Buchla 200e

The Buchla 200e is a modular analog synthesizer designed by electronic music pioneer Don Buchla and built by Buchla and Associates.

Modules

200e synthesizer platform includes several modules that roughly correspond to the canonical analog synthesizer's ones:
* Voltage-controlled oscillator: [http://www.buchla.com/200e/259e.html 259e] , [http://www.buchla.com/200e/260e.html 260e] , [http://www.buchla.com/200e/261e.html 261e]
* Voltage-controlled filter: [http://www.buchla.com/200e/291e.html 291e] , [http://www.buchla.com/200e/292e.html 292e] , [http://www.buchla.com/200e/297.html 297]
* Voltage-controlled amplifier: [http://www.buchla.com/200e/227e.html 227e] , [http://www.buchla.com/200e/292e.html 292e]
* Envelope generator: [http://www.buchla.com/200e/222e.html 222e] , [http://www.buchla.com/200e/225e.html 225e] , [http://www.buchla.com/200e/249e.html 249e] , [http://www.buchla.com/200e/250e.html 250e] , [http://www.buchla.com/200e/266e.html 266e] , [http://www.buchla.com/200e/281e.html 281e]
* Low frequency oscillator: [http://www.buchla.com/200e/259e.html 259e] , [http://www.buchla.com/200e/261e.html 261e] , [http://www.buchla.com/200e/266e.html 266e] , [http://www.buchla.com/200e/281e.html 281e]
* Ring modulator: ???
* Sequencer: [http://www.buchla.com/200e/249e.html 249e] , [http://www.buchla.com/200e/250e.html 250e] , [http://www.buchla.com/200e/266e.html 266e]
* Mixer: [http://www.buchla.com/200e/210e.html 210e] , [http://www.buchla.com/200e/227e.html 227e]

But the Buchla 200e modules were not designed to fit perfectly into these categories. Rather, each module implements and crosses category boundaries according to Buchla's vision of analog synthesis. The synthesizer sound basics entry offers a helpful introduction to understanding how to compose sound. With that as background, there are two ways to think about making sounds with the 200e: the electronic view and the sonic view.
* The electronic view represents three networks: the audio network (which results in the ultimate audio signal that is actually heard), the continuous control voltage network (where voltages ranging from zero to 10 volts DC represent the full scale of all parametric values), and the pulse network (which conveys transient and sustain information).
* The sonic view is that sound is perceived as having a characteristic pitch (or not in the case of noise), a characteristic timbre, and a characteristic sound that notes have when played and released. This view can be represented as a sonic pipeline that starts with an oscillator (or noise) feeding a filter (timbre) contained in an envelope (attack, decay, sustain, and release or ADSR).

Taken together, the electronic view allows us to explore the sonic properties of networks we can construct with the hardware available, while the sonic view helps us focus on how to make the electronic connections necessary to realise a sound we have heard only in our minds.

Creating audio tones

Since both views begin with an oscillator, we will begin with a description of the primary modules for generating an initial pitch and timbre, the [http://www.buchla.com/200e/259e.html 259e] and the [http://www.buchla.com/200e/261e.html 261e] Complex Waveform Generator. Both the 259e and the 261e have two oscillators: a modulation oscillator and a principal oscillator (aka a carrier wave). The 259e can produce two distinct audio signals (one from each type of oscillator), while the 261e can also produce a pre-processed signal in each oscillator. The pre-processed signal of the 261e modulation oscillator is presented as a sine wave (i.e., before being shaped by the variable wave shaper), whereas the pre-processed signal from the 261e principal oscillator is presented after LFO modulation but before timbral modulation. Thus the 261e can generate a total of four distinct audio signals.

