Realgar Red — Service Manual

1General

1.1Scope

All figures in this manual were measured on the instrument's own test bench: at 96 kHz where a circuit is measured alone and at 48 kHz where the assembled instrument is. Every figure quoted is held to its number on every build. If a figure here and the instrument ever disagree, the instrument is at fault and the build does not pass.

1.2The reference unit

Serial number 00000 is the reference unit. Every part in it is nominal. It is never issued to a customer. Factory presets, demonstrations and the figures in this manual are made on it unless a serial is stated. Several tests state serial 40117, an ordinary unit chosen for the purpose.

1.3Notice concerning derived values

Notice. The following values were derived from the physics of the circuit and not calibrated against a hardware specimen: the SLEW filter's knee and rail (and therefore the pitch at which it sings); the FOUR-POLE OP-AMP filter's resonance behaviour; the ageing coefficients of section 3.2. They behave correctly in kind. Their magnitudes are engineering estimates and are marked † where they appear.

2Identification: the serial number

2.1Issue

The first time the instrument is opened on a computer it draws a five-digit serial number between 10000 and 99999 and writes it to a text file:

%APPDATA%\Aphelion\Realgar Red\serial.txt

It is read from there ever after. The number is not a licence. It identifies no person. It is never transmitted. The display's second line shows it at all times.

2.2What the serial determines

Every part in the unit that has a tolerance is given a deviation drawn from the serial number, by the part's name, its bay and its card. The draw is a bell curve with its tails cut off at the tolerance limits, as a sorted batch of parts is. The same serial is the same instrument on any computer, for ever, to the sample: serial 40117 built twice differs from itself by 0.000000 of full scale, and from serial 40118 by 1.127.

Because draws are by bay and by card, the same board fitted in bay A and in bay B are two different examples of the circuit, and card 3's example is not card 4's.

2.3To obtain a different instrument

Close the host. Delete serial.txt. A new serial is drawn at the next opening. To return to a former instrument, write its five digits back into the file. Keep a note of a serial you are fond of.

2.4Sessions and visiting units

A saved session carries the serial it was made on, where CALIBRATE last left all ninety adjustments, the arpeggiator's custom lane, the lanes of the automata, the sequencer's steps and locks, and which cards were pulled. Opened on any computer, the instrument becomes that unit for that session and the display reads A VISITOR after the serial. The computer's own serial is not altered. A button on THE CAGE page returns the session to the home unit; this rebuilds every part and the session will no longer sound as it was saved.

A preset is a patch and not a unit. Loading one does not touch the serial, the calibration, or the pulled cards.

3Theory of the unit

Six mechanisms act on a unit. Each is separate, each has its own control on THE CAGE page, and each opens at half of full scale: full scale is the physical extreme. At zero the mechanism is absent.

3.1GRADE: the tolerance of the parts

Position	Tolerance	Remarks
0.1 PER CENT	±0.1 %	Laboratory parts. Nine cards very nearly alike.
1 PER CENT	±1 %	As the instrument opens.
5 PER CENT	±5 %
10 PER CENT	±10 %	Commodity parts.

A grade is a build. Select another and the unit is rebuilt from those parts and leaves its factory as any unit does: new, warm and trimmed (serial 40117 rebuilt from 10 % parts: its worst oscillator of twenty-seven reads 0.86 cents at A4, as it did at 1 %). It then ages to whatever AGE says. GRADE scales how far every part leans. It does not change which way any part leans, so a unit keeps its character across grades. Some parts count for more than their tolerance: a timing capacitor counts double, a matched pair several times.

GRADE is what no trimmer reaches. Pitch can be trimmed out at any grade: nine cards fresh from the factory, built of 10 % parts, spread 0.00 cents at A4. Nothing trims an envelope's capacitor: the same nine cards' amplitude-envelope fall times spread 2.5 % at the 1 % grade and 37.7 % at 10 %.

3.2AGE: parts walk

Parts do not only scatter; they move with the years, each kind its own way, and most of the movement is in the first decades. The walk of each individual part is scaled by its own draw, so two electrolytics in one unit do not dry at the same rate. (The reference unit ages the textbook amount.)

FIG. 1 † The walk of each kind of part, as a fraction of its value. Coefficients are derived (see 1.3).

Forty years on (reference unit)	New	Aged	Remedy
SAW CORE at A4	+0.86 cents	+12.4 cents	CALIBRATE returns it to +0.86.
LOGIC oscillator	0	+18.3 cents	No converter. CALIBRATE sets its TUNE and returns it to 0.00 at A4.
Amplitude envelope, fall to one tenth	450 ms	310 ms	None. The electrolytic has dried. Move the slider.

A calibration made when the unit was new does not hold when it is old. After changing AGE, calibrate.

3.3WARM-UP

From the moment the plug-in is opened the enclosure climbs from room temperature toward its operating temperature with a time constant of seven minutes. At full WARM-UP the end cards settle 18 °C over the room and the middle card 23 °C over: the middle of the cage is the warm end of the oven.

FIG. 2 Settled temperature rise by position in the cage.

The exponential converters of the SAW CORE and TRIANGLE CORE boards are temperature-compensated, imperfectly, by an amount drawn per board. The DCO, LOGIC and DIVIDE-DOWN boards have no converter and are indifferent to temperature. The rule that follows is the rule for the hardware: the unit is in tune at the temperature it was tuned at.

FIG. 3 Upper trace: a unit trimmed warm at the factory, from switch-on. Lower trace: the same unit with CALIBRATE pressed at switch-on. Marked points are measured; the traces between them are drawn.

A temperature error is a scale error, not an offset: it is larger at the top of the keyboard. On serial 40117, calibrating cold moves card 4's oscillator scale adjustment from +305 to −515 parts in a million.

3.4SUPPLY

One regulator feeds nine cards. With all nine sounding flat out the rail stands 2.5 % low. A reservoir capacitor makes the droop slow (30 ms). Every board leans on the rail by its own amount:

FIG. 4 Pitch moved by a rail 2.5 % low (all nine cards flat out, SUPPLY at full). The DCO's clock alone leans; the DIVIDE-DOWN bank leans as one.

