Envelope layer

analyze reads the envelope layer after the pitch layer: the amplitude envelope of each note, pooled over the notes, and the sidechain pump of the stem. The layer writes the envelope group of layers.json; the layer report page lists its fields. The tags are those of the pipeline page.

The stages follow the envelope of a synth: an attack from the note-on to the peak, a hold at the peak, a decay from the peak to the sustain level, the sustain level, and a release from the note-off [fact]. The layer reads the attack, hold, decay and sustain, the time of the note-off knee, and the release and tail after it [fact].

Figures come from cargo xtask eval --layer envelope, 1191 generated parts at 44,100 Hz scored against their recipes, or from the acceptance tests at 22,050 Hz, through the release build and with the true note list [synthetic]. The tables of the release and tail come from one-off generated sets, named where they appear, that are not committed [synthetic]. A real stem adds filters, reverb, bleed and separation artefacts.

The eval is local [fact]. It writes one file, the --json path, and only when that flag is given [fact]. Run it with a release build; a debug build of the library is far slower:

cargo run --release -p xtask -- eval --layer envelope --json records.jsonl

--json writes one record per part, so two builds compare record by record [fact]. A part renders only when --part selects it, and the run holds one part at a time: in a release build the whole set took 53.5 s and 56 s of wall time and 0.6 GB over two runs, against 160 to 179 s and 4.4 GB before the change [synthetic].

Each check pairs a read note with its true note by onset, and a note the layer skips fails its check [fact]. A row that scores only the parts that read a value prints how many read none [fact].

What the layer reads

• The note list after the cleanup, or the notes that --notes gives [fact]. A stem without notes gets values: null with the reason no_note_list and the flag no_notes [fact].
• The mono mix at the native rate [fact].
• The two channels of the stem for the side vote of the tail, when it has two [fact].
• The beat grid of the used tempo, from 0 s, for the pump [fact]. The offset is never estimated: a stem whose first beat is late shifts every beat window [fact].
• A note with no harmonic to read, or that is too short for a track, is skipped and counted in the summary [fact]. A harmonic cannot be read when it lies within 30 Hz of a harmonic of a note it overlaps, or when its band reaches 0 Hz or the Nyquist frequency; the summary counts these as no free harmonic [fact]. A note whose amp proxy peaks at -120 dB or lower is skipped as silent: over a silent stretch, a listed note would read a 0 dB sustain at the tracks’ floor [fact, proposal for -120 dB].
• Every time is audio time from the start of the stem [fact].

Level tracks

Each note is read on a 1 ms hop from 30 ms before its onset to its end [fact]. Three tracks exist:

• Centred RMS over whole periods of the fundamental: one period for a note’s attack, the fewest whole periods that span 2 ms or more on a high note [fact]. One period gave the rise times the issue measured; two periods read a 16 ms rise at 55 Hz as 34 ms [synthetic].
• A sliding DFT of one harmonic over one period of the fundamental, for a note that overlaps no other [fact]. It has no filter transient, so the peak does not overshoot [fact]. A fourth-order low-pass on the band magnitude overshot the peak and read decays long [synthetic].
• The zero-phase band magnitude of one harmonic, for a note that overlaps another [fact]. The low-pass cutoff is half the distance to the nearest harmonic of another sounding note, or to the note’s own next harmonic, clamped to 12 to 40 Hz [fact]. The filter runs forward and backward, so the track does not lag [fact].

The amp proxy is the note’s lowest harmonic among the first three that lies 30 Hz or more from every harmonic of the notes sounding with it [fact]. A filter sweep moves the high harmonics and leaves the low ones, so the lowest free harmonic follows the amp envelope [fact]. On a 110 Hz saw under a closing low-pass, the sum of harmonics 1 to 3 read the fall 8 % short, and the fundamental alone within 10 % [synthetic]. Octaves and unisons leave the upper note no free harmonic; the layer skips it and has no residual method [fact].

Levels are dB from the note’s peak on the amp proxy, read no lower than -60 dB [fact].

Attack

• attack_s is 1.25 times the 10 to 90 % rise of the linear amplitude: the full 0 to 100 % time of a linear ramp [fact]. The rise reads the RMS track for a note that overlaps no other, and the amp proxy for one that does [fact].
• The rise ends at the attack’s top: the first frame from the onset that the level exceeds by less than 1 dB over as long again as it took to rise to it from under 10 % of it, and at least over the shortest rise the track can tell, the same figure as the upper bound’s below [fact]. Without that floor, a wobble of the window early in the rise read as a top [synthetic]. The 10 and 90 % shares are of the highest frame over that span [fact]. A slow attack has no top before its end, since a linear ramp keeps rising by more than 1 dB until 1 dB below its peak [fact].
• The peak of the whole note is no top: a real note swells or ripples after its attack [fact]. At 110 and 261.63 Hz, a 50 ms attack that swells by 3 dB over 600 ms read 514 ms against the peak and reads 52 to 55 ms against the top; at 261.63 Hz, a 10 ms attack under a 6 dB ripple at 5 Hz read 30 ms and reads 12.5 ms [synthetic].
• A swell finds no top when it rises 1 dB or more over the attack’s own length [fact]. A 300 ms attack under a swell over 0.8 s reads 324 to 370 ms up to 2.9 dB and 640 to 706 ms from 3.1 dB, at 55 to 440 Hz and 22.05 to 48 kHz; at 3 dB it reads either [synthetic]. The 50 ms attacks above lie far from that edge [synthetic].
• The factor of 1.25 holds for a linear rise, so a rise that flattens near its top reads long [fact]. Loud isolated bass notes on real stems read 141 and 156 ms where the level crosses -1 dB at 103 and 105 ms and -3 dB at 72 and 42 ms, on 9 and 22 notes [fact]. Loud isolated keyboard and synth notes on real stems read 15 and 20 ms against -1 dB crossings at 18 and 14 ms [fact].
• A periodic wave gives one amplitude sample per period, so a rise under about 1.5 periods cannot be told from a shorter one [fact]. The attack is an upper bound when the rise is shorter than 1.5 RMS windows, or, on the amp proxy, shorter than 0.98 over its cutoff, which is twice the rise of the filter on an instant step [fact]. attack_is_upper_bound is set when more than half the pooled attacks are upper bounds [fact]. attack_s then still reports the read, and a preset should not take it [fact]. Each note record carries its own attack_upper_bound [fact].
• #69 writes an attack from 1.5 periods. The layer tests the rise, 0.8 of a linear attack, so its flag covers attacks up to about 1.9 periods, which is 45 ms at 41.2 Hz [fact]. It departs from #69 on the safe side: a 2.2 period attack is the shortest in the tests that reads its time [synthetic].

