Learning Synthesis: Envelopes
Part Two: Complex Envelopes, Arbitrary Functions, & Beyond
So to reiterate the key ideas mentioned in Learning Synthesis: Envelopes Part 1, envelopes are most often one-shot fluctuating signal sources, triggered by some kind of initiating event—most often a keypress, or a sequencer, or some other gate source in a modular system. Whereas LFOs (the other most ubiquitous modulation source) usually have fixed wave shape, envelopes provide continuously variable shape control.
The envelope's shape is organized into internal segments called stages; there are multiple types of stages that imply their function relative to the initiating event (e.g. keypress) and the terminating event (e.g. key release). Traditionally, envelopes have fairly simple shapes—two, three, four, and five stages are relatively common. However, things don't have to be this simple.
Plenty of instrument designers throughout the ages have devised ways to create complex, nuanced shapes in order to make sounds that transcend the sonic limitations of two or three stages, and means of control that transcend the keyboard as an event initiator. As with many of the "weird" concepts in synthesis, these ideas can be traced many decades back.
Buchla & the Looping Function Generator
Thus, we revisit the work of Don Buchla. While the 180 Dual Attack Generator has its own remarkable features and charm (again, discussed in Learning Synthesis: Envelopes Part 1), some of its shortcoming were addressed in the later 200-series envelopes: most notably in the 280 and 281. The 280 (a relatively simple envelope with AD/AR modes) added a pulse output to the envelope: a pulse signal that went high as soon as the envelope was completed. By including this output, more complex envelope arrangements could be created—events could be made to coincide with the endings of previous events, and envelopes could be cascaded to create multiple attacks and decays in succession. Moreover, an envelope's pulse output could be connected back into its own pulse input—in the AD "Transient" mode, this causes the envelope to cycle indefinitely, much like an LFO with continuously variable waveshape. This behavior is often referred to as looping or self-cycling. This type of envelope can also be found in the Model 212 Dodecamodule, as well as the 284, a slightly more complex version of the 280.
The Model 281 Quad Function Generator, perhaps the best-known 200 Series envelope generator, added voltage control to the attack and decay times, allowing for any CV source to modify the duration of these stages during performance. The 281 also features a psuedo-quadrature mode and adjustable "analog OR" outputs for each pair of envelopes, allowing the continuous splicing together of two signals to create complex, evolving shapes. (A similar feature is available in Make Noise's Maths—with careful adjustment of channels one and four, Maths and the 281 can be made to behave like a standard ADSR.)
The power of this type of envelope becomes apparent in the Krell Muzak patch, a now-famous generative patch created by composer and Buchla performer Todd Barton in 2012. In the original Krell patch, Barton used a modern Buchla 200e system to create a simple, single-voice generative design that produces uncannily musical variations in pitch, timbre, and articulation—all driven by a single cycling envelope generator. See below for a basic patch breakdown.
At its core, the Krell patch is about using a cycling envelope generator to trigger the creation of multiple random voltages, which each control some other aspect of the sound: perhaps most critically, the envelope attack and decay times themselves. This yields a sound where every note has a different duration and different style of articulation—sometimes slowly evolving, sometimes quickly articulated, and everything between. This patch can be adapted by routing the random voltages and envelope output to any number of destinations; the core of its character, though, is the simple internal structure of a looping envelope randomizing its own attack and decay times.
Buchla & the Arbitrary Function Generator
Perhaps not best-known, but certainly most impressive of the 200-Series envelope generators is the 248 Multiple Arbitrary Function Generator—the MArF. The MArF can serve a ton of basic synthesis functions, and is exemplary of Buchla's concepts of programmable multifunction control.
The MArF is something of a hybrid between an envelope, a step sequencer, and a quantizer...and perhaps was a module that 1970s technology was not quite ready to handle (original MArFs are quite rare, and a bit notoriously bug-laden). The concept, however, is brilliant: a bank of individually tunable stages which can be advanced through in order or selected by an external CV source. It was used to create complex envelope shapes and sequences, and became a cornerstone of the performance techniques of artists such as Suzanne Ciani (who has recently returned to performing with Buchla synthesizers, including a modern clone of the MArF).