As a control voltage, pitch on the 200e is represented as 1.2 V/octave (0.1 V/semitone). Since the 200e was designed to maintain 0.01 V accuracy, it means that tuning is within 10 cents. If we assume that 440 Hz/A5 is 5 V (the center of the 10 V control voltage scale), then the pitch control knob ranges from 27.5 Hz/A1 through 7040 Hz/A9 (see piano key frequencies) and voltages are as follows
* A1 is 5 V - 4.8 V = 0.2 V
* A2 is 5 V - 3.6 V = 1.4 V
* A3 is 5 V - 2.4 V = 2.6 V
* A4 is 5 V - 1.2 V = 3.8 V
* A5 is 5 V
* A6 is 5 V + 1.2 V = 6.2 V
* A7 is 5 V + 2.4 V = 7.4 V
* A8 is 5 V + 3.6 V = 8.6 V
* A9 is 5 V + 4.8 V = 9.8 V

There are two basic ways to control audio oscillator pitch for each oscillator, and there are differing rules for what works in what mode, but the math works something like this:

259e: $V\_\{main\; osc\; pitch\}\; =\; V\_\{MIDI\; note\}\; +\; CV\_\{main\; osc\; in\}\; *\; CV\_\{main\; osc\; scale\}$

259e: $V\_\{mod\; osc\; pitch\}\; =\; V\_\{main\; osc\; pitch\}\; +\; V\_\{mod\; osc\; freq\}$

261e: $V\_\{main\; osc\; pitch\}\; =\; V\_\{MIDI\; note\}\; +\; CV\_\{main\; osc\; in\}\; *\; CV\_\{main\; osc\; scale\}$

261e: $V\_\{mod\; osc\; pitch\}\; =\; V\_\{main\; osc\; pitch\}\; +\; V\_\{mod\; osc\; freq\}\; +\; CV\_\{mod\; osc\; in\; *\; mod\; osc\; scale\}$

and if pitch tracking (and remote enable) is off, then each oscillator of both modules implement

$V\_\{pitch\}\; =\; V\_\{freq\}\; +\; CV\_\{in\}\; *\; CV\_\{scale\}$

By feeding MIDI pitch into the control voltage inputs it is possible to scale tuning from essentially flat (increases in MIDI pitch voltage are exactly offset by increased negative scaling of the control voltage) to 2 semitones per semitone of MIDI pitch. And with the 256e voltage control processor, additional stretch tunings can be achieved.

Pitch need not be constant, as the vibrato entry teaches. The vibrato effect can be realized by modulating the principal oscillator with a low-frequency oscillator. The modulation oscillator of both the 259e and the 261e can be set between a range of 1/4 Hz and 64 Hz and both modules support an internal connection whereby the modulation oscillator can modulate the pitch of the principal operator by selecting the "pitch" MOD TYPE with no external cables are needed. But other LFO sources may be employed. See the Extra-Low LFO using the 281e section for information on constructing other LFOs.

Pitch need also not also be constant as the portamento entry teaches. It would be wonderful if portamento were an intrinsic function of the 225e MIDI controller, not least because it would have the benefit of stable and reliable pitch. See the Portamento using the 266e and 256e entry in the Neat tricks section for details on how to work around this apparent limitation.

Creating initial timbre

259e Programmable Complex Waveform Generator

Once pitch has been established, timbre is next. The modulation oscillator of the 259e offers three baisc wave shapes: falling sawtooth, square, and triangle. As audio signals (the "hi" range of the modulation oscillator), these shapes have the timbre of a bowed violin string (sawtooth), a classic synth lead (square), and a woodwind instrument such as a clarinet (triangle).

The principal oscillator of the 259e offers far more variety: a sine wave is used to drive two digital wave tables, which are called "red" and "green". The "morph" voltage pans between the two tables and the "warp" voltage controls the amplitude of the sine wave that drives the tables. (In [http://www.keyboardmag.com/story.asp?sectioncode=30&storycode=11606 Keyboard Magazine] Jim Aikin's review of the 200e claims that warp produces higher overtones by sweeping more of the digital wavetable.) In both the red and the green tables, the first wave table is a simple sine wave (meaning that what goes in is what comes out, and that increasing the amplitude of the driving wave merely increases the amplitude of the resulting output wave). But waves 2 through 8 are different between red and green, and each one offers a palette of unique timbres. Moreover, it appears that the higher the warp factor the more high harmonic content is present in the resulting waveform. TODO: build a table of screenshots using xoscope images. TODO: Identify which Buchla wave sequence looks like the Shaper sequence of the K2600. Who is copying whom?