The attack ladder: one saw note with a linear attack, read attack in ms, bound for an upper bound [synthetic]:

Every attack over 4 periods reads within 15 %, and every one under 1.5 periods reads as a bound [synthetic].

Hold, decay and sustain

• hold_s is the time from the first frame within 1 dB of the peak to the start of the decay, 0 when under 10 ms [fact, proposal for 10 ms].
• decay_s is the time between the first frames after the peak at which the level falls through 10 % and 90 % of the sustain level in dB, linear between frames, divided by the gap between the two shares [fact]. The first share is at least 0.5 dB down, so ripple at the peak does not end the hold, and it rises above 10 % for a sustain shallower than -5 dB [fact]. The decay starts that share of its time before the first share’s crossing [fact]. A regression in dB from the peak read the decay 6 to 22 % long, since the knee at the sustain level bends the line [synthetic].
• sustain_db is the median of the last 30 % of the held part [fact]. The held part runs from the first frame within 1 dB of the peak to the note-off knee, or to 25 ms before the note’s end without one [fact].
• Decay and sustain are null when a note with a knee holds for less than the attack, the hold and three decay times [fact]. A note without a knee, such as a pluck, sustains at its end level [fact].
• fit_residual_db is the median over the pool of the RMS in dB of each held part against the model: 0 dB over the hold, a fall linear in dB to the sustain level over the decay, then the sustain level [fact].
• ripple_db is the median, over the pooled notes whose sustain is observable, of the 90th minus the 10th percentile of the sustain window after its line [fact]. Unison and chord beating show here [fact].
• A Levenberg-Marquardt refine of a piecewise linear model over the pooled dB curve, with a floor, a peak and a fixed note-off, is not applied [fact]. Fitted from each note’s top with the peak free, it moved the decay error on 72 lines with decays of 50 to 600 ms from a median of 4.4 % and a 90th percentile of 8.7 % to 9.9 % and 26 %, and left the median sustain error at 0.24 dB [synthetic]. A fit in dB trades the two ends of a fall against each other, which the read at 10 and 90 % of the fall does not [fact].

On a grid of 240 lines of eight saw notes, decays of 50 to 600 ms, sustain levels of 0 to -24 dB, holds of 0 and 30 ms and releases of 20 to 300 ms [synthetic]:

A decay linear in amplitude starts slowly in dB, so its first 0.5 dB reads as hold: up to 104 ms with no true hold [synthetic]. The fit assumes a decay linear in dB, and its residual rises on the other law [fact].

Plucks on 55 and 220 Hz with an exponential decay and no note-off knee sustain at their end level: -57 dB for a time constant of 150 ms, -21.5 dB for 400 ms and -8.6 dB for 1 s [synthetic].

Note-off knee

The knee is the time the note-off starts the release [fact]. It is read on the linear amplitude of the amp proxy, from the first frame within 1 dB of the peak to 25 ms before the note’s end [fact]:

• At each split, a line over up to 100 ms before it and one over up to 200 ms after it are fitted against one line over both [fact]. The right line stops where the level falls under 2 % of the mean before it, so silence after the release does not flatten it [fact].
• A split counts when the right line is steeper by half the mean before it per second, falls by half that mean over its side, and the two lines leave at most half the squared error of one [fact, proposal for the shares].
• Splits that count in a row form a corner, and within a corner the split with the largest gain wins [fact]. A hold that breaks into a linear decay forms an earlier corner; the largest gain over all splits took it for the note-off [synthetic].
• A later corner replaces an earlier one unless it looks like a fade of a reverb tail, whose fades form corners too [fact]. Taking the last corner put a knee over 1 s past the note-off [synthetic]. Two tests tell a fade from a note-off [fact, proposal for both]:

  • The level between the corners bends: the median size of its second difference in dB, 10 ms each way, is over 0.4 dB. A decay and a sustain are near 0 dB, as both are straight in dB, however short the sustain.

  • The level after the corner rises by more than a twentieth of the mean before it. A note-off falls for good. The rise reads the first 20 ms as they are and the mean over every 20 ms span, since a noise floor wobbles over the silence after a release [fact, proposal for 20 ms]. The rise and the read of the fall stop before a next note that overlaps, by the frames that the band’s filter rings ahead of its attack, and half a level window before the end of a note that overlaps no other [fact]. A later corner past the stop reads no rise, so it replaces an earlier one whenever the bend allows it [fact]. That keeps the note-off of a note held over a shorter one [synthetic].

  • A later corner past the stop replaces nothing when the note has ended and the level has come back [fact]. The note has ended when the mean over the last 10 ms before the stop lies under a fiftieth of the earlier corner’s level, -34 dB, the floor of the release side. The level has come back when the mean over the 100 ms before the later corner lies at least a quarter above it, and the left line’s end lies above it too [fact, proposal for the quarter]. The corner is then the next note’s. Without this test, a long gap after a note-off took the next note’s corner, since the bend over silence reads near 0 dB (#312) [synthetic].

  • Each read guards one case [synthetic]. A held sustain under the floor, with its note-off past the stop, reads a mean near 1 times the stop level: a ripple of 1 % or a rise of 1e-6 a frame must not decide it, so the mean must lie a quarter above. The 10 ms mean at the stop keeps a ripple of 25 % over 10 frames from deciding it too. A transcribed note on the generated tally rises over the last 10 frames into its note-off: its line ends above the stop level, while its mean reads 1.08 times it. A note that falls straight into a note-off past the stop has a mean over a quarter above, while its line ends under it. A next note after a silent gap reads mostly 1 to 3 times the stop level on the bass line below. A quarter keeps 8.9 % of the long notes late under the pump there, against 7.1 % at a tenth and 13.0 % at a half.