The Verbos Electronics Voltage Multistage a complex function generator directly inspired by the MArF. Extensively acquainted with Buchla's designs, Mark Verbos boiled down many of the MArF's concepts into a considerably more affordable and reliable form. While Voltage Multistage seems to most commonly be used in a sequencer-like role, it can easily act as an envelope: to create an eight-stage envelope, for instance, patch the eighth stage's gate output into the sequencer "stop" gate input, and then patch an external trigger into the "start" gate input. The A & B outputs will produce eight sequential voltages, tuned by their respective rows of sliders. Using the switches above the sliders, one can choose whether the transition between each individual stage is stepped or sloped ("slide"), creating envelopes that feature a mix of abrupt and contoured voltage changes—a feat not possible with a typical ADSR, for instance.
Adding to this trick—in this context, the "Time" knob, which more commonly acts as a control for the rate of a sequence, becomes a control for the overall timescale of the envelope, with short envelopes to the left and longer envelopes to the right. By sending a control voltage into the Time CV input, the envelope's general shape can be retained while automatically altering the timescale (this could be a cool place to send a keyboard's velocity CV, for instance—so that harder keypresses yield shorter envelopes, for instance). Furthermore, one could patch CV B's output into the Time CV input—creating an envelope with arbitrarily definable duration for each stage. Combined with the various other analog and gate inputs, extremely complex function generation becomes easily accessible...hence the original designator: Arbitrary Function Generator.
Buchla's envelope concepts only became more intense and powerful as time went on: after the birth of the 200 Series, he went onward to develop the digitally-controlled 500 Series and 300 Series systems, which allowed for computer specification of arbitrarily complex Voltage Functions, not unlike the MArF itself. The 364 Multiple Arbitrary Function Generator was a software/hardware hybrid which enabled these Voltage Functions to be sent to 48 output jacks built into small patch bays between rows of modules (and had an additional 16 internal connections that could be sent directly to up to four 259 complex oscillators—specifically to their Frequency, Mod Index, Pitch, and Timbre parameters). Each stage offered independently definable timebase (from 0 to 65 seconds), interpolation, voltage level, and "Control Commands" (which allowed complex behaviors including conditional sustaining, stopping, or jumping to new stages altogether).These same types of arbitrarily definable function generators remained in the largely digital Buchla 400 and 700 Series instruments as well, though they certainly became easier to program as time went on.
Buchla was historically known for producing instruments that were well ahead of their time—but the increasing interest in his designs, including an enormous array of Eurorack-inspired incarnations of some of his concepts, is a testament to his brilliance. Perhaps soon we will see more instruments that go beyond the ideas of the 200 Series and into the weird, hardly explored realm of his later instruments.
Serge & the Slew
A discussion of complex envelope generation is not complete without mentioning Serge Tcherepnin, whose own ideas about control voltage generation have developed into their own ubiquitous paradigms for modular synth control. Serge along with Buchla formed the backbone of what for decades has been referred to as West Coast synthesis. The details of the West Coast/East Coast metaphor are perhaps best discussed in another post, but for our current purposes, it is safe to say that those designs often classified as "West Coast" are those that intentionally leave the means of sonic organization very open-ended, and not strictly beholden to traditional musical concepts.
Having met composer Morton Subotnick (a close collaborator of Don Buchla's) in New York in the late 1960s, Serge was invited to work and teach at the California Institute of the Arts, at which Subotnick was spearheading an experimental music program in the early 1970s. When at CalArts, Serge developed what at the time was called The People's Synthesizer—a modular synthesizer platform that could be assembled from relatively affordable kits. Not only was it affordable—it also made no extensive suppositions about its intended musical use, making for an extremely open-ended musicmaking experience. According to Serge, many of his ideas were borne from observing the schematics and inner workings of Buchla's designs; where Buchla might choose only to surface specific points of a circuit to serve his own conception of its purpose, Serge took notice of even more interesting nodes hiding beneath the surface. This type of thinking evolved into what in many ways characterizes the overall Serge approach: simple, elemental modules whose behaviors can be modified extensively by changing how they are patched, often via the surfacing of parts of a circuit without an obvious musical purpose. This concept is called patch programmability, and again is worth much more in-depth discussion than we can afford here.