Because the 259e uses digital wave tables, the output waves exhibit aliasing when used at frequencies above their nominal frequency. Aliasing artifacts are quite audible above 440 Hz in both the modulation and the principal oscillators, hence the 259e is likely best used for bass and low melody notes unless aliasing is a desirable feature of the timbre. (Trent Resnor's "dirty" sound on the Nine Inch Nails CD Pretty Hate Machine could be an example of "desirable" aliasing.) Another source of aliasing can come from the way the oscillators are synchronized. When synchronized to MIDI note events, the oscillator waveform resets to its initial state when a note on event is received. If the waveform was near the peak of its amplitude when the note on event arrives, one may hear an audible "click" as the waveform resets to zero. (Such momentary aliasing can be eliminated by running the signal through an envelope with a non-zero attack value.) Similarly, if the modulation oscillator is synchronized to the principal oscillator using "hard sync", then every time the principal oscillator completes a full wave cycle, the modulation oscillator is reset, regardless of where it was in its wave cycle. The aliasing caused by hard sync is periodic as opposed to momentary, hence it really affects timbre (usually making it sound hard or edgy). The "soft sync" option uses a phase-locked loop to bring the modulation oscillator into step with the principal oscillator without an abrupt discontinuity (or audible aliasing). The point is: among other factors, timbre is affected by aliasing effects. Caveat approximator,.

The 259e has a special internal connection between the modulation oscillator and the principal oscillator. This connection is established by selecting one or more MOD TYPE connections and then adjusting the MODULATION INDEX (which seems to be another way of saying modulation amplitude). When the MOD TYPE is "freq" and the modulation oscillator runs in the audio range, the 259e acts as a dual operator FM synthesizer, albeit a very non-standard FM synthesizer. FM Synthesis is achieved by modulating the frequency of a carrier signal with a modulation signal that is harmonically related to it (usually the 1st, 2nd, or some other Nth harmonic). Sine waves present the most simple case: sine waves are fundamental tones, so the harmonic relationship between the two waves is precisely the relationship between the two fundamentals. A sawtooth, square, or triangle wave consists of a rich set of harmonics, which means that even if there is a simple harmonic relationship between the fundamental of a sawtooth modulator and a sinusoidal carrier wave, the relationship of all the other harmonics gets complicated very quickly. If the carrier wave is also a complex wave, the result is going to be "complex". Technically the 259e is capable of FM synthesis, but it is not capable of the most basic form of FM synthesis: a sine wave carrier modulated by a harmonically related sine wave. I concur with Jim Aikin that the FM synthesis using the 259e may be suitable for brash effects, but not mellow, bell-like tones.

The 259e is no longer on Buchla and Associate's list of currently available modules (2007).

261e Complex Waveform Generator

At this point we introduce the 261e, the other Complex Waveform Generator in the 200e line. The 261e modulation oscillator can generate a sine wave, and the 261e principal oscillator can also generate a sine wave, so that simple, "classic" FM synthesis can be accomplished using the 261e. (Indeed, when connecting the modulation and principal oscillators using the internal modulation bus, "only" the pre-processed sine wave is used regardless of the modulation oscillators wave shaping parameter.) And the 261e is 100% analog across its whole range, which eliminates a major source of aliasing that the 259e can produce. And the controls are a bit more intuitive, since all selections are based on a continuum of descriptive elements (rather than the obscure nature of "green 3" or "red 4" and the equally mysterious effect of warp on each). Indeed, by using the internal connection between the modulation oscillator and the principal oscillator, it is quite easy to dial up familiar FM tones from mellow to brassy. That's the good news.

