Amplitude Modulation
Introduction to Modulation
Installed Modulated signals are those which are changed regularly in time, usually by other signals. They can get pretty complicated. For example, modulated signals can modulate other signals! To create a modulated signal we begin with two or more oscillators (or anything that produces a signal) and combine the output signals of the oscillators in such a way as to modulate the amplitude, frequency, and/or phase of one of the oscillators.
The applet at the beginning of this section shows what happens, in the case of frequency modulation, if the modulating signal is low frequency. In that case we'll hear something like vibrato (a regular change in frequency, or perceived pitch). We can also modulate amplitude in this way (tremolo), or even formant frequencies if we wanted. Low frequency modulations (that is, modulators which themselves are low frequency signals) are excellent ways to produce interesting sonic effects.
LFO (Low Frequency Oscillator) Modulation. A sine wave modulating the frequency of a triangle wave.
We might be more familiar with the term modulation in relationship to radio. Radio transmission utilizes Amplitude Modulation (AM) and Frequency Modulation (FM) — we too can create complex waveforms by using these techniques.
Amplitude Modulation equation: here the DC offset (a signal which is essentially a straight line) is added to the signal m(t) and multiplied by a sinusoid with frequency fc. Ac is the carrier amplitude and ka is the modulation index.
But for making really complex sounds, we are generally interested in high frequency modulation. We take two audio frequency signals, and multiply them together. More precisely, we start with a carrier oscillator and attach a modulating oscillator to modify and distort the signal that the carrier oscillator puts out. The output of the carrier oscillator can include its original signal and the sidebands or added spectra that are generated by the modulation process.
Amplitude Modulation
The diagram below shows how we might construct a computer music instrument to do amplitude modulation. The two ovaloids are often called unit generators, and they refer to some software device like an oscillator, a mixer, filter, an envelope generator, or something like that which has inputs and outputs, and makes and transforms digital signals.
Soundfile .x A lowpass moving filter that uses a sinewave to control a sweep between 0 Hz to 500 Hz.
Soundfile .x A highpass moving filter that uses a sine wave to control a sweep between 5000 Hz to 15000 Hz.
A lowpass moving filter that uses a sawtooth wave to control a sweep between 0 Hz and 500 Hz. A highpass moving filter that uses a sawtooth wave to control a sweep between 5000 Hz and 15000 Hz.
Soundfile .x
Soundfile .x
Tenney made use of some simple modulation trajectories to control timbral parameters over time (like amplitude modulation rate, spectral upper limit, note-duration, and so on). By simply coding these functions in the computer, and linking the output to the synthesis engine, Tenney was able to realize a number of highly original works in which he controlled the overall , large-scale process, but the micro-structure was largely determined by the computer making use of his curves. Phases was released on an Artifact CD of James Tenney's computer music.
Figure .x James Tenney's Phases, one of the earliest and still most interesting piece of computer-assisted composition. The pictures above are his "notes" for the piece, which constitute a kind of score.