In practice: an A4 held alone, then with eight more keys put down under it, moves −10.9 cents as the rail goes 2.04 % low. The rail's state is shown on THE CAGE page.

3.5CROSSTALK and FLOOR

With only oscillator A on the grid, oscillator B stands −60.1 dB under it at the output (with CROSSTALK at zero, −94.7). Adjacent cards bleed into each other through the backplane by a smaller amount. A note stands 46.4 dB over its card's own noise with PUSH at 10 and 69.4 dB with PUSH at 90: a quiet PUSH sits nearer the hiss, because the hiss enters at the filter's input at a fixed level, and what PUSH turned down is made up afterwards, hiss and all.

4Adjustments

The cage page of the panel — **FIG. 5** THE CAGE page. (1) each card, with how far each of its oscillators stands from A4, in cents (2) the rail (3) CALIBRATE.

4.1Adjustments provided

One: CALIBRATE, on THE CAGE page. The instrument has no tuning pots and no service page. Inside, each card still carries ten adjustments (SCALE and OFFSET for each of the three oscillator bays and each of the two filter bays, ninety in all), but nobody turns them by hand: the factory sets them, CALIBRATE sets them again, and where it left them is saved with the session.

Adjustment	Travel	Effect
SCALE	±1 % (±10 000 ppm)	Volts per octave. An error here grows up the keyboard: 1 % is 48 cents across the four octaves from A2 to A6.
OFFSET	±40 mV	Moves every note alike: 1 mV is 1.2 cents, full travel ±48 cents.

THE CAGE page reads each card's three oscillators at A4, as a needle either side of true and a figure in cents. A needle is amber inside 3 cents.

4.2CALIBRATE, and what it reaches

CALIBRATE measures every oscillator and filter on every card against test notes and sets SCALE and OFFSET, through a converter with a finite step (100 ppm of scale, 0.2 mV of offset), as the unit stands at that moment. Expect residuals of up to a cent or so. The factory's calibration is finer, and is made warm. A board with no converter (LOGIC) has its TUNE set to zero error at A4 in the same press; its scale is fixed by the circuit.

Condition	CALIBRATE	Remarks
SAW CORE or TRIANGLE CORE out of tune: parts, temperature, age	Yes	SCALE and OFFSET.
Filter corner off, or not tracking	Yes	SCALE and OFFSET.
LOGIC oscillator out of tune	Yes, at A4	No converter: its TUNE is set, and what A2 and A6 then read is the board. Its scale has no adjustment.
DCO	Not needed	A counter. Nothing to adjust and nothing needing it.
DIVIDE-DOWN	Not needed	TOP OCTAVE is arithmetic. TWELVE MASTERS' detunings are the unit's.
Sine not pure (TRIANGLE CORE)	No	SINE PURITY, the board's own knob on THE CARD. The shaper's purity wanders with age. Symmetry has no adjustment.
Envelope or LFO time changed with age	No	A dried capacitor. Move the panel control.
VCA does not quite shut	No	OTA bleed grows with age. Fit the VACTROL board, or live with it.
Pitch sags under chords	No	The supply. See 3.4.

4.3Procedure

Open the instrument and leave it for at least thirty minutes. (At seven minutes it is still 11 cents from settled at A6.) Play nothing: a loaded rail is a flat instrument.
Go to THE CAGE and press CALIBRATE.
Read the nine cards. That is all of it.

4.4When to calibrate

Warm, unloaded, and after any change of AGE, WARM-UP or ROOM (each moves the unit away from the state it was trimmed in: serial 40117 aged thirty years with nobody touching it reads 47.5 cents out at worst, and 0.86 after CALIBRATE). A change of GRADE, or a newly fitted oscillator board, arrives factory-trimmed and needs nothing until the unit ages or the room changes. A unit calibrated cold is 31 cents flat at A6 an hour later (fig. 3).

5Fault-finding

Symptom	Probable cause	Remedy
Whole instrument sharp for the first minutes, worse at the top	Not yet warm (3.3)	Wait. Or reduce WARM-UP. Do not calibrate cold unless you intend to play cold.
Flat an hour into a session	Was calibrated cold	Calibrate again, warm.
A held note goes flat when a chord is added	Supply sag (3.4)	Normal. Reduce SUPPLY, or fit boards that lean less (fig. 4).
One note in nine is out	One card's calibration, or that card's draw at a coarse GRADE	Read the cards on THE CAGE page. CALIBRATE, or pull the card.
Top octave flat, oscillator otherwise in tune	SAW CORE reset time; TRIANGLE CORE comparator delay (−6.08 cents at A7)	Characteristic of the circuit. On SAW CORE, shorten RESET TIME.
Envelopes faster than the sliders say; LFO faster	Aged electrolytics (3.2)	None. Move the control, or reduce AGE.
Sine wave has an edge	Shaper purity trimmer has wandered	SINE PURITY on the card.
An oscillator is faintly audible when absent from the grid	Crosstalk (3.5)	Normal at −60 dB. Reduce CROSSTALK.
Hiss with PUSH low	Make-up gain after the filter (3.5)	Raise PUSH; reduce FLOOR.
Faint sound with all keys released	OTA VCA bleed	Normal, below −75 dBFS. With IDLE CARDS on, an unplayed card is asleep and silent.
LOGIC oscillator wanders with every chord	It leans on the rail four times as hard as a saw core	That is the board.
Single notes move about the stereo field	POLY deals cards round in turn, and SPREAD places them left to right	Reduce SPREAD. MONO is always central.
Two DCOs a few cents apart do not beat	They share one clock. Their sum's level moves 0.000 dB in twenty seconds.	Normal. The phase the keys caught them in is the tone. For beating, fit any other board in one bay.
FM knob does nothing	Receiving board is DCO, LOGIC or DIVIDE-DOWN	These have nowhere to put it.
Display reads A VISITOR	Session was made on another unit (2.4)	None needed. Button on THE CAGE to convert.
Session sounds different on a colleague's computer	It should not: the unit travels with the session	Confirm both run the same version.