The bad news is that it is not obvious how to get similarly good-sounding results by routing the modulation oscillator output signal into the "fm in" signal input of the 261e (or the 259e for that matter). Instead of a pleasing FM tone, the sound gets really grainy as soon as the knob related to the "fm in" input is moved beyond its zero position. This is very unfortunate, because if this worked as expected, one could build some complex, but controlled, FM operators. I have found one work-around which suggests an error in design and/or implementation: by attenuating the modulation output (which can be accomplished by routing it through a 210e Control and Signal Router attenuating the connection a few clicks below unity), results are more in line with expectations. For now, absent any other information or known work-arounds, the best way to do conventional and controlled FM is to use the internal connections, which means that two-operator FM synthesis is the order of the day.

Another source of confusion for me is why, when applying audio-rate frequency modulation to the principal oscillator, the pitch appears to go sharp or flat. I'd expect the pitch to remain stable and only the timbre to change.

In any case, the principal oscillator of the 261e has three timbre-shaping parameters which are voltage controlled:
* Timbre, which generates rich, analog overtones
* High Order, which seems to control something like a high-pass filter
* Symmetry, which seems to asymmetrically drive up the rising edges of the wave without affecting the falling edges. When Symmetry is applied turned up on a sine wave, it becomes a sawtooth wave.

260e Duophonic Pitch Class Generator

The 260e generates its tones at all octaves, thus an "A" on the 260e generates sine waves at 27.5 Hz (A1), 55 Hz (A2), 110 Hz (A3), 220 Hz (A4), 440 Hz (A5), 880 Hz (A6), 1760 Hz (A7), 3520 Hz (A8), and 7040 Hz (A9). The timbre of such a tone sounds very much like a pipe organ with all ranks open.

The 260e has a "barber pole" mode in which an internal computer controls both pitch class generators. One parameter controls how rapidly the pitch changes (+/- 2.5 octaves/sec) and the other controls the number of steps per octave (from 2 to 24; 2 steps per octave are tri-tones; 12 steps per octave is the familiar semitone scale; 24 steps per octave are quarter-tones). A mode setting controls whether the steps are continuous (portamento), quantized (ordered), or eccentric (randomly ordered).

The 260e can also be used to generate Shepard tones which are best heard when wrapped in a staccato or marcato envelope. Such envelopes can be created using the 281e and 292e modules as illustrated below.

266e Source of Uncertainty

The 266e generates white, pink, and blue noise--not a very controlled oscilator, but it is a generative source of an audio signal, albeit one without a pitch, so we introduce it here, though we will treat it in more detail elsewhere. Noise can be pitched by feeding it through one or more narrow band-pass filters.

Creating envelopes

With the basics of how to establish initial pitch and timbre introduced, we can now look at forging our tones into notes. When using only the audio generators by themselves, we can make continuous tones that have some distinguishing characteristics. But without distinctive beginnings and endings, we cannot really call these tones notes; drones, perhaps, but not notes. To make notes we need to have beginnings and endings. This takes us to the opposite end of the audio production chain: the envelope.

281e Quad Function Generator

In his pioneering work, Vladimir Ussachevsky established the concept of an envelope comprised of Attack, Decay, Sustain, and Release (or ADSR). The 281e Quad Function Generator makes it possible to create a variety of envelope models. To create a classic ADSR with individual control over each component, two Function Generators can be coupled as follows:
* A Attack of X milliseconds (ms)
* D Decay of Y ms
* S Sustain level of Z%
* R Release of W ms

# Set the input mode of the A (resp. C) generator to single impulse.
# Set the input mode of the B (resp. D) generator to sustained impulse.
# Set the attack of both the A and B (resp. C and D) generators to X ms.
# Set the decay of the A (resp. C) generator to Y ms.
# Set the decay of the B (resp. D) generator to W ms.
# Wire the Pulse input of the A and B (resp. C and D) generators together.
# Set the OR output level for the A OR B (resp C OR D) to Z%.

