{"id":177,"date":"2013-06-01T11:00:45","date_gmt":"2013-06-01T19:00:45","guid":{"rendered":"http:\/\/www.earlevel.com\/main\/?p=177"},"modified":"2019-02-24T15:05:27","modified_gmt":"2019-02-24T23:05:27","slug":"envelope-generators","status":"publish","type":"post","link":"https:\/\/www.earlevel.com\/main\/2013\/06\/01\/envelope-generators\/","title":{"rendered":"Envelope generators\u2014ADSR Part 1"},"content":{"rendered":"

After discussing the exponential decay of the one-pole filter in a recent article, I couldn’t help but think about envelope generators. Besides, it would be handy to have one to test out some of these other components I’ve been writing about.<\/p>\n

The staple of analog synthesizers is the ADSR envelope generator. Sure, when creating an envelope computationally, we don’t have the limitations of hardware, so we could make envelopes of unlimited complexity. But the abundance of “virtual analog” plug-ins attest to the fact that the simple ADSR is a very effective design\u2014and mandatory if we’re simulating most vintage gear. And it’s more manageable to explain how to make an ADSR, and let you take it from there if you wish.<\/p>\n

States and gates<\/h3>\n

Envelope generators are defined by their states<\/em>. Typically, an envelope generator of a synthesizer at rest is in an idle<\/em> state, outputting zero level. When you press a key, it raises a gate to the “on” state, triggering the envelope generator into its initial attack<\/em> state. The output of the envelope generator begins to rise at an attack rate determined by a user control. As long as the key remains down, keeping the gate “on”, the envelope rises until it reaches its maximum output. At that time, it switches to the decay<\/em> state, and moves towards the user-defined sustain level (set anywhere from zero to maximum output) at the rate set by another user control. Upon reaching the sustain level, the envelope generator switches to the sustain<\/em> state, and remains there as long as the key is held. Once the key is released and the gate changes to “off”, the envelope generator switches to the release<\/em> state, and begins moving towards zero at the rate set by a fourth user control.<\/p>\n\n
\n\n\n\n\n\n\n
State<\/td>\nAction<\/td>\n<\/tr>\n
Idle<\/td>\ndo nothing (output remains at zero)<\/td>\n<\/tr>\n
Attack<\/td>\ncontinue increasing output at attack rate; if max is reached, change state<\/em> to Decay<\/td>\n<\/tr>\n
Decay<\/td>\ncontinue reducing output at decay rate; if sustain level reached, change state<\/em> to Sustain<\/td>\n<\/tr>\n
Sustain<\/td>\ndo nothing (output remains at the sustain level)<\/td>\n<\/tr>\n
Release<\/td>\ncontinue reducing output at release rate; if zero is reached, change state<\/em> to Idle<\/td>\n<\/tr>\n<\/table>\n

Note that the Idle and Sustain states have no exit rules. Moves out of these states are driven by a gate<\/em> signal\u2014driven by a synthesizer key press and release, typically, though the gate can be from a low frequency oscillator or step sequencer, for instance. Here are the additional state rules, driven by the gate transitions:<\/p>\n\n
\n\n\n\n
Gate transition<\/td>\nAction<\/td>\n<\/tr>\n
from “off” to “on”<\/td>\nset state<\/em> to Attack<\/td>\n<\/tr>\n
from “on” to “off”<\/td>\nif state<\/em> is not Idle, then set state<\/em> to Release<\/td>\n<\/tr>\n<\/table>\n

Curves<\/h3>\n

Some envelope generators\u2014more often of the software variety than hardware\u2014have attack, decay, and release segments that rise or fall in a straight line. But hardware envelope generators use exponential segments, typically. The exponential moves come from the charging and discharging of capacitors with current limited by resistors\u2014one-pole filters, basically. Besides being easy to design with simple transistors, resistors, and capacitors, the exponential segments work especially well for amplitude envelopes, since we hear on a log scale (the exponential control against the log response makes the volume changes sound linear with respect to loudness).<\/p>\n

Let’s take a look at how this works in our one-pole filter. You can view a one-pole filter as simply feeding back a percentage of the previous output, with the percentage value controlling the rate of the resulting exponential curve.<\/p>\n

A simple AR envelope generator<\/h3>\n

To get the leanest view of how an envelope generator works, let’s start with the simplest. Synthesizers generate gate signals, typically, when a key is pressed\u2014the gate starts at 0v with no keys down, jumps to 1v when a key is pressed, and back to 0v when the key is released. If we use that as the control signal to our VCA, we’d have an organ-like instant on and off\u2014not very flexible.<\/p>\n

But if we route that into a one-pole filter\u2014a resistor feeding a capacitor to ground\u2014the processed gate would ramp up and down with an exponentially-shaped curve, at a rate depending on the resistor and capacity values multiplied together. (Since it’s more difficult and costly to make variable capacitors, we use a fixed capacitor and a variable resistor.) Here’s a circuit simulation of this basic AR (Attack-Release) envelope generator:<\/p>\n

\"one-pole<\/a>
\n\"one-pole<\/a><\/p>\n

This generator is just as simple in software\u2014a gate that toggles from 0 to 1, fed into a one-pole filter, which is a delay and a multiplier taking the place of a capacitor and resistor. Here’s an iterative simulation done in a spreadsheet, using a feedback value calculated to be equivalent to the capacitor and resistor values shown in the circuit:<\/p>\n

\"AR<\/a><\/p>\n

Next: ADSR<\/h3>\n

But the AR isn’t a very flexible envelope generator\u2014it’s a simple shape, and a single control value sets both attack and decay times. It would be useful for flute-type sounds, but not for guitar, for instance. For guitar, we’d like a fast attack, a slow decay, and a quick release. For that kind of complexity, we need a more elaborate circuit, with transistors to switch in difference resistances and target levels for capacitor charging.<\/p>\n

Next up, we’ll delve into the specifics of an ADSR envelope generator in software.<\/p>\n","protected":false},"excerpt":{"rendered":"

After discussing the exponential decay of the one-pole filter in a recent article, I couldn’t help but think about envelope generators. Besides, it would be handy to have one to test out some of these other components I’ve been writing … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[25,9,23],"tags":[],"_links":{"self":[{"href":"https:\/\/www.earlevel.com\/main\/wp-json\/wp\/v2\/posts\/177"}],"collection":[{"href":"https:\/\/www.earlevel.com\/main\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.earlevel.com\/main\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.earlevel.com\/main\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.earlevel.com\/main\/wp-json\/wp\/v2\/comments?post=177"}],"version-history":[{"count":3,"href":"https:\/\/www.earlevel.com\/main\/wp-json\/wp\/v2\/posts\/177\/revisions"}],"predecessor-version":[{"id":825,"href":"https:\/\/www.earlevel.com\/main\/wp-json\/wp\/v2\/posts\/177\/revisions\/825"}],"wp:attachment":[{"href":"https:\/\/www.earlevel.com\/main\/wp-json\/wp\/v2\/media?parent=177"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.earlevel.com\/main\/wp-json\/wp\/v2\/categories?post=177"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.earlevel.com\/main\/wp-json\/wp\/v2\/tags?post=177"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}