6Board data sheets

One sheet per board. "As built" means the value your unit drew for that part. A board control at its centre leaves the board exactly as built (verified to 0.0000 cents and 0.0000000 of output on every oscillator, filter and VCA board).

Filter boards compared

FIG. 6 PUSH from 10 to 95 on each board in bay A: change in a saw's 20th harmonic against its fundamental, corner near 500 Hz.

At each board's nominal level, corner wide open and resonance at zero, the six pass a saw at between −0.79 and −0.06 dB. With resonance at 50 the LADDER's passband is −9.8 dB (a four-pole ladder's passband is 1/(1+k)) where the DIODE's is −0.2: that loss is the circuit and is left in.

All filter bays: the corner's SCALE is set by a film resistor and its OFFSET by a trimmer, both drawn per bay and per card; the corner follows the card's temperature; it leans on the rail at 10 cents per per cent (−25.0 cents at full load).

SAW CORE OSCILLATOR BAY

Circuit: A capacitor charged by an exponential converter and emptied by a reset comparator.
WAVE: SINE – TRI – SAW – PULSE
Board control: RESET TIME: 1/16 µs to 16 µs, centre 1 µs. The longer the reset, the flatter the top octaves.
FM · sync: Linear FM stalls at zero (index 3: carrier moves +480.6 cents). Hard sync, reset at its instant inside the sample: loudest non-harmonic −98.3 dB under the fundamental.
Reset: The capacitor empties in RESET TIME, and the emptying is on the waveform: the saw falls along it rather than jumping, the triangle (the saw rectified) turns round on it, and the sine (a differential pair's curve of the triangle) has the notch it makes. The ramp's top, its bottom and every corner are found at their instants inside the sample and drawn band-limited.
Purity: At A7, the loudest line under 20 kHz that is not a harmonic: sine −91.3 dB under the fundamental, triangle −91.7, saw −77.4, pulse −85.4.
Autotune: Reaches it. SCALE and OFFSET.
Rail: 6 cents per per cent. −15.0 cents at full load.
Temperature: Converter compensated 91–99 %, drawn. +31.5 cents at A6 at switch-on when trimmed warm.
Parts drawn: Scale resistor (film); offset trimmer; compensation; starting phase.
Ages: †+0.86 → +12.4 cents at A4 in forty years as its parts walk. Recoverable: CALIBRATE returns it to +0.86.

TRIANGLE CORE OSCILLATOR BAY

Circuit: An integrator reversed at two thresholds. Sine by shaper, saw by flipping the falling half, pulse by comparator.
WAVE: SINE – TRI – SAW – PULSE
Board controls: SINE PURITY: shaper drive ×0.4 to ×2.5 about as built. SAW STEP: the mid-ramp step, 0 to 4× as built. Switch: sync REVERSE / RESET.
Tracking: A4 −0.76 cents, A7 −6.08: four comparator delays of 250 ns a period.
Sine: −37.8 dB THD at the shaper's null (third harmonic −54.6); −28.5 with the purity trimmer 20 % low. A symmetry error of 0.1 raises the second harmonic from −154.3 to −24.7 dB.
FM: True through-zero. Index 3: carrier moves −1.4 cents.
Sync: REVERSE turns the wave round and keeps it continuous: −51.1 dBFS above 6 kHz where RESET has −35.3. RESET's loudest non-harmonic: −94.2 dB.
Purity: Each turn-round is a corner, found at its instant and drawn band-limited, as are the saw's flip and the pulse's edges. At A7, the loudest line under 20 kHz that is not a harmonic: sine −114.1 dB, triangle −112.6, saw −77.4, pulse −85.4.
Autotune: Reaches pitch. Does not reach the shaper.
Rail · temp.: As SAW CORE.
Parts drawn: Scale, offset, compensation; purity trimmer and symmetry trimmer (both wander with age); saw step; starting phase.

DCO OSCILLATOR BAY

Circuit: A ramp reset by a counter dividing one master clock. The key loads the counter; bend, vibrato and the matrix move the clock.
WAVE: SUB – SAW – SAW + PULSE – PULSE
Board controls: CLOCK: 0.25 to 16 MHz, centre 2 MHz (a slow clock is audibly out at the top). CURRENT STEPS: the ramp current's converter, 2 to 10 bits an octave, centre 6.
Tuning: A4 +0.173 cents from true; worst key C2 to C7, −0.79. These are the arithmetic of integer division and agree with it to 0.0000 cents.
Bend: The ramp's current does not follow the clock. Bent up a tone: saw −1.00 dB; a 30 % pulse becomes 33.7 %.
Beating: None between DCOs: one clock serves the whole unit. The phase the keys caught two voices in is the tone (second harmonic −7.3 to +9.8 dB against the fundamental, by phase).
Level: Twelve keys of an octave within 0.09 dB through the six-bit converter.
Purity: At A7, the loudest line under 20 kHz that is not a harmonic: saw −79.1 dB, pulse −87.6.
FM · sync: None. There is nowhere to put either.
Autotune: Not applicable. No trimmers.
Rail · temp.: 1.5 cents per per cent (its clock only): −3.7 at full load. Indifferent to temperature.
Parts drawn: Ramp current error (film); one clock for the unit.

LOGIC OSCILLATOR BAY

Circuit: A Schmitt-trigger gate charging a capacitor through a resistor.
WAVE: TRIANGLE – SQUARE. No pulse width.
Board controls: None.
FM · sync: None.
Autotune: No converter: CALIBRATE sets its TUNE at A4 (4.2). No scale adjustment.
Rail: 25 cents per per cent: −62.5 cents at full load. It hears the supply more than anything else in the instrument.
Temperature: Indifferent.
Purity: The gate's flips are steps and the capacitor's turn-rounds are corners, each found at its instant and drawn band-limited. At A7, the loudest line under 20 kHz that is not a harmonic: triangle −95.0 dB, square −87.6.
Parts drawn: Timing capacitor (film); timing resistor (carbon).
Ages: †+18.3 cents in forty years as the carbon resistor creeps. CALIBRATE returns it to 0.00 at A4.