The A OR B (resp. C OR D) output is the ADSR envelope function, and is driven by a pulse delivered to the A or B (resp. C or D) input.

For the special case where the sustain level equals the attack peak (such as a pipe organ, i.e., there's no decay between attack and sustain), the sustain input mode suffices directly and no complex hookup is needed.

Similarly, for the special case where there is no sustain, just attack and release (such as an acoustic guitar), the impulse input suffices directly.

The Quadrature Mode, generators A and B (resp. C and D) operate in tandem as follows:

# When a pulse is received, A (resp. C) transitions from low to high according to its Attack parameter
# At the end of A's (resp. C's) attack, B (resp. D) transitions from low to high according to its Attack parameter
# At the end of B's (resp. D's) attack, A (resp. C) transitions from high to low according to its Decay parameter
# At the end of A's (resp. C's) decay, B (resp. D) transitions from high to low according to its Decay parameter

One use of quadrature mode is to implement delayed attack and delayed release (with the A (resp. C) generator implementing the delay parameters and the B (resp. D) generator providing the delayed attack and delayed decay envelopes).

It is important to note that the Quad Function Generator operates solely on control voltages--they do not, themselves, alter the dynamics of an audio signal. To do this, the 292e Quad Dynamics Manager is needed. In its simplest mode as a VCA, this module controls the signal level of four separate audio signals (plus a mix of all four signals if that's useful) based on three separate control voltage parameters: a level parameter (such as the output of a Function Generator), an optional Velocity parameter (typically taken from the 225e MIDI Decoder), and a knob setting that can range from full off to full on (in which case the signal passes through unchanged). Thus, with three modules (or four if you want to decode MIDI notes into control voltage signals), one generating a tone, one generating an envelope, and one applying the envelope to the tone, we have the basics of an analog synthesizer than can play notes, albeit one at a time.

It should also be obvious that we can implement tremolo by feeding the output of an LFO into either the level or velocity input of one of the Quad Dynamics control voltage input. Since control voltages sum when banana plugs are combined, tremolo can be added to circuits that already have both level and velocity assigned without using an additional dynamics control circuit.

249e Dual Arbitrary Function Generator and 250e Arbitrary Function Generator

The 249e and 250e Arbitrary Function Generators can be used to create quite complex envelopes, with any combination of smooth and stepped stages, looping segments, etc. This may seem like overkill, but you would be hard pressed to find a more comprehensive envelope generator on any modular instrument.

The 249e is no longer on Buchla and Associate's list of currently available modules (2007).

Creating complex timbre using filters

Let us now return to timbre, something as intrinsic to audio tone as color is to light. We have already discussed using modules to create tones that have an "initial" timbre. And we have talked about carving notes from tones by using envelopes. We will now talk about carving "that sound" from timbre.

In the documentary film Moog (film), Robert Moog talks about one of the greatest influences of the synthesizer on modern music: the sound of "wow" (say it slowly, w-o-w). The sound of "wow" (or wah-wah) is perhaps the most cliched timbric modulation. It can be synthesized by applying a bandpass filter to a harmonically rich tone such as a sawtooth wave (sine waves need not apply!) and moving it from 200 Hz to 1000 Hz and back again. With the right filter parameters and the right envelopes driving the filters, we can perceive the production of a dynamic, shifting formant. This effect, which sounds almost linguistic, suddenly imparts a whole new dimension to the way we interpret the tone. Time-dependent filter modulation is what makes the guitar of Jimi Hendrix "open up" in the song Foxy Lady, or throb in the hands of Eric Clapton in the song Sunshine of Your Love.