Serge modules for a good while did not feature any modules that directly resembled a traditional envelope. This is not to say that the Serge system did not have dedicated "envelope" modules—only to say that those modules labelled "Envelope Generator" were anything but typical. The early 1970s model Envelope Generator provided very Buchla-like functionality: rise and fall time controls, the ability to self-cycle, CV input for envelope duration, etc. A dedicated Keyboard Envelope Generator also emerged, with more typical ADSR-style behavior.
Serge's systems can create envelope-like functions in a number of other ways, though—usually based around the sheer power of slew generators. A Slew Generator—also commonly referred to as a slew rate limiter, lag processor, slope generator, and a host of other names—is a circuit intended to introduce sloped curves to voltages with hard, sudden jumps in value...essentially acting as a smoothing function for stepped voltages. A slew generator usually has a control for slew rate: the amount of time it takes for the module's output to "catch up" to its new input value. One could also think of this as a "glide time" setting...in fact, slew generators are how portamento is implemented in analog synthesizers: in that scenario, they apply a lag between the keyboard's output and the oscillators' CV inputs.
Some of the earliest Serge slew generators included the Positive Slew and Negative Slew—modules which would only apply smoothing to voltages moving upward or downward, respectively. To slew voltages in both directions, one would run the two modules in series, thereby earning independent rising and falling slew times. In a later generation of modules, Serge introduced the now famous Dual Universal Slope Generator: perhaps one of the most powerful analog modules to date.
The Serge Dual Universal Slope Generator
The Dual Universal Slope Generator (DUSG) is in some ways similar to a Positive Slew and Negative Slew connected in series, albeit with a more succinct set of controls. With its combination of features, it can perform an almost paralyzing number of distinct functions: it can act as an envelope, oscillator, LFO, envelope follower, filter/waveshaper, subharmonic generator, track & hold...and probably far more than we could ever realize. In its use as an envelope, it can easily produce AD and AR shapes—and because of its extensive utility, it has arguably become the most popular and ubiquitous Serge envelope option, its popularity extending well beyond the legacy of the Envelope Generator or Positive and Negative Slew modules.
As an AD envelope, the DUSG is quite simple: it offers a trigger input for beginning the function, with Rise and Fall time controls acting as Attack and Decay controls, respectively. The DUSG can be made to loop—originally, this behavior was achieved much as in Buchla's 280 and 212, by patching the gate output into the trigger input (a characteristic shared by many of Serge's other modules as well, such as the Positive Slew, Negative Slew, and SSG).
As an AR envelope, the DUSG's inner nature more immediately reveals itself—and the power of slewing functions becomes more apparent. By patching a gate into the DUSG's Signal input rather than its Trigger input, one can apply variable amounts of slew to the gate's rising and falling edges. This simple patch provides perfect AR behavior: Attack time is defined by the Rise parameter; the envelope Sustains for as long as the incoming gate is held high; and the envelope Releases to zero at a rate defined by the Fall parameter (see the diagram to the side for illustrated details of this process). Of course, behaviors similar to Buchla's MArF are also possible using a combination of modules: complex multistage envelopes, for instance, could be yielded with a combination of the TKB (Serge's keyboard/sequencer), a DUSG, and a Bidirectional Router module. Perhaps we'll dig more deeply into these modules' potential in a future article...
In any case, the DUSG's sheer versatility exemplifies much of the magic of the Serge ideal of patch programmability. As such, it has inspired countless spinoffs and variations in Eurorack format—Make Noise's Maths and Befaco's Rampage, for instance, are directly inspired by the DUSG. And of course, Random*Source produces an updated, licensed version of the DUSG in both 4U and Eurorack formats, providing an authentic 21st century take on all of the insane things a slope generator can do.
DUSG-Inspired Eurorack Modules
Complex Envelope Concepts: Digital Synths in the 1980s
Analog synthesizers in the early and mid 1970s for the most part utilized envelopes like those we have discussed so far: mostly AD, AR, ADSR, and minor variations were available, with only rare exceptions (such as Buchla's MArF, for instance). As the 1970s continued, though, more manufacturers began to implement digital control—and by the 1980s, of course, fully digital synthesizers were the norm. And while the most commonly discussed implications of digital control often pertain to sound generation, digital technologies also had a profound impact on synthesizers' internal means of control.
