On Synthesizers: Amplitude And Ring Modulation

March 21, 2016

Continuing our celebration of 40 years of Keyboard, we are presenting Bob Moog's original "On Synthesizers" columns in their entirety.


In addition to frequency modulation (the subject of my last two columns), most synthesizers provide for at least one of these common types of modulation: amplitude modulation, ring modulation, filter (or formant) modulation, and waveform width modulation. In this column I will talk about amplitude and ring modulation, the simplest and most basic types of modulation.

The amplitude of an audio signal is its volume or strength. Pure amplitude modulation only makes the sound stronger and weaker, without affecting its frequency, waveform, or harmonic content. The tremolo function in guitar amplifiers is a good example of amplitude modulation of the audio signal by a slow sine wave. Guitar amplifiers generally have two tremolo controls: speed and intensity. The speed control determines the frequency of the modulating signal, while the intensity control determines the amount of modulation that is applied to change the audio signal's amplitude. Another example of amplitude modulation is repeat percussion, the effect on electronic organs that suggests the fast picking of a banjo or mandolin. Repeat percussion uses a sawtooth wave rather than a sine wave as the modulating signal. Fig. 1 shows the unmodulated audio, modulating waveforms, and modulated audio signals of tremolo and repeat percussion.

If your synthesizer is patchable, you can set up amplitude modulation by feeding the output of a modulating oscillator through an attenuator, to a control input of a voltage-controlled amplifier (VCA). The audio to be modulated is fed into the amplifier's signal input, and the modulated signal appears at the amplifier's output. If the VCA has a gain control, it is set so that the gain with no control signal is about half the maximum gain of which the amplifier is capable. This allows the modulating waveform to increase as well as decrease the audio signal's amplitude without distortion.

When the modulating frequency is in the audio range, the sum and difference tones (sidebands) produced by the amplitude modulation become audible. The number of sum and difference tones actually depends on the harmonic content of the unmodulated audio and the harmonic content of the modulating waveform. For instance, let's assume that the unmodulated audio is a 500Hz sine wave (no harmonics other than the fundamental) and the modulating waveform is a 100Hz sine wave. With no modulating waveform, the amplitude modulator output contains only a 500Hz component (the unmodulated audio). As the amount of 100Hz modulating waveform is increased, one 600Hz sum frequency and one 400Hz difference frequency appear at the output along with the 500Hz "unmodulated" component. This forms a natural (not tempered) major triad. When the ratio between the unmodulated audio and the modulating frequencies departs from 5:1, the musical intervals among the three components at the output change radically, and in general are not consonant. As the modulating frequency is increased from 100Hz, the difference frequency decreases from 400Hz and the sum frequency increases from 600Hz. When the modulating frequency is 500Hz (same as the unmodulated audio), the difference frequency is zero, and the sum frequency is 1000Hz. Musically, the difference frequency at this point is inaudible, the sum frequency is the second harmonic of the unmodulated audio, and the resultant output sounds like a single 500Hz tone instead of a triad! As the modulating frequency is further increased above 500Hz, the difference frequency increases from zero. Mathematically, the difference tone has a negative frequency. As far as our ears are concerned, however, there is no difference between negative and positive frequency, and we hear both the sum and the difference frequencies ascend, with a constant frequency difference of 1000Hz between them.

The amplitude modulation of one sine wave by another is technically the simplest type of modulation. Only two sidebands are produced. But look at the variety of musical textures that are available! When the modulating waveform is slow, tremolo is produced. As the modulating frequency is increased, we hear first a closely spaced three-note cluster, then a triad, then two tones whose pitches move in opposite directions, then a single tone with enhanced harmonic content, and finally, three tones, two of which ascend with constant frequency difference.

When the audio and modulating signals have harmonic content to begin with, the modulating products become very complex indeed. If each of the signals has only one harmonic in addition to the fundamental, the modulation products include four sidebands; if each of the signals has ten or so harmonics, there are over a hundred sidebands! Thus the amplitude modulation of complex waveforms is an efficient means of generating thick, dense textures which may subsequently be filtered to produce distinctive clangorous (quasi-pitched) sounds.

Ring modulation is a special case of amplitude modulation, in which the VCA has zero gain in the absence of a modulating signal, and alternately positive and negative gain in response to the alternations of the modulating signal. Fig. 2 shows typical unmodulated audio, modulating signal, and ring modulator output waveforms. Note that the output signal goes to zero twice for every modulating waveform cycle. The result of this balanced modulation is that only the sum and difference frequencies appear at the modulator output. The unmodulated audio and the modulating waveform are both suppressed. Musically speaking, a ring-modulated tone has the same articulation as the unmodulated audio, but a completely different spectral profile. This property of ring modulation has been used extensively by electronic musicians for processing 'live' sounds from acoustic musical instruments, ordinary noises, and even other electronic instruments.

Next month's column will contain more on modulation.

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