Let’s make a sharp turn now from MIDI specifications to the mathematics and algorithms under the hood of synthesizers.
In Section 6.1.8.7, envelopes were discussed as a way of modifying the parameters of some synthesizer function – for example, the cutoff frequency of a low or high pass filter or the amplitude of a waveform. The mathematics of envelopes is easy to understand. The graph of the envelope shows time on the horizontal axis and a “multiplier” or coefficient on the vertical axis. The parameter is question is simply multiplied by the coefficient over time.
Envelopes can be generated by simple or complex functions. The envelope could be a simple sinusoidal, triangle, square, or sawtooth function that causes the parameter to go up and down in this regular pattern. In such cases, the envelope is called an oscillator. The term low-frequency oscillator (LFO) is used in synthesizers because the rate at which the parameter is caused to change is low compared to audible frequencies.
An ADSR envelope has a shape like the one shown in Figure 6.25. Such an envelope can be defined by the attack, decay, sustain, and release points, between which straight (or evenly curved) lines are drawn. Again, the values in the graph represent multipliers to be applied to a chosen parameter.
The exercise associated with this section invites you to modulate one or more of the parameters of an audio signal with an LFO and also with an ASDR envelope that you define yourself.