291e Triple Morphing Filter

The 200e has two modules that filter audio signals: the 291e Triple Morphing Filter and the previously mentioned 292e Quad Dynamics Controller. The 291e provides three bandpass filters that can operate separately or in parallel. It also provides a summing input so that multiple 291e modules can be ganged together. Filter frequency, bandwidth, and level are each controllable via voltage. The module allows up to eight different filter "snapshots" to be defined (a mini-sequencer) which it can then "morph" over time. To achieve the rhythmic pattern of dotted-quarter/eighth note ("da-- di da-- di da--") at a 4/4 tempo of 100 bpm, two stages are needed in a loop. The duration of the first stage is 3/2 * 1 * 60 / 100 = 0.90 seconds and the duration of the second stage is 1/2 * 60 / 100 = 0.30 seconds. The morphing filter will then update the parameters from the values set in the first stage to the values set in the second stage and repeat. Transitional options allow the filter parameters to "jump" from one setting to the next, otherwise they transition smoothly ("morph") during the stage.

To make the transition smooth and still distinct, stages can be broken into two phases, a stable phase and a morphing phase. If we want the morph in the previous example to take place in the time of a 1/16th note, the four stages would be

# 0.90 - 0.15 seconds = 0.75 seconds
# 0.15 seconds
# 0.30 - 0.15 seconds = 0.15 seconds
# 0.15 seconds

The 291e also supports frequency modulation of each input which makes it possible to build both simple and complex FM operators. The fm circuit of the 291e is different than that of the 259e and 261e and less prone to aliasing. Combined with a 210e, the 291e supports the following FM algorithm constructs:
* M -> C This is the basic FM operator, where the ratio of M and C are simple integers, usually N:1, but can be whatever you choose. The 291e can provide three such operators.
* (M1 + M2) -> C A complex parallel FM operator (requires a 210e to sum the modulation signals). The 291e can provide three such operators.
* M1 -> M2 -> C A complex series of FM operators. This requires two 291e inputs.
* (M1 + M2) -> M3 -> C A more complex series of FM operators. This requires two 291e inputs.
* M1 -> (M2 + M3) -> C A more complex series of FM operators. This requires two 291e inputs.
* M1 -> M2 -> M3 -> C Requires all three 291e inputs. This basic algorithm has numerous variations as M1, M2, and M3 can each be summed (or not) with additional modulation inputs.

Thus a 291e can be a powerful FM workstation independent of its filtering abilities.

292e Quad Dynamics Manager

Bandpass filters are great for synthsizing formants, but two other filter types are also quite useful for creating "that sound" from a timbre: a low-pass filter and a high-pass filter. Consider the square wave which theoretically has an infinite number of only odd-order harmonics. If we want to "soften" the sound, we need to remove all the higher-order harmonics above whatever frequency we perceive as "harsh". For example, let's say that harmonics above 2.2 kHz are objectionable. For a square wave at A5, that's the 5th harmonic and above. For a square wave at A3, that's the 7th harmonic and above. For a square wave at A6, that's the 3rd harmonic and above. A low-pass filter can uniformly remove all offending high-frequency signals regardless of whether they are the 7th, 11th, or 13th harmonics, creating a greater consistency of tone than merely saying "let's just compose a wave consisting of the 1st, 3rd, and 5th harmonics", which gets it wrong for the higher registers.

The signal chain of the 292e Quad Dynamics Manager has a voltage-controlled low-pass filter that can operate in tandem with or instead of the VCA (aka gate). There appears to be no way to control the slope of the low-pass filter; it is fixed at 12db/octave. A popular enhancement to low-pass filters is resonance, which compensates (or overcompensates) for signal attenuation at the cutoff frequency. Since a resonant peak overlaid on a low-pass filter sounds a lot like a band-pass filter with some extra mojo, resonant low-pass filters have formant-forming qualities. The 292e does not support a resonance parameter, but the signal from a 292e can be added to a band-passed signal from a 291e to create a similar effect. FIXME: how do we tune the two different modules so that we know the resonant peak and the low pass filter are really in agreement? FIXME: is there some trick way to combine the two audio signals without burning a column of the 210e?

One way to achieve the effect of a high pass filter, other than possibly the warp control of the 259e and the timbre control of the 261e, is to mix together a lopass filtered signal with the original signal, with one of them inverted in polarity. Buchla mixers are a single inverting stage and therefore running one signal through the simple mixer on the 227e before mixing them together in the final mixer will make that happen. This is untested on a 200e, but has been proven on an original 200 system.