  • Under a pump that strips, the test also reads the note’s level as it was before the strip, and the later corner replaces nothing when either level shows the note ended and the level come back [fact]. The strip lifts the frames in a beat’s dip by up to the pump’s depth, and the last 10 ms before the stop can lie in a dip while the next note’s band already rings ahead of its attack. Read on the stripped level alone, the stop then lay over a fiftieth of the hold, or the next note’s corner lay under a quarter above the stop, and the knee took the next note’s corner (#323) [synthetic]. On the long notes of the bass line below, the strip put 156 knees over 15 ms further off than the same signals read unstripped, by a median of 0.56 s [synthetic]. Read on the level before the strip alone, the ring in the dip can come back by under a quarter there while the stripped level comes back by more: under a 12 dB pump with list ends 5 ms past the next onset, 2 of 2137 notes then read about 0.5 s late [synthetic].

  • Notes on the signals that strip, against the same signals generated dry, mean error and notes over 150 ms off [synthetic]:

    Pump, notes, list end past the next onset	Notes	Dry	Test on the stripped level	This rule
    5 dB, 1.37 to 2.74 s, 20 to 200 ms	2757	40.8 ms, 148	66.2 ms, 249	33.9 ms, 117
    5 dB, 0.34 to 1.37 s, 20 to 200 ms	2818	10.9 ms, 35	14.5 ms, 53	10.4 ms, 28
    5 dB, 1.37 to 2.74 s, 5 ms	2748	17.9 ms, 56	24.3 ms, 83	20.1 ms, 63
    5 dB, 0.34 to 1.37 s, 5 ms	2854	5.8 ms, 11	8.0 ms, 17	7.3 ms, 13
    8 dB, 1.37 to 2.74 s, 5 ms	2065	19.8 ms, 47	29.4 ms, 74	22.7 ms, 53
    12 dB, 1.37 to 2.74 s, 5 ms	1913	17.9 ms, 39	37.9 ms, 86	23.9 ms, 45
    24 dB, 1.37 to 2.74 s, 20 to 200 ms	1885	41.3 ms, 101	314.3 ms, 853	96.5 ms, 253

    Only the 5 dB pump with list ends 20 to 200 ms past the next onset reads no worse than dry. With list ends at the next onset, no note changes. No note reads over 15 ms worse than the test on the stripped level, except one at 24 dB, which reads 0.43 s early against 0.40 s late: there the stripped track holds no corner at the note-off, and both knees take another corner [synthetic]. The strips do not change [synthetic].

• When the level stays at 85 % or more of the left line’s end for over 10 ms more, the knee is where a line over its fall from there to half that level crosses that level [fact, proposal for 85 %]. A hold that wobbles under a reverb can win a split 50 to 100 ms before the note-off, and an exponential release can win one past it [synthetic].
• Of the eval’s knees within 15 ms, a sustain shorter than its decay reads 120 of 144 and a dry tremolo with a release of 200 ms or more reads 12 of 64, against 108 and 9 at commit 057d63c, which took the last corner [synthetic].
• The knee is where the left line crosses a line over the first 10 ms after the split, or the split itself when the crossing lies outside the two lines [fact]. A step down followed by a slow fall crossed 20 ms before the search started [synthetic]. The crossing of the two fitted lines read a linear release late, since the right line averages the release’s tail [synthetic].
• No split counts on a pluck that decays at one rate, and its knee is null [fact].

note_off_offset_s is the note’s end in the note list, or the stem’s end when that comes first, minus its knee, over the pooled notes with a knee [fact]. On the grid, all 1920 knees lie -2.0 to +0.01 ms from the true note-off [synthetic]. Read in dB, a 200 ms linear release placed the knee 168 ms late, because a linear fall in amplitude bends in dB [synthetic].

Release and tail

After the knee, relative to the median level over the 50 ms before it, or since the note’s onset when that is nearer, the level follows a linear release plus a decaying tail [fact]:

env(t) = max(1 - t / release_s, 0) + tail_weight * 10^(-3 t / tail_rt60_s)

• The fit is a simplex on the squared error in dB, from 4 releases and 3 RT60s as starts, down to -55 dB [fact]. It keeps every frame for 200 ms and every fifth after that, weighted to count the same [fact]. The project has no least-squares crate, so it uses the simplex of the pitch fits [fact].
• The fit agrees with scipy.optimize.least_squares on the curves of the golden vector tail-fit, within 1 % and 2 ms or 0.002 dB [synthetic]. cargo xtask golden regenerates it [fact].
• It reads the one-period RMS, not the amp proxy: a reverb of one harmonic fades deeply, and many harmonics fade apart [synthetic]. A note that overlaps another reads the band of the amp proxy [fact].
• It stops at the note’s end or the next note that overlaps it, half a level window before that note [fact]. At 41 and 55 Hz that window otherwise reads the next note and left residuals of 6 dB on dry lines [synthetic].
• A note with no knee has no fit, so a pluck reports no release [fact]. A given note list that ends at the note-off shows no knee and reads no release [fact].

