Harmonics and Waveforms

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Salutations again synth seekers! Last time, we discussed the nature of oscillation and, in turn, oscillators. These controlled oscillations in voltage are translated into definable pitch and sound: slower oscillations result in lower pitches while faster ones yield higher pitches. And if you combine different oscillators, you’ll wind up with multiple notes at once (AKA a chord).

While having actual notes to use is a key staring point, it’d be nice to be able to mold and sculpt these pitches/oscillators as we see fit. Do we want something bright and brash? Or perhaps soft and mellow? Perhaps something hollow and mysterious?

To achieve these different tones/timbres, one of the first variables to adjust is the waveform of each oscillator. We’ll discuss four (technically five) basic waveforms today, but to understand waveforms, you first need to know a little bit about harmonics.

Harmonics are a science unto themselves, so if you really want to dive deep, click here to go wild with math, graphs, etc. For everyone else, I just want to touch on the basics, so you’ll feel more comfortable with the world of waveforms.

In the most basic sense, harmonics are the means by which we create different pitches. A very basic example is to take a string (like on a guitar, violin, etc.) and pluck it. That is the basic fundamental pitch. If you cut that string in half (either by holding it down or literally cutting it), the pitch will now be twice as high (one octave). Other basic fractions of the string will yield different pitches (2/3 the length of the string is a perfect 5th, etc).

Quick side-note #1: if you’d like to know more about intervals in music, check out this post from Master Claset’s Theory Corner!

Additionally (and more practically to our synth studies), harmonics also serve the function of creating different tones and timbres for different instruments.

One of the core elements of this is something called the Harmonic Series, which is shown in the following image:

Harmonic_series_intervalsKnowing exactly what the picture above means isn’t crucial. What I want everyone to take away from this is to imagine that each note can act like a light switch. The bottom note (lower left corner) is always on. That’s the basis of a pitch itself. By turning the other “light switches” on and off, you will generate different tones and timbres. One combination of switches might create a piano tone while another combination might create a trumpet.

In short, different combinations of harmonics yield different sounds. With those ideas in mind, we can get back to the waveforms!

Since we’ve largely been using Moog Synthesizers as a basis for our discussion, I figured I’d refer to my Minimoog Voyager Manual for a brief description of each primary waveform as Moog provides such a concise description of each:

Waveformswhite

Sawtooth: “The sawtooth wave is the richest sounding of the four waves. It contains all of the harmonics, and has a bright, buzzy sound. Sawtooth waves are ideal for brass and string sounds, bass sounds and rich accompaniments.”

Square: “The square wave possesses a hollow sound compared to the sawtooth, owing to the fact that it contains only odd harmonics. This hollow characteristic is ideal for distinctive lead and sustained (pad) sounds.?An interesting aspect of the square wave is that the waveshape can be changed to make the top and bottom parts asymmetrical, creating a pulse wave. By changing the shape of the wave, new harmonics are introduced. Pulse waves are ideal for creating clavinet-like sounds, but are also useful for creating lush pads.”

Quick side-note #2: When Moog refers to changing the shape of a square wave and creating “pulse waves,” these are also known as rectangle waves because you are “crushing” the square shape (see imagine above) into a rectangle.

Triangle: “Like the square wave, the triangle wave only contains odd harmonics, but the levels of the harmonics in a triangle wave are much less. The triangle wave has a soft, slightly buzzy sound that is suitable for high- pitched leads (like a flute) or adding a beefy sub-bass to bass sounds.”

Sine: “The sine wave is the purest waveform of them all. It has no harmonics, so it produces a very pure tone. Because of this, sine waves generally aren’t used as primary audio signals, but are often used to reinforce or enhance other waves. They are also used as modulation sources.”

Quick side-note #3: The Minimoog Voyager I will be using for examples doesn’t make a pure sine wave via its oscillators. I can create one using another means, which I will demonstrate but will save the explanation of that section of the Voyager for another day.