Neat tricks

4-pole LPF using 292e

I'm guessing that the 292e implements a 2-pole (aka second-order) LPF, but what if one wants a 4-pole LPF? Simple, just allocate 2 292e circuits, feed them with identical CV inputs, apply identical knob settings, feed the signal to be filtered into the first, the output of the first to the input of the second, and the output of the first will be a 4-pole LPF.

If I'm wrong and the 292e just implements a first-order filter, the above will give the effect of a second-order filter and all four units will need to be connected to implement a fourth-order filter.

Portamento using the 266e and 256e

Here is a method I've discovered to jury rig a portamento effect by using the 266e Source of Uncertainty in a certain way. The basic idea is simple: since portamento is a glide between one pitch and another, we need a way to capture a pitch so that when a new pitch is played we can glide from the original pitch to the new target pitch. We do this by configuring the Stored Random Voltages section of the 266e as a Sample-and-Hold function: set "skew " to none (leftmost, not middlemost position) and "degree" and "chaos" to zero. The output of the Sample-and-Hold function is our original note (sort of) and the current MIDI pitch (as a control voltage) is the target pitch. To glide from one to the other, we put the two pitch voltages into the two source inputs of a 256e Control Voltage Processor circuit and use the output of a 281e Quad Function Generator to pan from the original pitch to the new pitch. The Attack parameter of the 281e defines the glide speed.

The pulse network is a bit tricky: the MIDI note on pulse triggers the 281e envelope, which is configured in transient mode. The output of the 281e drives not only the selection logic of the 256e, but also a second circuit in the 256e. This second circuit is configured to generate a pulse at the end of the attack phase by using a breakpoint function (in value = 8 V, out value = 0 V). The output of this second circuit drives the "update" input of the 266e. The 281e produces a pulse at the end of the decay phase of the envelope, but that is too late: we need to sample the pitch before the decay, else our selection logic will drop back to the initial pitch and we'll hear a glitch. By sampling the pitch just as we reach the top, there won't be a glitch when the 281e envelope decays and the first 256e circuit switches back from MIDI pitch to sampled pitch.

Would that it were so simple! For reasons I do not yet understand, the 266e flattens out voltages, which has the effect of changing an octave scale into something not quite an octave. If it stretched pitch instead of shrinking it we could fix the problem with a single 256e circuit. This is because we could raise the Output @ 0 V, lower the Output @ 10 V, creating a transfer function of something like 0.8:1 and the product of the two would be a nice 1:1 transfer function. Since the incoming scale is flattened, we need a transfer function that's more like 1.25:1, and that requires two 256e circuits. The first circuit uses a breakpoint function to produce 10 V at approx 8 V input. The second circuit uses a breakpoint function to produce 0 V at approx 2 V input. By running these in series we get our (> 1):1 transfer function, and pitch is restored (to within perhaps 20 cents, because all these pitch transformations add up their pitch errors). The output of the corrected sample pitch is the actual input we use for the 256e selection circuit, not the output of the 266e directly.

Of course we can also use this portamento method to drive the frequency of a 291e or 292e filter to get the classic ELP effect of a glide opening up with a big "BWAHH!" at the finish.

n.b. It is also possible to save two 256e circuits by doing the following. By using two separate pitch busses on the 225e unit we can tune the offset of each separately. Let's call the first bus the Hold bus (used to feed the 266e Sample-and-Hold circuit) and the second bus the Now bus (the pitch currently being played). By using a 210e CV circuit, we can flatten the pitch of the Now bus so it has the exact same slope as the output of the 266e (which is fed by, but is not itself, the Hold bus). Tuning the offsets of the two pitches helps set the slope correctly across a range of notes. Now that both inputs to the poramento selector circuit behave the same for a given pitch, we can correct the flat slop by using a breakpoint function. By setting the breakpoint out value to zero and setting the in value to around 2 V, we create a slope that is greater than unity, offsetting the less-than-unity slop of the 266e and the intentionally less-than-unity 210e output. We tune the 256e circuit until the slope of the breakpoint function cancels out the slopes of the input functions and now we can feed the CV output to the CV input of an oscillator like the 261e, tune it to 1.2 V/octave and we're good to go. It's a good idea to conserve 256e circuits because they can be useful for other things...