The write rule reads the medians over the pooled notes with a fit, and never the release, which is what fails to fit [fact]:

• A tail_weight over 0.5 or a residual over 3 dB writes no release_s, and release_confidence reads low [fact, proposal for 3 dB]. Both still report the tail [fact].
• A written release_s reads low, with tail_wobble, when the median residual is over 2 dB and the median second difference of the level in dB over the 300 ms before the knee, 25 ms each way, is over 0.3 dB [fact, proposal for all three]. A tremolo carries on through the release, which the fit cannot follow [synthetic]. Of 2000 dry tremolos of 0.3 to 3 dB at 1 to 12 Hz, 727 read medium and 139 of them lay over 50 % off before this rule. It lowers 96 of the 139 wrong ones and 141 of the 588 right ones, which leaves 43 of 490 [synthetic]. On 2000 stems each it lowers 18 wrong and 11 right short sustains, and 3 wrong and 3 right reverbs, 1 wrong and 3 right on the first 1000. It lowers none of the plain dry or legato stems and 2 wrong chords [synthetic]. The rest of the move in the reverb figures below comes from the knee rule [synthetic]. Its effect depends on the recipe: another set of generated tremolos, with a wrong share of 23 %, lost 66 of its 637 right and 63 of its 189 wrong medium releases, for a wrong share of 18 % [synthetic].
• tail_rt60_s reads over the notes with a tail_weight of 0.05 or more whose frames span a 15 dB fall of it, and is null, with tail_light, under a median tail_weight of 0.05, because a dry note often leaves a little weight whose RT60 is noise [fact, proposal for both].
• tail_rt60_s is null, with tail_smooth, when the median tail_weight is over 0.5 and the median residual is at most 1.1 dB [fact, proposal for 1.1 dB]. A dry exponential release fits the tail term alone, at a weight of about 1 and an RT60 equal to its fall, while a reverb’s level wobbles [synthetic]. Of 15 dry falls of 60 dB over 0.1 to 1.5 s at 55 to 220 Hz, 14 read this way, and the fall of 0.1 s at 55 Hz stays a false RT60 at a residual of 2.7 dB [synthetic]. A curved release model waits for the calibration of the decay law under #69 [fact].
• tail_rt60_s is null, with tail_band, when a note that overlaps another reads a median RT60 under 6 periods of its narrowest band’s cutoff [fact, proposal for 6]. The band rings by itself: a dry chord with a release of 20 or 50 ms read 0.13 to 0.2 s on 18 of 18 stems before this rule and on none after it [synthetic]. The same chords through a reverb read an RT60 on 13 of 18 stems at a true 0.3 s and 36 of 36 at 0.6 and 1.5 s [synthetic].
• release_confidence is null when no pooled note has a fit [fact].

The set: 4000 stems sampled over 41 to 440 Hz, releases of 20 to 800 ms, dry or with an RT60 of 0.3 to 3 s at 0.05 to 0.8 wet, three timbres, 1 to 6 notes of 0.3 to 1.2 s, gaps of 0.2 to 1.5 s, sustains of 0 to -12 dB, mono or wide reverbs, and a reverb whose highs fade first [synthetic]. Shares hold within about 2 percentage points at this size. On it:

• The median written release over its truth on dry stems is 0.98 to 1.12 by release, with the 1.12 at 20 ms [synthetic].
• Over the true RT60, the median read is 1.16 at 0.3 s, 1.02 at 0.6 s, 0.95 at 1.5 s and 0.95 at 3 s, and 33 to 44 % lie within 10 % [synthetic].
• tail_weight over 0.5 holds out 4.8 % of stems at a true 0.05 wet, 30 % at 0.4 and 55 % at 0.8 [synthetic]. Of the 661 reverb stems over 0.5, 79 read as smooth and lose their RT60 [synthetic].
• A knee lies within 15 ms of the note-off in 98.8 % on dry stems and 69.6 % under a reverb, against 98.8 % and 42.1 % at commit 057d63c [synthetic].
• On a line of 6 notes with a release of 50 ms at 0.15 wet, over 60 noise reverbs each, the RT60 lies within 10 % on 53 of 60 at 0.6 s and 56 of 60 at 1.5 s, with misses from 0.529 to 0.692 s and from 1.289 to 1.768 s, and the release reads 43 and 44 ms [synthetic].

Votes that a tail is reverb

tail_votes counts five signs, each over the pooled notes with a fit and by majority where it reads notes, and null where nothing could be read [fact]. All thresholds are proposals [fact].

A dry stem reads none of the first three, as its tail ends with the release [synthetic]. Two or more votes pass on none of the 1372 dry stems and on 68 % of the 2628 under a reverb [synthetic]. A noise floor reads as a tail: on dry lines at 55 to 220 Hz under noise at -50 and -40 dBFS, 54 of 54 stems pass two votes [synthetic]. tail_is_reverb stays false: a reverb is stated only when the votes agree and a space layer reads medium or better, and no space layer exists yet [fact].

Pooling and confidence

• The pool leaves out a note whose peak lies 12 dB or more below the peak of a note it overlaps: a quiet second voice, such as another part’s bleed or a ghost note, has an envelope of its own [fact, proposal for 12 dB]. Eight A2 notes decaying over 300 ms, each over an E3 18 dB quieter decaying over 50 ms, read the A2 decay within 20 % with the gate; the E3 notes would otherwise fill half the pool [synthetic].
• Of the other notes, the pool holds those whose length to the knee, or to the end without one, lies within a factor of 2 of their median length, and whose pitch lies within 12 semitones of their median pitch [fact, proposal].
• Each statistic is the median and the interquartile range over the pool [fact]. It reads low over fewer than 3 notes, or with an interquartile range above half its median [fact]. Its reasons are too_few_notes and relative_spread, and the attack adds upper_bound_share [fact]. A median of 0 under an interquartile range above 0 has no ratio, so the statistic reads low with zero_median, that range, in place of relative_spread [fact].
• level_spread_db is the 90th minus the 10th percentile of the full-band levels of the pooled notes, null under 3 pooled notes with a level and always low: no stem has tested the rule [fact, proposal]. A note’s full-band level is the peak of the centred RMS of the mono mix over one period of its fundamental, on a 1 ms hop, from its onset to its note-off knee, or to 50 ms before its end in the list without one, never past the next later onset on a mono line [fact]. A mono line is one whose voices layer reads at most one voice at a time, or counts none, when --profile pad did not run the notes step; so the layer reads the levels after the voices layer [fact]. The amp proxy’s peak_db reads one harmonic per note, so two notes on different harmonics do not compare; the full band does (owner decision, 2026-11-05) [fact]. Notes 0, 3, 6 and 12 dB apart read 0.1, 3.0, 6.0 and 12.0 dB [synthetic]. On the generated chords of equal notes, the amp proxy read 4.6 to 7.8 dB and the full band reads 0.9 dB [synthetic]. On a chord the full band is the mix, so it cannot tell two chord tones of different levels apart [fact].
• The group’s own confidence is medium with 3 or more pooled notes, else low, and no estimate when no note was read [fact].

