On Synthesizers: Oscillating Filter Modulation & Waveform Modulation

Synth pioneer Bob Moog's original column for Keyboard explored issues affecting musicians and technology developers.
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Continuing our celebration of 40 years of Keyboard, we are presenting Bob Moog's orginal "On Synthesizers" columns in their entirety.


My past five columns have dealt with modulation in general, and with the specific properties of frequency, amplitude, and filter modulation. In this column I'll go into some characteristics of oscillating filter modulation and waveform modulation. Then compare the sideband spectra produced by these modulations for one particular combination of modulating and audio frequencies.

The resonance or emphasis control on a synthesizer filter usually determines the amount of feedback from the filter's output back to its input. (See my column for May/June '76.) If this control is turned up enough, the filter will oscillate by itself. The waveform is generally sine (very little harmonic content) and the sound suggests whistling or singing. The modulation of an oscillating voltage-controlled filter is exactly the same in principal as frequency modulation of a regular voltage-controlled oscillator, except for the sine waveform of the oscillating filter output.

When a filter is oscillating and an audio signal is fed into its input, the incoming audio attempts to synchronize the filter oscillation with its own frequency. If the incoming audio is close in frequency to the natural frequency of the oscillating filter, then the filter oscillation will lock onto the incoming frequency. If the incoming frequency is then changed a little bit (as in a normal vibrato) the filter oscillation will shift in phase, but not in frequency, with respect to the incoming signal. However, if the incoming signal is first set so that it locks the oscillating filter onto its frequency, and then is varied several semitones, the filter oscillation will break out of sync. When this happens, you will hear the incoming audio and the filter oscillation beating with each other at the filter's output.

You can hear all of this clearly if you have a synthesizer with a filter that can be made to oscillate. First turn off the oscillator signals that feed the filter. Set your filter's feedback control so the filter oscillates. Set the filter oscillation frequency to about 500Hz (an octave above middle C). Next, turn the feedback off. Turn one oscillator on, feed it through the filter, and set it close in pitch to the pitch that was just produced by the oscillating filter. Now, turn the filter feedback up again. Move the oscillator frequency up and down a little. At one point you will hear a pure tone. The filter oscillation is now synchronized with the incoming signal. As you lower the frequency of the incoming tone, you will hear the filter oscillation break out of sync and produce a pulsating, lawnmower-like beating. As you lower the incoming frequency still further, you will hear the filter modulation again synchronize to the incoming signal, but this time to its second harmonic (octave). Thus, it is possible to synchronize an oscillating filter to any strong harmonic of an incoming waveform, simply by carefully adjusting the filter frequency relative to that of the incoming frequency.

A distinctive, voice-like vibrato can be imparted to an oscillator tone by feeding it through an oscillating filter and modulating the filter as well as the oscillator with the vibrato control signal. Fig. 1 shows the block diagram for this patch. Tune the oscillating filter carefully to the second harmonic of the VCO. Adjust the amount of oscillator modulation control for a pleasing vibrato, and then turn up the amount of filter modulation control as far as possible without the filter oscillation breaking out of sync. The waveform at the filter output has a very strong second harmonic whose phase relative to the fundamental is modulated at the vibrato rate.

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Rectangular waveform modulation (also called pulse width modulation) is generally achieved by modulating the position of one vertical edge of the wave while leaving the other edge unmodulated. This has the effect of modulating the frequencies of the fundamental and lower harmonics more than those of the higher harmonics, thereby slightly detuning the harmonics. When the modulation is slow, we hear it as a "chorus effect" that fattens the sound. This effect is most pronounced at low audio frequencies, and becomes less noticeable in the upper part of the spectrum. Of course, waveform modulation also results in amplitude modulation of the individual harmonics. (See my column for Mar./Apr. '76.)

Comparison Of Modulation Spectra
Fig. 2a shows the spectrum of the sine output of a VCO that is being modulated from 250Hz to 1kHz by a 100Hz sine wave. Fig. 2b shows amplitude modulation of a 500Hz sine wave by a 100Hz sine wave. Fig. 2c shows the output of a low-pass filter which is being fed by a 100Hz sawtooth wave, and whose cutoff frequency is being modulated from 250Hz to 1kHz by a 100Hz sine wave. Finally, Fig. 2d shows a 500Hz rectangular waveform whose width is being modulated by a 100Hz sine wave.

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The sideband frequencies are the same in all cases: sums and differences of the audio and whole number multiples of the modulating frequency. The sideband levels depend on the type of modulation. The simplest is amplitude modulation: only simple sum (500 + 100) and difference (500 - 100) frequencies are present. Next in order of complexity is filter modulation. Many more sidebands are present, but the strongest are centered around the frequency of the unmodulated audio. Frequency and waveform modulation are even more complex, with prominent sidebands spaced far from the 500Hz unmodulated frequency. To our ears, the exact level of each individual sideband is not critical. What is important is the total amount of sideband energy, and how it is distributed in the frequency spectrum.

We'll get into amplification for synthesizers in my next column.