Constant Rate Portamento

The previous method gives a constant time portamento: whether the pitch difference is one semitone or 48, it takes the same amount of time to g-l-i-d-e up or down to the next pitch. A constant rate portamento moves some number of semitones per second, meaning that the portamento between notes close together will be almost imperceptible, whereas notes several octaves apart will give a very strong portamento effect. To do this we need to calculate the difference between two pitches and use that as a factor of how quickly the Attack parameter of the 281e envelope changes the selection between the original note (which we'll call P1) and the target note (P2).

To calculate the difference between two notes we need two circuits of the 256e and a summing circuit from the 210e. The first 256e circuit is configured as a negative transfer function giving us 10 V - P1 for an input of P1. We use the 210e to add (10V - P1) /2 with P2/2, giving 5 V + (P2 - P1) /2 and feed this output to the input of the second 256e circuit. The second 256e circuit is configured as a non-linear transfer function that looks like the letter V. I.e., it gives 10 V - 2*Vin when Vin <= 5 V and 2*Vin - 10 when Vin > 5 V. When P1 is near P2, then 5 V + P2 - P1 is near 5 V and the non-linear transformation gives us a value near 0 V, a very short time for the portamento glide time. When P1 is two octaves (2.4V) less than P2, then 5 V + P2 - P1 is 7.4 V and the non-linear transformation gives us 14.8 V - 10 V or 4.8 V, a good amount of glide time. Similarly when P1 is two octaves above P2 (2.4V), then 5 V + P2 - P1 is 2.6 V and the non-linear transformation gives us 10 V - 5.2 V = 4.8 V, an equally good amount of glide time. In either case, the 4.8 V can be multiplied by the attack time of the 281e unit to get the right amount of portamento time.

This setup uses 3 210e inputs, 4 256e circuits, 1 266e input in the Stored Random Voltages section, 1 281e envelope generator circuit, and 2-3 MIDI pitch outputs of a 225e circuit, not including the number of oscillators, evelope generators, filters, and VCAs needed to generate a sound.

Extra-Low LFO using the 281e

When the input mode is set to periodic, the 281e Quad Function Generators can function as Low Frequency Oscillator with a frequency ranging from 1/20th Hz (producing a triangle wave) to 1/10th Hz (becoming a rising or falling sawtooth wave), to any type of wave in between triangle and sawtooth up to 500 Hz.

Shepard Tone Example

FIXME

Tips and hidden features

* You can enable or disable the Remote Enables of all modules in a system with the Preset Manager section of the 225e. Use the DATA switch to select "global". The top line of first global page reads Remote Status. The DATA knob will now enable and disable remote all the modules in a system.

Gotchas

The "Remote Enable" switch has a dual meaning on several modules.
* 259e and 261e: causes the principal oscillator to track midi notes. This can lead to surprising results when you've configured your oscillator to run off a CV pitch and use Remote Enable just to restore other parameters of the module.
* 281e: causes the envelopes to open for MIDI note on events. Again, this can lead to surprising results when you just want to restore envelope attack types (continuous, transient, or sustain) or quadrature mode.
* 292e: causes the "VCA"s to react to Velocity.

See also

* Synthesizer
* Analog synthesizer
* Moog synthesizer
* LADSPA

External links

* [http://www.buchla.com/200e/200e.html Buchla 200e Website]
* [http://www.mortonsubotnick.com/ Morton Subotnick]
* [http://www.sevwave.com/electronic%20music.html Suzanne Ciani]
* [http://www.cyndustries.com/links.cfm Cyndustries]