Envelopes got weird in the 1980s. More and more synthesizers embraced the concept of multi-stage envelopes, each in their own quirky way. Some of my favorite examples of novel envelopes in 1980s synths include the envelopes in the Sequential Circuits Prophet VS, the Casio CZ-101, and the Technos Acxel. I have already written slightly deeper overviews of the Prophet VS and Acxel, so feel free to check those out; but it's definitely worth revisiting their envelopes here.
Envelopes in the Prophet VS
Released c. 1986, the Sequential Circuits Prophet VS was the first synthesizer to employ Vector Synthesis—a concept imagined by Chris Meyer in which four different oscillators (or four different waveshapes) could be interpolated between by conceptualizing the individual shapes as corners in a two-dimensional space. This differs from wavetable synthesis in which tables are directly interpolated or switched between, providing a much smoother way of mixing and crossfading between multiple base timbres. The VS allows the user to navigate this timbre-space in a handful of ways—perhaps most iconically via the joystick. It also allowed for X and Y axis modulation independently via LFOs and other modulation sources.
One of the most interesting (and most overlooked) parts of the Prophet VS is the envelope section. Inspired in part by the aforementioned Buchla 400's remarkably complex envelopes, the Prophet VS was built with the knowledge that a simple ADSR would not be sufficient for addressing the timbral possibilities that vector synthesis provided. Instead, the designers opted to create an envelope that would allow access to more variegated modulation scenarios, providing considerably more interesting options for a sound's internal animation. For a while, Sequential Circuits considered licensing the technology/concept behind the Buchla 400's envelopes, but for one reason or another that didn't work out. Nonetheless, they came up with their own fascinating design, which strikes a favorable balance between complexity and approachability.
The Prophet VS provides three complex envelopes per voice, which respectively control the Waveform Mix, Filter, and Amplifier. Each envelope features five stages, with a number of ways of advancing through the stages as a key is held. The first four envelope points offer level controls, and the last four additionally provide rate controls—making it such that each stage can be set to start at any desired level, with any desired duration. The truly fascinating thing, though, is the looping behavior—once the envelope reaches point 3, it can be made to loop back to any previous point as long as the key is held. The looping can be unidirectional or bidirectional, as well...making for the potential to create modulations that traverse back and forth along the specified envelope shape, or that simply repeat themselves over and over. This means a ton of crazy shapes are available, all with a fairly simple means of programming and conceptualizing the shape.
Programming the Waveform Mix envelope is particularly special. Since the Waveform Mix is a two-dimensional parameter, it is not easily editable with a single data entry slider: and that is part of the magic of the Joystick. When defining each "point" in the envelope, the user needs only to move the joystick to the desired position to create a set of coordinates, automatically creating movement along two axes without independent editing of two envelopes. It's pretty clever, and works perfectly for the synthesis scheme it is meant to accompany.
Envelopes in the CZ-101
Casio's CZ series synthesizers boasted an (at the time) new synthesis method called Phase Distortion. In the heyday of Yamaha's DX Series and patented Frequency Modulation technology, Phase Distortion was intended to provide an alternative means of creating FM-like timbres. It additionally sought to offer classic analog-like tones without the use of analog tech, with convincing means of creating sounds not unlike sweeping resonant filters. Like many of the 1980s synths meant to explore new sonic techniques, new modulation structures seemed necessary: so Casio implemented 8-step envelopes into their instruments.
In the CZ-101, the oscillators, waveshape, and amplitude each feature their own independent envelopes with up to eight steps each. Users could define envelope shapes by specifying a Level and Rate for each point, much like in the Prophet VS: the Level corresponding to the envelope's level at the end of each segment, and the Rate corresponding to the speed at which the next point is reached (which can also be conceptualized as the segment's overall slope). Additionally, any point can be specified as the Sustain point—the point at which the envelope is held until the triggering key is released. This allowed the creation of everything from simple envelope shapes to more complex contours, including sounds that seem to have multiple attacks as they advance.