DIVIDE-DOWN OSCILLATOR BAY · ONE BANK SERVES THE CAGE

Circuit: Twelve top-octave notes, each divided by two down the keyboard. Every note is always running; a key opens a gate on it. Every octave of a note is locked to it for ever.
WAVE: SQUARE – RAMP. The ramp is a staircase network, as the hardware made it: the tap's square and the three dividers under it, each at half the weight of the one before, sixteen steps a cycle (the top octaves, with fewer dividers under them, have fewer).
Build: Set on THE CAGE page. TOP OCTAVE: twelve integer divisions (478 down to 253) of one 2.00024 MHz clock. TWELVE MASTERS: twelve separate oscillators, each with its own drawn timing capacitor.
Tuning, TOP OCTAVE: C4 to B4 against equal temperament, cents: −0.58 +0.08 −1.19 −0.80 +1.19 −0.12 −0.60 −0.44 +0.11 +0.76 +1.15 +0.87. The fifth C–G is 478/319 = 1.4984326 (equal temperament wants 1.4983071), and is that ratio on every unit.
Tuning, TWELVE MASTERS: A fifth is two oscillators and beats; an octave is one and does not (2.00000011).
Bend: Moves the clock, or all twelve masters: the whole bank bends together. Bend is not this board's to apply per card.
Tunings: With a Scala tuning of twelve notes to the octave and the TWELVE MASTERS build, the masters are retuned to it and each key finds its tap by the tuning's pitches (quarter-comma meantone's major third measures 386.32 cents, against 386.31). Any other tuning, or TOP OCTAVE, plays the nearest of the twelve.
Autotune: Not applicable.
Rail: The bank leans as one: 2 cents per per cent as TOP OCTAVE, 4 as TWELVE MASTERS.
Purity: Every divider's edges fall where the counter says, found at their instants and drawn band-limited. At A7, the loudest line under 20 kHz that is not a harmonic: square −87.1 dB, ramp −78.6.

DIODE SHAPER OSCILLATOR BAY · 128 DIODES

Circuit: A saw core's ramp (exponential converter, reset comparator, the same trims) driving a ladder of 128 biased diodes: y = a0 + a1·x + Σ c·S((x − b)/w)·w, S the diode knee (softplus), w = n·Vt/Vswing = 0.0093 of the ramp at 300 K. Fitted by least squares to one of sixty-four shapes, the knees placed where the shape bends; the fit is deterministic and shared by every copy.
WAVE: The shape, 1 to 64, and a scope in the bay draws what this card's ladder makes of it.
Parts drawn: Scale resistor, offset, compensation, starting phase, as the saw core; then every knee (a 0.1 % divider) and every slope (1 % film, and it walks), the drive and the bias.
Board knobs: PW is DRIVE, a third of the shape to three times over (past one the ramp runs off the end and comes in at the other). KNEE: junction capacitance, ×¼ to ×4 of the part. BIAS: the ramp's centre on the shape. SWEEP: saw (once through; where the ends meet is the edge the ramp's reset makes) or triangle (forward and back, no seam).
Fit: †Sixty-four shapes fitted together in about 80 ms: −71.6 dB of error on average, −20.6 at worst (DOUBLE SAW). A vertical edge is as sharp as a knee, so the square, the pulses, the stairs and THREE LEVEL fit between −20 and −30 dB; the rest under −30.
Purity: †SINE through the ladder at A4: second harmonic −92.9 dB, third −112.9.
Drawn: The ladder's output is integrated exactly over every sample, weighted by a triangle two samples wide (the knee's integrals are the dilogarithm and the trilogarithm, tabulated once), so the 128 knees, each narrower than a sample, are drawn band-limited and not read at the sample instants. The seam, a sync and DRIVE's wrap are jumps, each found at its instant and drawn band-limited. At A7, the loudest line under 20 kHz that is not a harmonic: SINE −117.9 dB, SAW −77.3, SQUARE −64.7, STAIRS 4 −63.9 (a vertical edge in the shape is a knee, not a jump, and the steepest are the hardest).
Autotune: Yes: SCALE and OFFSET, as the saw core's. The ladder itself has no adjustment.
Ages: The converter as the saw core's; the slope resistors walk as film does, so an old ladder draws its shape a little wrong in a way CALIBRATE does not reach.