To close today, all of these visual and text descriptions are great but hearing an actual example of these waveforms would be equally if not more helpful. In this video, I’ll have one oscillator on and will cycle through the basic waveforms. The Minimoog Voyager is quite interesting and versatile in that it can “blend” between waveforms, so I’ll move the knob slowly, so you can hear the transformation from one type to another and will pause on each pure waveform. Lastly, I’ll create a pure sine wave via another means (per “Quick side-note #3”).

With our oscillators oscillating and our waveforms morphing, we can prepare ourselves for the world of filters and envelopes!

Oscillation of Oscillators

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Salutations synth seekers! Last time, we discussed a brief history and overview of analog synthesis.

Additionally, I left everyone with two major points that will act as the bedrock for all topics moving forward:

1. Everything is made of waves.
2. Anything can be a source OR a destination.

While that’s all well, swell, and good, it won’t help us at all until we have some basic sounds to work with.

To do so, we should briefly discuss the nature of sound. Most of us learned in school about how sound is made of vibrations in the air and our ears picking up on those vibrations via changes in air pressure.

One term that I’ve noticed doesn’t get used as often is oscillation. An oscillation is a movement back and forth at a regular interval. In sound, those oscillations are the vibrations that we just mentioned. It could be the oscillation of a guitar string vibrating back and forth after being strummed; it could be the oscillation of a drum head after being struck by a stick; it could be the oscillation of your own vocal chords when you sing your personal tribute to the glory of synthesizers.

In an analog synthesizer, we will always find at least one oscillator as the catalyst for creating basic pitches. Many synthesizers have two or three oscillators, so you can create chords (multiple pitches sounding at the same time) or use those oscillators as other sources for modulation (this will be covered later on).

These oscillators have a voltage that is translated to a certain pitch. The higher the voltage, the higher the pitch and vice versa.

Some synthesizers, like my Minimoog Voyager pictured at the top of this page, can actually generate such a low voltage that the pitch becomes subsonic – meaning that human ears can’t perceive it. I’ll use this concept later on to demonstrate how the increasing oscillations lead to higher (and perceivable pitches), but I believe I can provide a more clear example using a metronome app.

The metronome on my phone far exceeds what most metronomes can do, and one of those items is that it can click so quickly that it winds up generating a pitch.

Imagine that as I increase the speed of the metronome, I’m really increasing the voltage of an oscillator on a synth.

You’ll notice that the clicks became so fast, they essentially “blurred” into a perceivable note. The same thing happens as we move from the subsonic to the sonic, but unless you’re a superhuman with super ears, an audio example of that wouldn’t carry the same meaning.

To put the velocity of this blurred speed into perspective, middle C (the note most of us learn first in the world of piano) vibrates about 261 times every second. That would be the same as hearing 261 of those clicks on that metronome app in a single second!

Lastly, regarding most synths, the oscillators have a few parameters that can be modified to change the sound:

1. Frequency
2. Octave
3. Waveform

The frequency is often a knob that allows you to shift the pitch up or down by a certain amount of steps (C to C# to D to D#, etc.). On my Moog, you can shift up or down each oscillator by a sixth (C to A as an example).

This can be used to generate chords, create a detuned (out of tune) sound, or many other items that will come into play in the coming weeks.

However, if you want to explore a larger range of pitches, you can incorporate the octave knob. This allows you to quickly jump a octave (C to C up or down) or more with a single action.

The range of octaves varies from synth to synth. Moog has always loved to push the envelope in this regard, so the Voyager can go through six octaves per oscillators. They are marked: 32′ 16′ 8′ 4′ 2′ 1′.

These marks are in reference to the pipes of a pipe organ. If you start with a pitch from a gigantic 32 foot pipe and cut it in half, you’ll get a pitch that’s twice as high (one octave) through a pipe that’s half as long. This process continues all the way to a one foot pipe.

Now that we’ve established what oscillators are, how they work, and how to get different pitches from them, we arrive at the waveform knob. This is a much deeper concept than just adjusting the frequency or octave, so it will be the topic of discussion next time.

Hopefully, you feel a bit more clear on the general idea of oscillation and how that concept has led to oscillators being the main generators of pitch in the synthesis world!