Having this type of envelope available for three parameters simultaneously meant the potential for remarkably complex sounds—even sounds that contain multiple internal silences, and sounds that take on their own strange, animated life only once the key is released. It's a very strange type of envelope, but one that became more and more common as the 1980s advanced. By this point it should be clear that an envelope can really have any number of stages, which can be advanced through in any order. Some instruments took this further than others, though...
Envelopes in the Acxel
The Technos Acxel must be one of the most peculiar synthesizers ever made. The Acxel for the most part eschews traditional subtractive synthesis concepts, instead focusing on making a streamlined user interface suitable for complex additive synthesis and resynthesis. Like something straight out of Star Trek, the Acxel's editing interface (the Grapher) features a matrix of over 2000 LED-embedded touchplates, which a user can employ to "draw" the various settings they might desire: the tuning of oscillators, waveshapes, filter curves, and more.
The Acxel's envelopes take the above ideas to the extreme. The Acxel features well over one hundred user-definable envelopes per voice, each dedicated to its own specific parameter. Some envelopes affect the voice on a global level (for control of voice volume, FM amount, filter frequency, etc.), but the majority operate on more low-level functions internal to the voice: the pitch and amplitude of the 32 oscillators that comprise each voice. One could edit tons of envelopes simultaneously, or could define distinct shapes for each envelope, providing a staggering number of options for sound design.
Each envelope is a 64-point graph defined by dragging one's finger along the matrix display. This allows the creation of envelope shapes with any arbitrary amount of complexity—one could even meticulously tune each stage of a pitch envelope, for instance, to create specific sequence-like melodies and counterpoints (yes, this is actually doable!). A hold stage can be defined anywhere along the envelope by tapping the Alphaline (the line of Alphabetical keys above the matrix display). One can even define a specific region of the envelope to loop as long as a key is held, much like in the Prophet VS above...but with way more stages, and way more options for how complex an envelope can be. Total envelope duration can extend up to over 30 seconds, allowing ample time for these sonic complexities to unfold.
I've personally found that the Acxel is best suited to long, textural sounds in which you have a lot of time to appreciate internal motion. But these absurdly powerful envelopes can serve a more practical function, much more in line with one of the Acxel's primary intended uses: resynthesis. The Acxel is capable of analyzing short segments of recorded audio (up to four seconds long) and determining which of a sound's overtones are most present, how their pitch changes over time, and how their loudness changes over time. After determining a sound's most pertinent characteristics, it builds a set of pitch information and envelopes, which it assigns to its internal synthesis engine in order to recreate the sound from scratch. This can reproduce a sounds of startling complexity, largely because of just how sophisticated the envelopes are—because of having so many stages, they can create sounds with striking levels of nuance.
Every type of envelope has its place—and as such, every type of envelope has persisted. Many keyboard synths stick to the classic shapes (AD, AR, ADSR, etc.), while some digital synths and Eurorack modules continue to push the boundaries of exactly what an envelope can be. Hopefully by this point, the blurry nature of what constitutes and "envelope" has become apparent: sometimes it is as simple as an attack/decay slope, but sometimes it is an arbitrary group of segments that can occur in any order and be re-arranged over time. Envelopes can impact pitch, timbre, loudness, and more. In the end, perhaps an envelope is simply any user-shapeable trajectory along which the details of a sound unfold. Some modern envelopes that warrant mentioning follow:
The ALM Busy Circuits Quaid Megaslope is a complex function generator that feels not unlike a combination of the MArF and the multi-segment envelopes of the 1980s. Quaid Megaslope has five independent stages, each of which have their own controls for level, duration, and slope. The slope control allows for everything from logarithmic to linear and exponential interpolation between stages—the transitions between individual stages can be very sudden or gradually interpolated. Stages can be advanced in traditional envelope fashion (using an incoming gate to trigger the envelope's beginning, and to determine how long the sustain stage should be held), in a constant loop, or sequentially according to an incoming trigger. Any stage can be the sustain stage (or the loop point, in looping or step modes). And the Megaslope also offers CV inputs for level and time on each stage...meaning that the envelope's shape and duration can undergo significant change by using even just a couple of external CV sources.