WEST COAST OSCILLATOR BAY · FIVE-CELL FOLDER

Circuit: The triangle core (its converter, trims, sine shaper, through-zero FM, REVERSE sync) driving the classic parallel wavefolder: five op-amp folding cells beside a direct path, summed by two inverting amplifiers. Each cell is dead below (R1/R2)·6 V and folds linearly above it; three cells reach the output inverted, two and the direct path (×5) upright. Modelled from the circuit's resistors, so every cell meets its dead band exactly. The output amplifier integrates: a one-pole lowpass at 1.33 kHz. The rails (±6 V) are never reached; the folded curve peaks at 4.2 V.
WAVE: SINE – TRI – SAW – SQUARE: the whole triangle core, into the folder. The square is a square: this board's PW knob is ORDER.
Board controls: TIMBRE: the drive into the folder, 0.55 V peak (just short of the first cell: a plain sine) to 10 V (five folds). SYMMETRY: a DC offset at the folder's input, ±2 V; its centre is the unit's own small offset. ORDER, on the PW knob: see below. The switch: nothing.
ORDER: The last crossfade before the output, after a modern reissue's description of the control (the original's circuit for it has not been published, so this is a reconstruction, not a model). Fully left: the folder, exactly. Fully right: TIMBRE crossfades from the core's sine to a second crossfade, which SYMMETRY sweeps from a sawtooth to an M. The sawtooth is the core's own ramp (the comparator's flip of the falling half, band-limited). The M is a pseudo-square, the square's first two harmonics, drawn from the sine by a cubic, (3x − 2x³)/√2, whose input is trimmed at the factory so the unit's sine reaches it at unit fundamental: harmonics at 1/k for the sawtooth, and a third at a third for the M, each within half a dB. They join the folder after its integrator, in step with it. The PW destinations in the matrix move ORDER.
Matrix: TIMBRE A–C: the whole of TIMBRE's range at full amount, added to the knob. SYMMETRY A–C: half of SYMMETRY's (±2 V at full amount). Both clamp at the knob's ends. Other boards ignore them.
Harmonics: Symmetric, odd harmonics only: at 220 Hz with TIMBRE centred every even harmonic is more than 120 dB down. Off centre the second harmonic comes and goes as the offset moves, from +2.4 dB to −41.6 dB (at +1.2 V the folds line up nearly symmetric again). The brightness breathes with TIMBRE for the same reason.
Drawn: The folder is fed the core's raw wave, not its band-limited output: the integrator is run a second time, exactly, and checked against the core every sample, so each turn, reset and square edge is known to the instant and drawn as a band-limited step and corner, and every threshold the raw wave crosses between them is solved for and drawn as a corner (the cell's gain times the input's slope). The core, the folder and the integrator run at twice the card's rate and a halfband brings them down (7.5 samples late). Up to 1760 Hz at full TIMBRE, on all four waves, the loudest line under 20 kHz that is not a harmonic is −91.4 dB under the loudest harmonic (a folded ramp can all but lose its fundamental).4 dB. At A7 with TIMBRE centred: SINE −74.1 dB, TRI −113.9, SAW −97.3, SQUARE −114.1.
Autotune: Reaches pitch. Does not reach the folder.
Parts drawn: As the triangle core (scale, offset, compensation, purity and symmetry trimmers, starting phase); and the folder's input offset, 20 mV at 5 %.

DIGITAL WAVETABLE OSCILLATOR BAY · NOT A CIRCUIT

What it is: A phase accumulator reading 85 banks of four single-cycle waves (340). Each wave is a spectrum, rendered by inverse FFT as ten mip levels (1024 down to 2 harmonics), each stored at four times its top harmonic's Nyquist and read with a six-point Lagrange; all of a wave's mips share one scale (its peak made 1), so a mip change or a morph never jumps in level. The tables are built once, off the audio thread, in about 50 ms (21 MB).
WAVE: The bank's four waves, morphed linearly between neighbours.
Board controls: BANK (85 positions). WARP MODE (eight positions: BEND, SQUEEZE, MIRROR, QUANTIZE, OFF, SYNC, FM, RING; OFF at the centre). WARP, on the PW knob, 0 to 1. The switch: nothing.
Warps: After a phase-warping wavetable module's: BEND a power curve (4^2w−1) above its centre and the same curve turned about the cycle's middle below it; SQUEEZE the first half of the cycle into 0.05 to 0.95 of it; MIRROR the cycle read forward then back, blended by w; QUANTIZE the phase in 64 − 61w steps; SYNC the table read 1 + 7w times a cycle; FM the phase moved by 1.5w times the next bay's output; RING the output times (1 − w) + w times it.
Drawn: The mip for the note keeps its top harmonic under 0.42 of the card's rate, divided by the warp's bandwidth factor, and is blended with the next so a glide never steps. Every jump and bend a warp makes (SYNC's and MIRROR's resets, MIRROR's and SQUEEZE's knees, BEND's knee, QUANTIZE's steps, a sync from another bay) is found at its instant and drawn band-limited; the board runs at twice the card's rate and a halfband brings it down. Warp off, at A7, the loudest line under 20 kHz that is not a harmonic: SAW −94.4 dB, SQUARE −100.1, VOWEL A −73.1 (against the fundamental; the worst of seven waves against the loudest harmonic, −78.6, a five per cent pulse). Every warp on a saw at 880 and 1760 Hz: −80.5 dB at worst (SYNC). A saw table hard-synced from another bay: −60.4 (the reset lands inside the table's own edge).
Pitch: Exact: 440 Hz asked, 440.02 heard (the measurement's resolution). No converter, drift, rail or temperature; CALIBRATE does not reach it and need not.

DIGITAL SUPER SAW OSCILLATOR BAY · NOT A CIRCUIT

What it is: Seven phase accumulators, each a saw (with SHAPE's copy of it half a cycle on), summed. Each plays the note times 1 + s·o, o = −0.110, −0.063, −0.020, 0, +0.020, +0.062, +0.107: asymmetric, so the beats never line up (after Adam Szabo's published measurement of the classic seven-saw ensemble, 2010). Each of the seven is heard where its ratio puts it, within a hundredth of a hertz.
WAVE: MIX, m from 0 to 1 across the knob: the centre saw at 0.998 − 0.554m, each side saw at 0.044 + 1.284m − 0.738m² (the same measurement's curves), the sum scaled to one saw's loudness with the phases uncorrelated. Across MIX and VOICES the level stays within 0.6 dB of one saw's.
PW: DETUNE: s = 0.003 + 0.18x + 0.817x⁶ for the knob's x (0 to 1), rising all the way (the measurement's own fitted polynomial dips just above the bottom). The outermost two are 39.8 cents apart at the knob's centre and 378 at full.
Board controls: SHAPE: each saw plus k times its copy half a cycle on, k from +1 fully left (the saw an octave up) through 0 at the centre (the saw) to −1 fully right (a square); every saw at unit peak throughout. VOICES, seven positions: 1, 3, 5, 7 (the centre), 6, 4, 2 saws; odd counts keep the centre saw, and the widest pairs are kept first. The switch is PHASE: FREE (running on) or KEY (a struck key, not a legato one, starts the seven at the same places, spread by the golden ratio). Gains and SHAPE glide over 2 ms, so a knob turned or a saw added never clicks.
Drawn: Each saw's reset and SHAPE's second edge found at its instant and drawn as a band-limited step, at the card's rate, as the SAW CORE draws its saw; a sync from another bay (all seven reset) and a KEY start the same. At DETUNE's centre and full, 1760 and 3520 Hz heard, the loudest line under 20 kHz that is none of the seven saws' harmonics is −78.4 dB under the loudest that is (saws; squares −81.1; the SAW CORE's saw at A7, −77.4). DETUNE off, at A7, against the fundamental: −83.8. Synced from another bay: −71.1.
Pitch: Exact. No converter, drift, rail or temperature; CALIBRATE does not reach it and need not. The unit only scatters where each card's seven saws stand when it is switched on.