Sidechain pump

A sidechain compressor keyed by a kick ducks a held part on every beat and lets it recover until the next [fact]. The layer reads the dip on the beats that one held note covers, and strips it before it reads the notes [fact].

• Track. The full-band centred RMS in dB over two periods of the lowest note, on a 1 ms hop [fact].

• Beats. A beat of the grid counts when the held part of one note covers it from 50 ms or more before its start to its end [fact]. A pluck struck on the beat never counts, nor a release at the end of a beat [fact]. The held parts come from a first read of the notes without the pump, and the notes are read again with it stripped [fact]. Plucks on every beat read 13.9 dB of ducking without this rule [synthetic].

• Curve. Each counted beat is binned into 64 phase bins and taken relative to the 90th percentile of its bins; the curve is the median over the beats [fact]. The pump needs 4 counted beats; with fewer it is null [fact].

• Period. A sidechain follows the song’s tempo, and a stem’s tempo may be off by 1 or 2 % [fact]. Over 32 beats a 1 % error moves the duck a third of a beat, so its beats no longer fold onto one curve [fact]. The layer searches periods within 2.5 % of the grid’s for the one whose counted beats fold onto the deepest mean curve, over up to 64 beats of the longest run of counted beats and then over all of them, in steps that move the last beat of the span by 1 bin [fact, proposal for 2.5 %]. The second stage searches one step either side of the first, so the reach follows the longest run of counted beats: up to 2.73 % at 4 beats, 2.81 % at 5, 2.60 % at 6, 2.68 % at 7, 2.66 % at 10, 2.58 % at 20 and 2.51 % at 64 [fact]. Of 72 ducks up to 2 % off the grid over 32 and 64 beats, 15 locked and stripped on the grid alone, and all 72 do with the search [synthetic]. pump_bpm reports the tempo of the read that stays [fact]. The search’s read must lock to the beat, and it replaces the grid’s read as follows [fact, proposal for 0.9, 0.15 dB, 60 cents, 3 bins and half a window]:

  • The grid’s read follows the notes: always, with no shape test.
  • The grid’s read locks to the beat: when both reads strip or neither does, the search’s fold error must be under 0.9 of the grid’s and 0.15 dB lower. The fold error is the standard deviation of the level minus the curve over the counted beats, each beat about its own mean, so a fade or a level step between beats does not count as misfit [fact]. When only one read strips, as a slower period counts fewer beats, the search’s read must be the one that strips and have the lower fold error. A 12 dB duck 2.5 % off over 16 beats reads 4.4 dB on the grid and 9.8 dB at its own period [synthetic]. Depth is no test: the search deepens a duck on the tempo by fitting a chord’s beating, and on the flat level of the 76,836 stems of Limits a gain of 1.5 dB moved 15 ducks on the tempo, against 3 with this rule [synthetic]. A sub’s fold error is small enough that a share alone moved ducks on the tempo at 174 BPM, and the sustain with them by up to 2.6 dB [synthetic].
  • The grid’s read runs free: when the line lies within 60 cents of a division, and the search’s curve falls faster than it recovers and takes long enough from half its depth back to a quarter: 3 bins, and half the level window in bins. A gate near a division folds onto one curve as well, but comes back at once, within the smear of the window [synthetic].
  • The grid’s read reads none: when the search’s curve falls faster than it recovers and takes 3 bins from half its depth back to a quarter. A gate off the tempo often reads no lock on the grid, and the level window’s share is left out because it costs real ducks under a low note; see Limits [synthetic].

  The set behind the numbers below holds 123,840 generated signals: a three-note chord from 55, 110 and 220 Hz, 60 to 174 BPM, runs of 8.9 to 32 beats, four phases for ducks and two for gates and saw tremolos. Each cell counts the signals that strip, from one build. The columns differ only for a grid read that runs free: it stays free, it takes any search read that locks, or it takes one under this rule. A free read never strips, so this rule reads no more than the column before it [synthetic].

  Signal	Off the tempo	Signals	Free read stays	No free rule	This rule
  Duck, release 80 ms or more	up to 2.5 %	47520	36008	36107	36078
  	3 %	8640	1343	5028	4883
  	3.5 %	8640	169	4132	1716
  	4 to 5 %	17280	122	4717	128
  Duck, release 30 ms	up to 2.5 %	15840	7440	7462	7453
  	3 %	2880	622	801	734
  	3.5 %	2880	426	612	459
  	4 to 5 %	5760	160	287	160
  Square gate	3 %	2880	21	768	25
  	3.5 %	2880	42	667	47
  	4 to 5 %	5760	14	603	14
  Saw tremolo	3 %	720	71	498	498
  	3.5 %	720	0	352	148
  	4 to 5 %	1440	0	293	0

  The first read’s strips on gates come from their own lock on the grid. A gate up to 2.5 % off strips either way; see Limits [synthetic].

• pump_depth_db is minus the curve’s minimum [fact].

• pump_recovery_s is the time from the minimum until the curve comes back within 1.5 dB, going on over the beat’s wrap, so a duck that sits late in the beat recovers into the next [fact]. It is null when the curve does not come back within one beat [fact].

• pump_tau_ms is the recovery over $\ln (\text{depth}/1.5)$, the time constant of an exponential recovery in dB, and null unless the pump locks to the beat: a dip that follows no beat has no recovery to model [fact].