The Mutable Instruments Stages covers similar ground as the Megaslope, and at first glance has a very similar user interface. However, Stages is a fairly different module that lends itself to different uses—in fact, Stages can perform most basic synthesizer functions with the right combination of settings and patching. Mutable calls Stages a "segment generator," and indeed it is: it allows users to chain together individual segments to create wide ranges of behaviors from traditional envelopes and sequencing to LFOs and even audio oscillation. Each "stage" can be an envelope-like slope, a static voltage, or a sequence-like step; each stage can additional have its own timebase, and offers a direct CV input whose function changes depending on which stage type is selected. The most interesting idea at work in stages is that the individual stages can be broken apart from one another to act with various degrees of independence: by using the gate inputs and per-stage outputs, one can separate the stages into small groups that work together. Individual stages can even be completely isolated—meaning that Stages could act as six independent oscillators, or a couple of envelopes simultaneously, or a couple of oscillators and a sequencer, or...basically any combination! Furthermore, multiple Stages can be chained together to create even longer sequences/envelopes/etc.—making for a dizzying number of options for creating complex curves and sequences.
The Xaoc Devices Zadar is yet another incredible Eurorack envelope. Zadar uses preset vector-based envelope shapes up to 1000 breakpoints long, which can extend all the way from less than a millisecond to half an hour in length. While there is no facility for directly editing the individual breakpoints, Zadar includes an enormous number of preset shapes (270 as of firmware version 2.0!). CV input can be assigned to envelope shape, time, "temporal warp," amplitude, number of repeats, and much more—basically, despite not having access to directly edit shape, Zadar provides an absurd range of options for modulation shapes, and is one of the most powerful envelopes currently available. Oh, and Zadar is a quad envelope generator—meaning four insane modulation sources all in one module.
And of course, a survey of powerful Eurorack envelope generators would not be complete without mention of Rossum's Control Forge—perhaps the most intense on this list. In fact, Rossum does not even directly call the Control Forge an envelope, but a Programmable Universal CV Generator...because, as we've seen, the line between what constitutes an "envelope" and any other type of control voltage source is a bit blurry, and the term "envelope" might be a bit reductive in this case. Like some of the other envelopes we've seen (CZ-101, for instance), the Control Forge is an eight-segment function generator with a definable target voltage and duration for each stage. This can make for traditional one-shot envelopes, for vastly long, evolving LFO-like modulations, and much more. Stage levels can be quantized and randomized, and duration may be modulated via CV or adjusted manually. The transition from stage to stage take on any of 67 preset transition shapes from traditional linear or exponential curves to considerably more complex and chaotic trajectories.
Control Forge becomes more interesting when examining its similarities to some of its more Buchla-like concepts. Like in the Buchla 300, envelope stages can allow for conditional jumps to other targeted stages: for instance, the presence of a gate at the Logic input can determine whether an envelope advances directly or to a different targeted stage. Similar conditions can be created using incoming control voltages. And what's more, multiple presets can be chained together to form preset sequences—allowing an already astounding set of modulation options to expand into incomprehensible territory.
Complex Envelope Modules
The concept of an envelope is mutable. They are present in almost every synthesizer, and can take any number of shapes from simple to complex. They are not always as straightforward as other modulation sources (like LFOs, for instance), and so we felt they were deserving of a deeper dive: an exploration into the various ways that manufacturers throughout the ages have applied their own inventive ideas to this basic synthesis concept. In the end, envelopes are all about creating motion through the defining of contours over time—sonic shapes that evolve along user-defined trajectories. In the end, one type of envelope is not necessarily any better than another. As with all things in synthesis, different musical approaches favor different tools, and where one user might favor the articulations afforded by a standard ADSR, another may find inspiration in the twisting paths forged by an arbitrary function generator.
There are no doubt even more modules and instruments with other peculiar approaches to envelope design and use. Hopefully this article has helped to clarify some of the many ways an envelope can take shape—or at least to make it clear that there is no real limitation to what an envelope can be like, or how it can be used. Whether used to create articulation, or to animate timbre, or to create sequence-like melodic materials, envelopes are simultaneously one of the most fundamental and one of the most interesting and powerful tools in a synthesist's toolkit.