603c0dfae8
Measured, not reasoned about. The three pieces the gate is built from are easy to mistake for one, and separating them is most of the page: an envelope follower with Attack and Release as its time constants, a binary decision against the threshold, and a fixed ramp that fades the gain once the decision flips. Attack and Release are the first piece only. They decide when the gate changes its mind, and they cannot reach the fade at all - that is 9.5ms opening and 95.9ms closing at every setting of both pots, which is two flat lines on the chart and the constants in chain_step() coming out where the arithmetic says they should. What the two do reach is worth knowing apart. Release moves the wait from a phrase ending to the gate shutting over six to one, 173ms to 1072ms, and every step of it moves. Attack moves the opening by 2.9ms across its whole travel, on a floor of 17.1ms that is there at every setting - a real control with a small authority. The Attack figure was checked against three thresholds and three definitions of where a note starts, because the first ruler tried gave a much more dramatic answer that did not survive the second one. Also: at the default -70dB threshold this recording never gates at all, because a digital file has a noise floor no room has. The timings are therefore measured at the top of the Gate range, and the page says so. And one control can make the other inert - ten decibels lower, the top of the Release pot stops closing the gate at all, because the envelope never gets down to the threshold before the next note arrives. Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
10 KiB
Signal Chain [CHAIN]
Not an effect, and it does not pretend to be one. It is the two ends of the chain: Trim (−20..20 dB) and Gate (−100..−40 dB) with its Attack (0..10 ms) and Release (50..500 ms) at the front, and Volume (−40..20 dB) at the back. It always runs, it is never in the routing, and it has no wet/dry mix — a gain stage cannot be blended against itself.
The two gains, which are exactly what they say
%%{init: {'themeVariables': {'xyChart': {'plotColorPalette': '#0072b2'}}}}%%
xychart-beta
title "Trim: gain applied to a 440 Hz tone"
x-axis "Trim setting, dB" [-20, -12, -4, 0, 4, 12, 20]
y-axis "measured gain, dB" -22 --> 22
line [-20, -12, -4, 0, 4, 12, 20]
Volume is the same line shifted: −28.0, −16.0, −10.0, −4.0, +8.0 and +20.0 dB at the settings that read that way. Both are exact to the second decimal, and this section exists only so that the rest of the page is read against something known to be boring.
The one wrinkle is at the bottom of Volume. Its range stops at −40 dB, but the pot's zero is an explicit silence rather than −40, so that CC 7 at zero means what a MIDI host means by it. −40 dB is a hundredth of an amplitude, so the step from there to nothing is inaudible.
Trim and Volume are two controls rather than one because the chain between them is full of things that are not linear. Where you sit on a triode curve, where the boost starts folding, how far over the compressor's threshold you are — all of that depends on the absolute level going in, and the DSP is calibrated to a 1 Vrms internal scale that any given guitar may miss by 20 dB either way. Trim puts a pickup onto that scale; Volume then makes it as loud as you want without disturbing any of it. Turn Trim up and Volume down by the same amount and you hear the non-linearity by itself with the loudness held still, which is the only honest way to judge it — louder always sounds better.
The gate is three separate things
Everything interesting on this page is the gate, and it is built in three pieces that are easy to confuse for one:
- An envelope follower on the untrimmed input, with Attack and Release as its two time constants.
- A binary decision: is that envelope above the threshold, or below it.
- A fixed ramp that fades the gain between 0 and 1 once the decision flips.
Attack and Release are the first piece only. They are the detector's ballistics — they decide when the gate changes its mind. They have nothing to do with the third piece, which is where the fade actually happens and which no control on the pedal can reach.
What the threshold is worth
Inputs/BassForLinus.mp3 is a friend of mine playing scales on a bass, 77
seconds of real dynamics, committed unmodified and scaled to −6 dBFS peak
(−25.9 dBFS RMS) for the same reasons the compressor page gives. Its quiet
passages sit around −57 dBFS and its 1st percentile is −78.
%%{init: {'themeVariables': {'xyChart': {'plotColorPalette': '#0072b2'}}}}%%
xychart-beta
title "How much of the take the gate silences"
x-axis "Gate threshold, dBFS" -100 --> -40
y-axis "% of samples silenced" 0 --> 12
line [0.0, 0.0, 0.0, 0.29, 2.01, 5.84, 11.08]
At the default −70 dB this recording never gates at all — 0.29% of it, which is the space between takes and nothing else. That is not a criticism of the default. A digital file has a noise floor no room has; the low end of the range is aimed at a quieter input than any file on disk, and the number worth setting it by is the floor meter, not this chart.
It does mean the rest of this page is measured with the threshold at the top of its travel, −40 dBFS, because that is where both timing controls have something to act on. Measuring a control somewhere it cannot act is how you conclude it does nothing.
Release: how long it waits
Measured as the time from a phrase ending — the input dropping below the threshold and staying there — to the output actually reaching zero. Fourteen such phrase ends in the take.
%%{init: {'themeVariables': {'xyChart': {'plotColorPalette': '#0072b2'}}}}%%
xychart-beta
title "Time from the phrase ending to the gate shutting"
x-axis "Release setting, ms" 50 --> 500
y-axis "measured wait, ms" 0 --> 1200
line [173, 348, 548, 747, 862, 1072]
A six-to-one range across the knob, and every step of it moves. Note that the measured wait is several times the number on the pot: the pot is a time constant, and what is being timed is an exponential decay falling all the way from the note's level to the threshold, which is several time constants' worth. So the knob is a rate, and the wait it produces also depends on how loud the note was and where the threshold sits.