• pump_beats counts the beats behind the curve [fact].

pump_locked_to names what the dip follows, tested in this order [fact, proposal for the thresholds]:

1. note: the beats with a note onset inside dip 3 dB or more, and the others under 1.5 dB, each group of 2 beats or more. An onset up to 50 ms before a beat belongs to that beat, as the transcriber places onsets a few milliseconds early [fact].
2. free: the level swings 1 dB or more at a rate of 0.5 to 20 Hz that lies 50 cents or more from every note division, read on the modulation spectrum over the longest covered span [fact]. It comes before the beat: a 5.3 Hz tremolo over 17 beats at 128 BPM left a 3.6 dB dip in the median curve that passed the beat test [synthetic]. A duck’s strongest line lies on the beat rate, so it reads free when that rate lies 50 cents or more from every division of the grid [fact]. That holds 3 % off the tempo, and over a short span from 2.5 %, where the line reads 50 to 52 cents [synthetic]. The period search then decides, as above [fact].
3. beat: the curve dips 3 dB or more in one run of bins half its depth down, and falls into its dip within 8 bins, reading on into the beat before and not round the beat’s wrap. The odd beats and the even beats must each do the same on their own median curves, to half its depth at its dip. Half the beats must fall by half its depth into its dip: from their highest bin over the 8 bins before the 3 bins either side of it to their lowest within those. A note that decays across the beat falls over most of it, and fails the 8 bins [fact]. The one run stops a tremolo at a division of the beat [fact]. A level that rises over each bar or two beats and drops back makes every beat’s curve start low, and round the wrap that read as a fall on every beat: 12 dB per bar and 6 and 12 dB per two beats all stripped [synthetic]. Those falls only come on the first beat of each bar or pair, so the rule reads no pump there [synthetic].
4. none otherwise.

The layer strips the curve from the note tracks only when it locks to the beat over 8 counted beats or more, and sets pump_stripped [fact, proposal for 8]. A stem can duck in one section only, so a note takes the strip only when the median fall of the beats over it reaches half the curve’s depth [fact]. With fewer beats, half of them is two or three, and other sounds on the beat pass the lock: a sine sub under a kick on every beat, whose tail beats against the sub, read 3.4 to 4.6 dB locked to the beat over 4 or 5 beats [synthetic]. On 1375 runs over the generated stems of the pitch layer, which hold no duck, 4 read such a lock, and none is stripped [synthetic].

A duck’s dip can read as a note-off knee in the first read and cut the held parts short [synthetic]. A read of the held parts that finds no pump, or one that locks to the beat over fewer than 8 beats, is therefore counted again over each note to 25 ms before its end, and strips when that count locks to the beat over 8 beats or more [fact]. A 6 dB duck on the chord at 174 BPM under noise at -20 dB read a false knee on each of its three notes and was not stripped; counted over the notes, it strips, and no knee remains [synthetic].

A constant three-note saw chord reads 1.64 to 1.94 dB from its own beating, so the 3 dB floor sits above it [synthetic]. Over all 1191 parts, all 826 locks read as built [synthetic]. A part with no pump reads as no lock, and a 3 dB duck counts as right when it locks to the beat or reads no pump, never when it reads free [fact].

Depth bias

The read depth is shallower than the duck, and the bias depends on the duck’s shape [synthetic]. A duck whose gain recovers exponentially, $1-(1-g_0)e^{-t/\tau }$, has a sharp minimum in dB; the RMS window and the 64 bins round it off [fact]. A cosine dip has a round minimum and reads near its depth [synthetic].

Measured minus true depth on a held saw chord and a held 55 Hz sub, two seeds, noiseless and with white noise at -30 and -20 dB, releases of 50, 80, 150 and 300 ms; median and range over 48 parts per cell [synthetic]:

• No duck reads 0 to 0.09 dB on the sub, and 1.64 to 1.94 dB on the chord from its beating [synthetic].
• Noise at -20 dB fills the dip: a 12 dB duck reads 1.5 dB shallower than without noise [synthetic].
• At 128 BPM on the noiseless chord, the bias over the releases is -0.2 to -5.5 dB for a duck linear in dB, -0.3 to -7.2 dB for one with a 5 ms fall, and +1.2 to -2.6 dB for a cosine dip [synthetic].
• The bias changes with the shape at the same depth, so no single factor corrects it, and the layer reports the depth as read [fact].

The recovery over the true time back within 1.5 dB, at depths of 6 dB or more, is 0.64 to 1.44 by release on the chord and 0.55 to 0.80 on the sub [synthetic]. The shallower read reaches 1.5 dB sooner on the sub, and the chord’s beating moves the crossing [synthetic].

Limits

• An attack under about 1.9 periods of the fundamental is an upper bound, and at 41.2 Hz that covers attacks up to 45 ms [fact].

• A decay linear in amplitude reads part of its start as hold [synthetic].

• The upper note of an octave or a unison has no free harmonic and is skipped [fact].

• A resonant filter that closes onto the fundamental changes the amp proxy itself [fact].

• A release that falls, flattens and falls again reads its knee at the second fall, since a later corner replaces an earlier one to pass over a decay [synthetic]. Its sustain window then reaches into the first fall [fact].

• A release over about 400 ms shows no knee, because its right line must fall by half the held level over 200 ms: no dry 800 ms release reads [synthetic]. Under a reverb, 28 of 401 such stems wrote a release, 4 of them within 50 %, from a knee in the tail [synthetic].

• Under a reverb, 30.4 % of the knees on the 4000 stems lie over 15 ms from the note-off [synthetic]. A fade in the tail with a smooth level before it and no rise after it still replaces the note-off [fact].

• A tremolo bends too: a swing of 1 dB at 12 Hz reads 0.38 dB and 6 dB at 5 Hz about 0.4 dB. When an earlier decay forms a corner, the note-off of such a sustain can lose to it [fact].

