On Synthesizers: Waveforms, Spectra, and Oscillators, Part 1

January 18, 2016

Continuing our celebration of 40 years of Keyboard, we present Bob Moog's third "On Synthesizers" column from our January/February 1976 issue, in its entirety.

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An oscillator is a circuit that produces a regularly repeating waveform. When used as the signal source of an audio path, an oscillator determines the pitch of the sound. Its counterparts in acoustic instruments are vibrating elements such as the strings of a guitar or the air column of a wind instrument.

What are we hearing when we listen to an oscillator tone? And what does that have to do with the waveform that we can see on an oscilloscope screen? The answers to these two questions are vitally important to the understanding of oscillators and their roles in synthesizers.

Sonic Acoustic Principles
A waveform is a graphic representation of a vibration. For instance, here is a graphic of the voltage at the sine wave output of an oscillator. The vertical axis is the voltage and the horizontal axis is time. As you look from left to right, you see that the pattern repeats regularly. One complete pattern is called a cycle. The frequency of the vibration is the number of cycles in one second of time. Hertz is a unit of frequency; one Hertz (Hz) is the same as one cycle per second. The average height of the waveform is called amplitude, while the shape of a complete cycle is called the waveform. Frequency, amplitude, and waveform are parameters of an audio signal. They are properties of the signal that we can observe and measure. You can see what they are by looking at the signal's graphic representation.

The sine wave that is shown in the above graph is the most basic periodic (regularly repeating) waveform. In fact, all other periodic waveforms can be synthesized (built up) by adding the appropriate sine waves together. Or, looking at it the other way, any periodic waveform can be analyzed (divided up) into a group of sine waves. Furthermore, the frequencies of these component sine waves are all whole number multiples of the frequency of the waveform as a whole. Engineers call these component frequencies harmonics, while musicians call them overtones. The difference is only in the way they are numbered. The frequency of a waveform as a whole (the fundamental frequency) is called the first harmonic, the component which is twice the frequency of the fundamental is called the second harmonic, and so on. On the other hand, the first component above the fundamental (the second harmonic) is called the first overtone, etc. For instance, in the case of a 100Hz wave, the fifth harmonic is the same as the fourth overtone.

What all this means is that there are two different but equivalent ways of describing a periodic signal. We can take pencil in hand and draw a graph of the vibration in time, or we can make a list of component (sine wave) frequencies. The first of these is the time domain or waveform representation, while the latter is called the frequency domain or spectrum representation. The spectrum of a sine wave contains just one frequency; it has no harmonics.

How Do Oscillators Work?
Virtually all synthesizer oscillators produce at least two different waveshapes simultaneously. Musicians frequently ask me, "Why were these waveforms selected for use in synthesizers? What's so special about them?" The answer is very simple: They are easy to produce with electronic circuits and the differences in the spectra are significant enough to give them separate musical applications. The waveshaping portions of oscillator circuits actually produce the individual waveform by electronic cutting and contouring—sort of superfast paper doll production. Oscillators generally do not synthesize waveforms by generating the component harmonics.

How Do Our Ears Work?
Our ears are fantastically sensitive and efficient analyzers of sound. Within the ear is a complex coiled tube called the cochlea that is only a couple of inches long and full of nerve endings. Each part of the tube is sensitive to a different frequency band. When a sound enters the ear, each component frequency turns on the nerve endings in its section of the cochlea, and the brain is notified accordingly. In other words, the ear picks apart a sound and tells the brain which spectral components are present. The brain then creates the sensation of sound. It figures out what the fundamental frequency is and creates a sensation of a specific pitch from that. And, from the spectral information, the brain creates the sensation of a specific tone color. Thus, our ears respond to spectrum, whereas synthesizer oscillators produce waveforms. The relation between the two is not simple, but is crucial to understanding synthesizers. More on this in my next column.

 

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