That last dependency is worth seeing, because at a lower threshold the top of the pot stops working altogether:
%%{init: {'themeVariables': {'xyChart': {'plotColorPalette': '#0072b2, #d55e00'}}}}%%
xychart-beta
title "Silenced at Gate -40 blue, at Gate -50 orange"
x-axis "Release setting, ms" 50 --> 500
y-axis "% of samples silenced" 0 --> 14
line [13.34, 11.33, 9.47, 7.62, 6.3, 5.22]
line [7.68, 5.99, 4.68, 3.68, 2.91, 2.63]
On the orange line the gate closes 8 times at 50 ms and 0 times at 500 ms — the envelope simply never gets down to the threshold before the next note arrives. Both controls are live; it is that one can make the other inert, which is the ordinary way two knobs on one detector interact rather than a fault in either.
Attack: about three milliseconds of say
The same measurement the other way round — from a note starting out of silence to the output reaching full.
%%{init: {'themeVariables': {'xyChart': {'plotColorPalette': '#0072b2'}}}}%%
xychart-beta
title "Time from the note starting to the gate fully open"
x-axis "Attack setting, ms" [0, 1, 2, 4, 6, 8, 10]
y-axis "measured delay, ms" 0 --> 22
line [17.1, 17.8, 18.2, 19.0, 19.4, 19.8, 20.0]
Monotonic, and much less than it looks. The whole travel moves the opening by 2.9 ms, on top of a floor of 17.1 ms that is there at every setting. The floor is the fixed ramp plus the detector's own lag; the pot supplies the rest.
So Attack is a real control with a small authority, and the gate's opening speed is mostly not up to it. This was checked against three thresholds and three different definitions of where a note starts, because the first ruler tried gave a much more dramatic answer that did not survive the second one.
The ramp, which no knob touches
%%{init: {'themeVariables': {'xyChart': {'plotColorPalette': '#0072b2, #d55e00'}}}}%%
xychart-beta
title "Fade time. Opening blue, closing orange"
x-axis [Release min, Release mid, default, Attack min, Attack max]
y-axis "milliseconds" 0 --> 110
line [9.5, 9.5, 9.5, 9.5, 9.5]
line [95.9, 95.9, 95.9, 95.9, 95.9]
Two flat lines, and that is the point of the chart. The gate fades in over
9.5 ms and out over 95.9 ms, and it does so at every setting of both
pots. The constants are written into chain_step(): linear(0.01f, mult, 1.0f)
going up and linear(0.001f, mult, 0.0f) coming down, each snapping to its rail
within a hundredth. That predicts ln(0.01)/ln(0.99) = 458 samples = 9.55 ms and
ln(0.01)/ln(0.999) = 4603 samples = 95.9 ms, which is what comes out.
The ramp is about not popping, and the asymmetry is deliberate and was set by ear. It opens quickly because you do not want to lose the front of a note when you start playing. It closes far more slowly because a long drawn-out decay suddenly going away is very noticeable — much more noticeable than the same amount of time spent opening. Whether 9.5 and 95.9 are the right numbers is a fair question and they have never been measured against anything; what they are is two values that sounded right.
An honest doubt about the design
The ramp exists because the gate is a binary on/off decision on the envelope, and a binary decision needs smoothing or it clicks. That is one design and not obviously the best one. The alternative is a gate that has no decision and no ramp in it at all: a multiplier that follows the envelope directly and clamps at unity above the threshold, so the fade falls out of the envelope's own ballistics and Attack and Release would then genuinely be the fade times.
What has kept it as it is, is a worry about amplitude modulation. A gain that tracks the envelope closely is a gain that moves at the signal's own frequency, and modulating a signal by something derived from itself is distortion — the compressor page measures exactly this happening, at 11 dB per octave down, which makes it a bass problem far more than a guitar one. A binary decision plus a fixed ramp cannot do that, because the ramp's shape does not depend on the signal level at all. It is a real trade and it has not been measured; the current design is the cautious side of it.
The trap this page was written around
The obvious way to measure a gate is to compare the total energy of the output against the ungated output. Do not. Over this recording:
| Release | energy vs gate off | silenced |
|---|---|---|
| 50 ms | −0.01 dB | 13.34 % |
| 500 ms | −0.00 dB | 5.22 % |
The gate's behaviour changes by a factor of two and a half and the energy number does not move. It cannot: everything a gate removes is, by construction, quieter than the threshold, so it contributes almost nothing to a sum of squares. An earlier attempt at this reported that Attack and Release "barely change anything" on precisely that evidence. They change a great deal. What was measured was the metric.
Everything above is therefore a timing, or a count, or a fraction of samples — and never an average over the take.
Reproducing this
cd Validation
make bench # a stale bench measures a pedal you no longer have
./analyse-signal-chain.py
Needs ffmpeg for the decode, which is deterministic for a given ffmpeg; the
script prints the sample count, raw peak and scaled RMS first, so if those move
and nothing else changed, the decoder did.
The gate multiplier is recovered by dividing the gated output by the ungated
one, sample by sample — chain_step() applies the trim and the gate as one
scalar multiply, so the quotient is the firmware's own chain.mult exactly.
Where a note starts and ends is decided here, from the input, and never from
the firmware's envelope follower: that is the thing being measured, so it
cannot also be the ruler.