• The bend and rise rule loses some notes that commit 057d63c read within 15 ms, on a one-off sweep of 1000 generated stems a set, and gains more [synthetic]. Commit 2d63f2e holds that rule with its stop, and the last column adds the test of the level at the stop. Worse and better count the notes of the last column against 057d63c:

  Set	Notes	057d63c	2d63f2e	This rule	Worse	Better
  Plain dry	2986	2453	2453	2453	0	0
  Short sustain	2698	2017	2064	2064	0	47
  Tremolo	2991	732	777	777	107	152
  Legato	3011	2962	2967	2967	0	5
  Reverb	3042	1220	1662	1662	25	467
  Chord	1176	820	841	861	6	47
  Noise at -35 dBFS	2898	2010	2065	2065	82	137
  Noise at -40 dBFS	2898	2200	2215	2215	33	48
  Noise at -50 dBFS	2898	2286	2315	2315	0	29
  Noise at -60 dBFS	2898	2306	2327	2327	0	21
  Legato, note end 10 ms past the next onset	1583	1194	1201	1222	0	28
  Legato, note end 20 ms past the next onset	1583	1220	1224	1229	1	10
  Legato, note end 40 ms past the next onset	1583	607	662	1091	0	484

  No note of any set reads worse than at commit 2d63f2e [synthetic]. Every column comes from the same sweep, run at each commit. The three legato rows list every note up to the next onset and the time named, on the legato notes of the plain set. They replace rows read on an earlier version of the sweep, which this one does not reproduce at commit 057d63c: 1227, 1172 and 1015 there.

• On the same sweep, 600 stems a row and 964 notes, a note list that runs further past the next onset [synthetic]:

  List end past the next onset	057d63c	2d63f2e	Worse	This rule	Worse
  120 ms	378	412	0	639	0
  220 ms	386	426	0	675	0
  420 ms	387	431	0	669	0

  Worse counts against 057d63c. These rows replace a table read on an earlier version of the sweep, which put 604, 609 and 589 at commit 057d63c. The rows without the stop are not measured again.

• Other generated recipes still read knees over 15 ms worse than commit 057d63c [synthetic]:

  Recipe	Notes	Worse	Better
  Mono bass line at 175 BPM, 14 notes a signal, under a 5 dB pump left unstripped, see #313	3570	11	2652
  The same line, medium notes, see #313	3530	31	2401
  A tremolo under a reverb	1500	42	270
  A next note 15 dB louder	1419	3	-

• On that bass line, with a gate of 55 to 90 % and list ends 20 to 200 ms past the next onset, over 500 signals, knees over 15 ms late [synthetic]:

  Notes	057d63c	2d63f2e	This rule	Stripped notes tested before the strip
  1.37 to 2.74 s, under the pump	81.4 %	53.9 %	8.9 %	5.2 %
  0.34 to 1.37 s, under the pump	61.4 %	11.6 %	4.2 %	3.5 %
  1.37 to 2.74 s, dry	80.9 %	53.5 %	5.4 %	5.4 %
  0.34 to 1.37 s, dry	60.8 %	11.3 %	3.2 %	3.2 %

  Both pump rows above and these rows come from this line. Notes count where both commits read a knee. The last column tests a stripped note’s level before the strip, see the rule above (#323). The long-note row replaces one read on another version of the line, 3038 notes with 44 worse, which this one does not reproduce.

  Dry, no note reads worse than at commit 2d63f2e. Under the pump, 25 long and 25 medium notes that commit 2d63f2e read right leave the 15 ms, 19 and 15 of them early [synthetic]. Of these, 21 and 13 lie in signals whose pump read changes: the pump strips on 42 and 7 fewer of the 500 signals, and on 21 and 4 more [synthetic]. The pump read counts beats over the held parts that the first read’s knees bound, so a knee that moves changes the parts it counts, see #313 [fact].

• A next note’s band rings ahead of its attack, and the 10 ms before the stop can read that ring over a fiftieth of the hold, with or without a pump [synthetic]. Then the knee takes the next note’s corner: on the long dry notes of that bass line, 188 of 3570 read over 150 ms late, and on long stripped notes 117 of 2757 [synthetic]. Read as the lowest 10 ms since the first corner, the stop cut the dry ones to 0, but lost the note-off of a filter that closes past the band’s harmonic before a next note that starts at the note-off, on 2 of the 1405 tally runs, 0.57 s early [synthetic].

• A sustain under -34 dB of the earlier corner’s level, with its note-off past the stop, loses that note-off to the decay corner when its level comes back without a next note: the knee reads 0.46 to 0.8 s early, where commit 2d63f2e reads it [synthetic, from generated probes]. This happens in two shapes:

  • A rise of about 1.3 times, 2.3 dB, or more over the last 100 to 400 ms before the note-off. The rise that loses it is 2.0 times over 60 frames, 1.5 over 100, 1.4 over 200 and 1.3 over 400.
  • A swell like a tremolo of ±15 % or more at 2.5 Hz or slower. At ±25 % over 400 frames, 12 to 20 of 96 cells lose it with the stop 150 to 200 frames before the note-off; at ±15 % over 400 frames, 24 of 96 with the stop 200 frames before.

• A next note at 1.4 to 1.7 times the level of a silent gap still takes its own corner, as commit 057d63c and 2d63f2e do [synthetic]. On a gap at 0.01 with the stop at its end, it forms a corner where its level flattens, which sees its release within 200 ms and whose 100 ms mean reads about 1.17 times the gap. That corner replaces the note-off, and the next note’s own corner then replaces it in turn. At 1.3 and at 1.8 or more the note-off holds.

• A medium release lies over 50 % off on 50 of the 875 reverb stems, 26 of them with a release of 20 ms, and on 23 of the 779 dry stems, all with a release of 20 ms, on the 4000 stems [synthetic]. Lowering every reverb release with a true vote or a median tail_weight of 0.05 would leave 2 of 8, and would also lower the 819 right ones, so the level stays [synthetic].

• Under a tremolo, 43 of the 490 medium releases lie over 50 % off, on 2000 dry stems, after the rule above [synthetic].

• The RT60 reads about 50 % high under a release of 400 ms: at a true 0.6 s and 0.15 or 0.4 wet the median is 0.90 s, on about half of 300 stems each [synthetic]. The space layer takes this up [fact].

• A dry stem can report an RT60, on 2000 generated stems a set [synthetic]:

  Set	With an RT60
  Plain dry	82
  Short sustain	211
  Tremolo	330
  Legato	25
  Chord	185

  The 4000 stems above read it on 55 of 1372 dry stems, so that 4 % is no general rate [synthetic].

• A note list that ends at the note-off shows no knee, so --notes with such a list reads no release [fact].

