw_Real), so it'll give a more natural sound. Change to Double Osc, and add Saw_filt2 on the other section. We can flip the Phase here on the front panel (and we get nothing), as well as offset the phase. Notice how we have three decimal places (It is essentially to the nearest 0.1%. In the Mod Tab/Transform there are 4 digits to enter, for Phase. I.e. to the nearest 0.01% +/-). And at 0.5 we have a Square wave.
We can also go to the LFO and modulate the phase by routing Oscil Main Phase. Then we'll take it up to less than a quarter (<25%), and I prefer the Triangle Wave (LFO); alter the rate. You can see that it's only going to a quarter length of the wave, which is about 180 degrees of Phase. If I go a little bit higher, it crosses over (the wave), and then changes polarity, and then backwards (Fig.5). If you'd like to download this Osc Wave template, follow this link.
Fig.5 - Modulating Pulse-width: Phase of 1st Saw wave with Absynth's LFO.
We go to 75% (mod) it is now three quarters of the way (540 degrees). 100% does a full scale. If we zoom out we see an interesting pattern here happening with the overall phase. Notice the alternating Pitch between + and - direction of the LFO. This contributes warmth. Now let's take it back down.
We can also simply Detune one of the waves. However, FM is needed to bring back the warmth from oscillating pitch. Here the PW is only moving in one direction.
There you have it.