"Modulation" means that some aspect of one signal (the carrier) varies according to an aspect of a second signal (the modulator). Tremelo, slow amplitude variation and vibrato, slow frequency variation, are examples of acoustic modulation. When the frequency is low, below 20 Hertz, you get tremelo; when the frequency of the modulator rises into the audible range (i.e. above 20 Hz), audible modulation products or "sidebands" begin to appear. These new frequencies are added to the spectrum of the carrier (typically on either side of the carrier).
The amplitude of the carrier wave will vary in accordance with a modulator wave. Amplitude modulation generates a pair of sidebands for every sinusoidal component in the carrier and the modulator. The amplitude of the two sidebands increases in proportion to the amount of modulation, but never exceeds half the level of the carrier.
"Pushing" a second waveshape, called the program signal, against this constant amplitude forces it to change, but while it changes in direct relationship to its own amplitude and the amplitude of the program signal, it retains its original frequency, with an output varying in amplitude in direct relationship to the frequency and amplitude of the modulating waveshape, or program. It is the frequency of the program that determines the speed or rate of amplitude modulation and the amplitude of the program will define the amount or peak of modulation. If a program frequency has a very low amplitude, the amplitude of the carrier will not be displaced very far; the greater the amplitude of the program, the greater the amplitude variation of the carrier signal.
By using a very low frequency modulator (0.1-7 Hz) it is possible to actually hear the program waveshape. For example, using a 2 Hz sine wave to modulat a constant carrier signal, one will hear a steady rise and fall in the amplitude of the carrier. If a triangle wave is used as the modulating signal (program), the amplitude of the carrier will rise gradually, then instantaneously drop to silence and gradually rise again, etc. By using a square wave as the program signal, the carrier will be instantaneously loud and soft, with no audible rise or decay time in the amplitude. Amplitude modulation with a 5 to 9 Hz sine or triangle wave will produce a very pleasing tremelo.
Amplitude modulation is not limited to the production of various rates of tremelo. As the frequency of the program signal approaches the audible range, it is more and more difficult for the human ear to detect each individual amplitude fluctuation in the carrier, and "sidebands" are produced. In amplitude modulation, if the program signal is approaching the audio range, at least three signals are produced. The most evident signal is the actual modulated carrier. In addition to this carrier, toe modulation process produces two entirely new frequencies known as "sideband" frequencies. One of those frequencies is the sum, in Hertz, of the carrier and the program frequencies; it is called the "upper sideband". The second new signal is the difference between the program and the carrier, or the "lower sideband". These sidebands are softer than the carrier signal and tend to sound like nonharmonic overtones and subtones; therefore, they are useful in timbral constructions. When a program signal consists of more than one frequency (i.e. a complex tone), two sidebands are produced for every frequency contained in the program. Such a complex program may be the result of very high harmonic content or a result of the mixing of two or more signals. In either case, the number of sidebands produced by the process of amplitude modulation is in direct proportion to the complexity of the program signal. The frequencies of the sidebands are always equal to the sums and differences of the carrier and program components.
As an example of amplitude modulation and sideband production, consider modulating a 1,000 Hz sine wave (the carrier) with a 100 Hz sine wave (the program). The result would be the original 1,000 Hz signal plus signals at 1,100 Hz and 900 Hz. If the program consisted of a 100 Hz and 300 Hz signal, the result would then be frequencies of 1,000 Hz, 1,100 Hz, 1,300 Hz, 900 Hz, and 700 Hz.
A good example of composing with amplitude modulation techniques is Karlheinz Stockhausen's Hymnen.
Amplitude Modulation in RTcmix
The RTcmix amplitude modulation instruments are AMINST/aminst for AM-based synthesis, and AM/am for signal processing where the carrier is an input soundfile. Here are some scores:
The first is an example of using a soundfile as the carrier signal:
If you copy this score into a file in your home directory and save it as AM1.sco, you can run this score in real-time by typing the following at the unix prompt:
AM < AM1.sco
This means that the AM instrument will take as its input score the file AM.sco.
Hit return and the computer will play the amplitude modulated version of the sound file you put in the rtinput() command.
