Linear or exponential?
Many real-world quantities change in a non-linear way. This can be due to the process involved or the way that the change is perceived. For example, the theoretical population growth curve of many animal species shows an exponential or power-law growth because the initial two animals produce two new individuals, who then eventually join the breeding population, and then these four individuals produce four new offsprings. The doubling of the population in each successive generation produces a rapidly increasing population curve. Conversely, because human ears perceive sound in a non-linear way, each doubling of the apparent volume level requires about 10 times the energy in the sound. Again, the relationship connecting the two variables is a non-linear one.
Many natural sound envelopes have non-linear curves. Changes are usually rapid at first and gradually slow down (Figure 3.3.28). This is particularly apparent with the attack segment of envelopes, where a linear rise in volume sounds too slow at first, whereas an exponential rise in volume sounds 'correct' – in fact, it sounds 'linear' to the human ear! Some EGs enable a switched selection between linear and exponential curves. EGs with breakpoints in the attack, decay and release segments can produce similar effects to exponential curves, albeit with a crude approximation.
FIGURE 3.3.28 An exponential envelope does not use linear slopes and often provides more realistic sounding envelopes.
The initiation of an EG is often assumed to be caused by a key being pressed on a music keyboard. Although this is the way that many synthesizers are set up, it is not the only way that envelopes can be started – an LFO or a VCO could provide a trigger which will start the EG. In this case, the envelope is not tied to the keyboard and can be used when a complex repeated CV is required (Figure 3.3.29).
FIGURE 3.3.29 The retriggering of an EG can sometimes be used to add in a break-point and start a new attack, normally from the level which had been reached by the envelope. The overall length of the envelope is controlled by the key being pressed down, or a similar gate control in synthesizer which are not controlled by a keyboard. The retriggering of the envelope is controlled by a trigger signal which is generated by the start of each new note. This is normally found on monophonic synthesizers, where the gate is produced globally from any keys which are being held down, whilst the triggers are produced individually by each key.
When the keyboard is used to start an envelope, two separate signals are produced. The 'gate' signal indicates when the key is up or down, whilst the start of the key depression is shown by a 'trigger' pulse (Figure 3.3.30). The response of an EG to these two signals depends on how the EG is configured.
FIGURE 3.3.30 The gate and trigger routing from a keyboard to the EG is normally fixed, whilst the keyboard CV can be routed to a number of destinations.
'Single trigger' EGs start when they receive a gate and a trigger and progress through the envelope, entering the release segment when the gate signal ends to indicate that the key is no longer being held down. 'Multitrigger' EGs start when they receive a gate signal and a trigger pulse, but additional trigger pulses will restart part of the attack segment and the decay segment. These extra trigger pulses are normally produced by monophonic synthesizers (one note at once) only when a key is held down and another key is pressed.
'LFO trigger' or 'external trigger' EGs normally ignore the trigger pulse and treat the input signal as a gate. The width of the LFO waveform or the length of the external signal sets the length of the gate signal.
Whereas sources of audio signals or CVs can be routed to almost any destination in a synthesizer, the routing of trigger and gate signals is often much more restricted – usually they are hard-wired from the keyboard in performance instruments.
Some EGs provide voltage control of the segment times and levels. This enables the shape of the envelope to be changed with one or more CVs. One use of this facility is for 'scaling', where the length of all the times in the envelope are changed to imitate variations in envelope shape with pitch, in which case the CV would be derived from the keyboard pitch CV. This type of facility is much more commonly found in digital synthesizers.
Table 3.3.1 Summary of Envelope Segments
Coming up in Part 4: Voltage-controlled amplifiers.
Printed with permission from Focal Press, a division of Elsevier. Copyright 2009. "Sound Synthesis and Sampling" by Martin Russ. For more information about this title and other similar books, please visit www.elsevierdirect.com.
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