WAVE WRAPPER EACH OSCILLATOR BAY'S LAST STAGE · NOT A BOARD

Circuit: A comparator ladder and a switched offset (the residue stage of a subranging converter, run as an effect). The bay, amplified by WRAP and offset by SHIFT, sits at a summing amplifier; twelve comparators each side watch it, at ±1, ±3, ±5 … windows (the window is the bay's own full swing), and each one that has tripped switches in a current worth two windows the other way. Output through a coupling capacitor (1 µF into 47 kΩ, 3.4 Hz).
Controls: WRAP: gain 8^x for the knob's x, one to eight times; a full swing of the bay wraps as many times as the screen says (2 at the knob's default of 0.35). SHIFT: ±1 window, added before the ladder. IN / OUT: a relay, eased over 3 ms. OUT is no stage: the bay passes sample for sample.
Parts: Each threshold and each step is a film resistor drawn for that bay on that card (tolerance by the unit's grade, walking with age); each comparator has a random offset of about 4 mV and 20 mV of hysteresis. Two units' first four thresholds differ by up to 3.7 % of the window; a laboratory unit's are within 0.3 % of exact.
Drawn: At twice the card's rate between halfband filters (the instrument's own 31-tap design, done polyphase). Each crossing is solved on a cubic through four samples of the summing amplifier's input and drawn as a band-limited step at its instant: 19 dB or more cleaner than the same wraps as bare jumps. For a sine, nothing that is not a harmonic within 65.8 dB at any drive to A6, and at 4.8 times at A7. A saw is the weak case, 50.0 dB to A6 at 4.8 times: the board delivers its reset already drawn, a steep curve a couple of samples wide, and at high drive the curve crosses every threshold inside it, where the analog saw would wrap once at the reset's instant. (First- and second-order antiderivative anti-aliasing of the whole transfer was measured and lost to the drawn steps by 15 to 30 dB.)
Level: A wrapped saw stays within 0.7 dB of the saw across WRAP's travel (exactly at odd whole drives, where the teeth cover the window once).
Matrix: WRAP A–C: the whole of WRAP's range at full amount, added to the knob. SHIFT A–C: the whole of SHIFT's. Both clamp at the knobs' ends. A bay that is OUT ignores them.
Latency: About 17 of the card's samples while IN (the halfbands and the drawn steps); the scope's trigger is delayed to match.
Cost: About 2 ms of a bay-second of the card's audio while IN; nothing while OUT.

DIODE FILTER BAY · THREE INPUTS

Circuit: A diode-tuned two-pole with separate low-pass, band-pass and high-pass inputs, all live at once.
Columns: LP IN, BP IN, HP IN. No mode switch: the response is where you send the signal.
Board control: DIODES: the diodes' knee, one third to three times as built (nominally 0.25 V). How soon PUSH tears.
Nominal level: 0.37
PUSH 10 → 95: +21.5 dB. Louder opens and tears.
Parts drawn: The diode pair's match.

CMOS FILTER BAY

Circuit: A state-variable filter built from logic inverters used as amplifiers.
Modes: LOW, BAND, HIGH, NOTCH
Board controls: None.
Nominal level: 0.25
PUSH 10 → 95: +0.9 dB. Louder blunts and fizzes rather than brightening.
Parts drawn: Inverter gain (nominally 25), as a matched set.

SLEW FILTER BAY

Circuit: A state-variable filter with no capacitors: the integrators are the slew limits of op-amps.
Modes: LOW, BAND, HIGH
Board controls: KNEE: ×¼ to ×4 about †0.15. LOPSIDED: slew asymmetry, ±0.25 about as built.
Nominal level: 0.3
Small signal: Whispered to, an ordinary two-pole: +6.02 dB at the corner for Q 2, −23.70 two octaves over.
PUSH 10 → 95: −27.9 dB. Louder is darker: a slewing integrator cannot follow an edge. A saw's 20th harmonic against its fundamental at input levels of 0.01, 0.3 and 2: −26.0, −28.1, −50.8 dB. It smears rather than clips: the level comes through (−4.8 to −6.1 dB).
Singing: Straight lines, not a sine (third harmonic −20.0 dB; a triangle's is −19.1). †It sings far under its corner, by what its swing costs, and tracks from there (an octave on the corner is 2.0005 on the pitch). Lopsided by 6 %, its second harmonic rises from −117.6 to −27.0 dB.
Parts drawn: Slew asymmetry; op-amp mismatch.

FOUR-POLE, OP-AMP FILTER BAY · SIXTEEN RESPONSES

Circuit: Four op-amp integrators in cascade. What saturates is the chase after an edge, not the note.
Modes: LP 24, 18, 12, 6 · HP 6, 12, 18, 24 · BP 12, 24 · NOTCH · ALLPASS · HP12+LP6 · HP18+LP6 · NOTCH+LP6 · AP18+LP6
Board control: KNEE: ×¼ to ×4 about 0.5.
Nominal level: 0.5
PUSH 10 → 95: −15.8 dB.
Keeps its bottom: A 55 Hz tone of one volt under a 2 kHz corner passes at −0.01 dB with −90.1 dB of distortion. The CASCADE board, its cells saturating on what the feedback leaves them, passes it as cleanly: −0.01 dB with −84.5.
Singing: †With a 1 kHz corner: 919.0 Hz at the edge of resonance, 803.6 Hz well past it. Tracks (2.0003 per octave).
Parts drawn: Cell offsets, as a matched set.

CASCADE FILTER BAY · SIXTEEN RESPONSES

Circuit: Four transconductance cells in cascade, with responses mixed off the taps by five resistors. Each cell's input node joins the stage's input and a feedback resistor from the cell's own output, so the cell's curve acts on how far the stage lags its input.
Modes: As FOUR-POLE, OP-AMP. Each response agrees with the arithmetic of its resistors to 0.003 dB. Notch depth −84.7 dB. All sixteen share the one resonance loop.
Board controls: None.
Nominal level: 0.3
PUSH 10 → 95: −16.2 dB. It keeps its bottom: in the passband a stage is never far behind its input, so what saturates is the chase after an edge and the resonance loop, not the note.
Singing: 983.9 Hz for a 1 kHz corner, from the high-pass tap as from any other.
Parts drawn: Cell offsets, as a matched set.

LADDER FILTER BAY

Circuit: The four-rung transistor ladder.
Modes: 24, 18, 12, 6: the four slopes off the four rungs.
Board controls: None.
Nominal level: 0.045. It wants millivolts.
PUSH 10 → 95: −3.7 dB.
Resonance: Costs the passband: −9.8 dB with RESO at 50. Left in. Compensate with VOLUME if wanted.
Parts drawn: The bay's corner scale and offset only.

DIODE LADDER FILTER BAY

Circuit: Four capacitors joined by rungs of bare diode pairs, driven from a transistor pair at the bottom. Nothing buffers the rungs, so each loads its neighbours and the four poles spread out; the resonance is fed back through a capacitor, so the bass is never in the loop. Solved every sample, the feedback inside the solve.
Modes: One output, the top of the chain: with the rungs loading each other the lower nodes are not slopes.
Board controls: None.
Nominal level: 0.045. The rungs are bare pairs and want millivolts, as the ladder's do.
PUSH 10 → 95: −2.8 dB.
Resonance: The spread poles sing above the corner the capacitors set, so the board pulls its corner down to meet the dial. It needs far more loop gain than the ladder to sing; the knob's top gives it.
Parts drawn: The bay's corner scale and offset only.

SCREAM FILTER BAY

Circuit: A discrete Sallen-Key filter: two poles in a Sallen-Key loop, the resonance fed back through a third. Its diodes are in the FORWARD path, at the output, where the circuit's first version had them (a later version moved them into the feedback): a pair of silicon diodes behind a resistor, solved from the diode equation every sample, the feedback taken after them.
Modes: LOW, HIGH: the chip is one topology or its mirror image, not a morph.
Board controls: None.
Nominal level: 0.25. The diodes' knee is near half a volt.
PUSH 10 → 95: +5.4 dB. The diodes are in the signal path, so they clip it even with the resonance down.
Singing: From the edge of the knob, squared off by the diodes and heard as they leave it.
Parts drawn: The bay's corner scale and offset only.

VELVET FILTER BAY

Circuit: The two-pole state-variable whose integrators are bare OTAs, kept near their linear range by an input attenuator. Their curve is inside the loop, solved every sample.
Modes: LOW, BAND, HIGH, NOTCH.
Board controls: None.
Nominal level: 0.3
PUSH 10 → 95: −1.1 dB. The passband stays clean; what compresses is a ringing resonance, from inside.
Singing: Never, by design: its damping stops short of it.
Parts drawn: The bay's corner scale and offset only.

FIZZ FILTER BAY

Circuit: The discrete two-pole state-variable: bare OTAs for integrators and a diode limiter across the damping path, both inside the loop and solved every sample. Rung up, the diodes weaken the damping, the loop drives deeper into the OTAs' curves, and it sits there spraying harmonics of its own ring: the fizz. It never runs away.
Modes: LOW, BAND, HIGH, NOTCH.
Board controls: FIZZ: how hot the loop runs against the OTAs' and the diodes' knees. At its centre, as built.
Nominal level: 0.5
PUSH 10 → 95: −20.2 dB.
Parts drawn: The two OTAs' input offsets, each its own (the even harmonics).

TWIN FILTER BAY

Circuit: A resonant two-pole highpass into a resonant two-pole lowpass, each an OTA state-variable with the OTAs solved in its loop, each with a corner of its own.
Modes: One.
Board controls: HP: the highpass's own corner, out of the way below 16 Hz across the bottom half of the knob and up to 4 kHz across the top, where it meets the lowpass (the dial) and the two carve a band. At its centre, as built.
Nominal level: 0.5
PUSH 10 → 95: −1.0 dB.
Singing: Never: both halves ring, and both stop short.
Parts drawn: The bay's corner scale and offset only.

GATE FILTER BAY

Circuit: A lamp and a dual photocell in a two-pole network of the cells, two capacitors and a load. The cell's carriers recombine in pairs, so it brightens fast and darkens hyperbolically, slower the darker it gets; the network's corner and its level both follow the cell. Both are solved exactly every sample.
Modes: One.
Board controls: None.
Nominal level: 1. The signal's path is linear: there is nothing for PUSH to push.
PUSH 10 → 95: −0.2 dB.
Cutoff: The dial is the lamp's current, on a log taper. The corner follows it, late.
Parts drawn: The bay's corner scale and offset only.

RESONANCE FOLDER ONE FILTER'S RING · NOT A BOARD

What it is: A wavefolder fed only the chosen filter's resonance. The card fits a TWIN beside each filter bay: the same board, built from the same parts, run on the same inputs and cutoff with its resonance at zero, only while the folder listens to that bay. The filter's output less the twin's is what the resonance changes; RESONANCE at zero, it is exactly nothing on every board. That difference, band-passed about the filter's own cutoff (state-variable, Q 1, unity at the centre), is the RING; the rest, the bass a ladder loses as it resonates included, stays with the body unfolded. A LADDER at 1 kHz and RESONANCE 0.9 under a 110 Hz saw: the ring's loudest line is the saw's harmonic at 990 Hz.
Cells: WEST COAST's five folding cells and direct path, the same resistors (paper eq. 18), summed by a plain inverting amplifier: no integrating capacitor. FOLD drives the ring into them, 0.55 V to 10 V peak for a ring of unit size (a filter singing), 0.55 · 18.2^x for the knob's x. SYMMETRY adds up to ±2 V at the cells' input, plus the unit's own offset. The cells' output at rest (the offset alone) is subtracted sample by sample; off-centre folding's DC leaves through the card's output capacitor.
Unity: At FOLD's minimum no cell works and the card plays its filter unchanged, only late: IN against OUT −53.2 dB (a LADDER at 800 Hz, RESONANCE 0.6).
Drawn: At twice the card's rate between halfbands. Every knee is a corner found at its instant on a cubic through four samples of the cells' input and drawn band-limited: a singing filter's ring up to A7 at any FOLD, nothing that is not a harmonic of the ring within 68.6 dB; 22 dB or more cleaner than the knees undrawn.
Latency: 17 of the card's samples exactly, the body held back as long, so body and ring meet in phase.
Relay: IN / OUT, eased over 3 ms; OUT is no stage. Switched in, it waits 40 ms for the twin to catch the filter up; changing FILTER opens it on the first bay and closes it on the second.
Matrix: RESO FOLD: the whole of FOLD's range at full amount, added to the knob. RESO SYMMETRY: the whole of SYMMETRY's. Ignored while OUT.
Cost: The twin (its board's own cost) and the cells: about 13 ms of a card-second on a LADDER while IN; nothing while OUT.

OTA VCA BAY

Circuit: A transconductance amplifier: millivolts in, made up after. It rounds the loud off.
Board controls: None.
Bleed: It never quite shuts. What six shut VCAs let through is −76.2 dBFS at most.
Parts drawn: Input offset (2 mV scale); bleed trimmer.
Ages: †The bleed trimmer wanders. No adjustment is provided.

VACTROL VCA BAY

Circuit: A lamp and a photocell whose carriers recombine in pairs, in a two-pole network of the cells, two capacitors and a load, solved exactly. It opens fast, lets go slowly and ever more slowly, and dulls as it closes.
Board control: LET GO: ×⅕ to ×5 about the cell as built (a tenfold fall of nominally 0.15 s: 30 ms to 0.75 s). One recombination rate sets both ways, so a cell that lets go slowly catches the lamp slowly too.
Parts drawn: The cell. Photocells vary widely: this part counts eight times its grade.
Note: The louder board of the two at like settings.

RC ENVELOPE BAY

Circuit: A capacitor through a resistor toward a rail: the attack that pops.
Parts drawn: The timing capacitor, an electrolytic: counts double its grade.
Ages: †Fall to one tenth, 450 ms → 310 ms in forty years. Not recoverable.

CURRENT SOURCE ENVELOPE BAY

Circuit: The same capacitor charged from a constant current: the attack is a straight line. Decay and release remain exponential.
Parts · ageing: As RC.

FUNCTION GENERATOR ENVELOPE BAY

Circuit: Rise and fall, held at the top while the key is down.
Sliders: A is RISE. R is FALL. S is SHAPE: centre is straight lines, one end the pluck, the other the cliff. D is not used.
Timing: RISE 10 ms, FALL 200 ms: top at 10.00 ms, bottom at 210.00. SHAPE bends the segments and leaves the times alone: halfway down it stands at 0.500, 0.215 (pluck) or 0.785 (cliff), and the bottom still comes at 210.00 ms.
Parts · ageing: As RC.

LFO MODULATION BAY

Circuit: A relaxation oscillator: a capacitor between two thresholds. Its triangle is made of gentle curves.
SHAPE: SINE – TRI – SQUARE – S+H
RESET: Restarts the cycle on each key.
Parts drawn: The timing capacitor, an electrolytic: nine cards' LFOs do not run at one rate, and they quicken with age.

FUNCTION GENERATOR MODULATION BAY

Circuit: The function generator, cycling. Usable into audio rate: it tracks volts per octave (three octaves up on its rate: +0.00 cents).
SHAPE: Where the peak falls: RAMP DOWN – TRIANGLE – RAMP UP.
Board control: CURVE: the bend of its segments. Does not move the rate.
Parts drawn: Timing capacitor (film).

SAMPLE AND HOLD MODULATION BAY

Circuit: A switch and a capacitor, sampling the card's noise on the bay's RATE.
SHAPE: How far short of its mark each sample lands: STEPS – CHASING – A RANDOM WALK.
Behaviour: With SHAPE at STEPS each sample lands on its mark; at the far end it moves 3 % of the way. It droops between samples. At audio rates its steps are drawn band-limited at their instant: loudest false line −107.6 dB, against −58.0 simply drawn.
Parts drawn: Hold capacitor (film): the droop, nominally 30 s.

DRAWN MODULATION BAY · NOT A CIRCUIT

What it is: A loop of up to 32 drawn points (each a place in the loop and a level, −1 to +1), played once every LENGTH sixteenths of the song's tempo. The loop's phase is the song's position (in sixteenths, divided by LENGTH), so every card reads the same place; with RESET, the position since the card's key.
Board controls: LENGTH (the board knob): 1 to 32 sixteenths, 16 at its centre. JOIN (the CLOCK switch): STEPS or SMOOTH. PHASE (SHAPE): the loop slid by the knob's distance from where it rests (0.33), −0.33 to +0.67 of the loop. RATE: nothing.
Curves: SMOOTH is a monotone cubic Hermite through the points, around the loop (Fritsch–Carlson slopes): it passes through every point and stays between each two. STEPS holds each point's level, slewed over 1 ms.
Timing: Sixteen steps at 120 BPM change within 0.69 ms of every sixteenth (the slew's half-way point). Kept between the engine's control ticks by the card's own clock.
State: Each bay's loop is saved in the session (engine state version 6, 4017 bytes); a preset restores the instrument's own three loops.

SHIFT REGISTER MODULATION BAY

Circuit: An eight-bit register whose top three bits are weighted into a voltage. It has no rate of its own: oscillator B's cycle clocks it, and whether oscillator A is high is the bit it takes in.
SHAPE: OPEN – LOOP 8 – LOOP 16 (looped through its inverting tap).
Behaviour: Looped it repeats every 8 or 16 clocks. Open, tuning the two oscillators that drive it, it visits all 8 levels and finds no short period.
Parts drawn: The three weighting resistors (carbon): the steps are not quite even, and creep.