• The 3 dB residual, the 0.05 weight of an RT60 and the five vote thresholds were chosen on generated signals and are untested on real tails; #91 checks them [fact].

• A release of 20 ms at 41 Hz is shorter than the level window: of the 116 reverb stems written more than 50 % off with a release up to 400 ms, 64 have a release of 20 ms [synthetic].

• #70 asks that the fit never returns a confident release more than 50 % off. Read with its scope, where the fit reports a tail_weight over 0.5, it holds, because no release is written there. It does not hold unscoped: the medium releases above lie over 50 % off under that weight [synthetic].

• The fit has no echo term, so a delay reads as release or tail [fact].

• The bench has no pre-delay, and the reverb is noise [fact].

• The beat grid starts at 0 s with the tempo as used. The period search finds one constant tempo within up to 2.81 % of it; a tempo that moves inside the stem still smears the curve [fact]. Its first stage reads up to 64 beats of the longest run, so a duck off the tempo that starts later in one held note can go unfound [fact]. On the 110 Hz chord, over runs of 10, 12, 16 and 32 beats and four phases, up to 2.5 % off the tempo, of 176 cells at each tempo [synthetic]:

  • A 12 dB duck with an 80 ms release locks in 173, 175, 176, 176 and 173 at 60, 80, 96, 128 and 174 BPM.
  • A 6 dB duck with a 150 ms release locks in 172, 165, 135, 159 and 131 at 60, 80, 96, 128 and 174 BPM. It locks in 8 of 16 on the tempo at 96 BPM, and in 1 of 16 at 2.5 % above at 174 BPM.

• A read that stays on the grid reports the grid’s tempo, though the duck can lie off it [fact]. Of 11,161 ducks up to 2.5 % off that stayed, the tempo was off by a median of 0.99 % and at most 2.56 %; of 33,787 fitted reads, by a median of 0.08 % and at most 2.22 % [synthetic].

• A duck on the tempo can move from a grid lock. On the 123,840 signals, 1 of 4847 grid locks does, 6 dB at 110 Hz and 60 BPM, by 0.89 %. The 76,836 stems, read through the layer, hold runs of 8.9 to 32 beats, ducks of 6, 12 and 18 dB and 4 phases, on a flat level, under fades of 12, 18 and 36 dB and under 6 dB steps every 4 beats. There 3 of 4595 grid locks move, by up to 0.89 %: 3 on the flat level and 0 under each fade or the steps. A wider set reaches more: 9,600 stems on the tempo per level, from 3 pitches and 5 tempos, with 10 runs of 8.9 to 32 beats, 8 duck settings of 3 to 18 dB and 8 phases. Its grid locks move in 6 stems on a flat level, 7, 12 and 10 under those fades, and 0 under the steps. These are ducks of 6 dB or less over 8.9 to 12.3 beats, by up to 2.7 %. A 6 dB, 150 ms duck at 110 Hz and 60 BPM over 10 beats, under the 36 dB fade, reads 59.479 BPM [synthetic].

• A grid read of none takes a fitted beat lock only when its curve falls faster than it recovers and takes 3 bins from half its depth back to a quarter, which holds out most gates. The price in ducks is small for releases of 80 ms or more and large at 30 ms, which loses 2004 of 6406 below. The set: 38,400 ducks on the tempo, from 3 pitches, 5 tempos, 10 runs of 8.9 to 32 beats, 8 duck settings of 3 to 18 dB and 8 phases; 46,080 ducks 0.5 to 2.5 % off, of 6, 12 and 18 dB with releases of 80 and 150 ms; 13,824 gates; flat and under fades of 12, 18 and 36 dB. Counted on this path alone [synthetic]:

  Fitted read over a grid read of none	Moves on the tempo	Ducks off the tempo that strip	Gates that strip
  No test	839	16,427	1733
  This test	653	16,150	59

  • The lost ducks are 277, or 1.7 %. Of them 132 lie at 55 Hz, 117 have a release of 80 ms and 160 of 150 ms [synthetic].
  • Short releases lose more, and slow tempos with them, as the test asks for 3 bins of a beat. On the 123,840 signals, on this path, ducks that would strip lose 2004 of 6406 at 30 ms, 61 of 4773 at 80 ms, 7 of 4079 at 150 ms and 2 of 3976 at 300 ms, and 998 of 4065 at 60 BPM, 523 of 3649 at 80, 326 of 4930 at 96, 141 of 3422 at 128 and 86 of 3168 at 174. Over all ducks of 30 ms up to 2.5 % off, 7453 of 15,840 strip, against 8996 with no test. A 12 dB, 10 ms duck over 480 beats does not strip [synthetic].
  • The moves left are 118 on a flat level and 181, 177 and 177 under the fades, by up to 2.46 %. There the duck is real: a move mostly shows that the grid read found no lock [synthetic].

• A chord whose level wanders with no pump can read as a pump. Under linear interpolation of Gaussian dB knots, spaced 0.25 to 1 beat, with sigmas of 1, 2 and 4 dB, at 55, 110 and 220 Hz, 60 to 174 BPM and 9, 16 and 32 beats, 5 of 2,592 strip, at 3 to 4 dB, 4 of them at a sigma of 4 dB [synthetic].

• A level step inside a beat stays in that beat’s fold error, and a step on a beat edge does not, so a slightly different period can win by moving an edge onto the step. One step of 6, 12 or 24 dB, about 0.35 or 0.65 through the run and up to 0.15 of a beat from a beat edge, at 55 and 110 Hz, 96 to 174 BPM and 16 and 32 beats, moves 21 of 4465 grid locks, by up to 1.15 % and with up to 1.09 dB of lost depth. A 6 dB, 150 ms duck at 110 Hz and 128 BPM over 16 beats, with a 12 dB step at 0.63 of the stem, reads 127.571 BPM. Its recovery reads 130 ms and its ripple 1.31 dB, against 203 ms and 0.69 dB on the grid. The same cause can hold a duck off its tempo. At 1 % off, a 48 dB fade over the last quarter finds the duck’s tempo in 18 of 29, and 6 dB steps every 4 beats in 22 of 31, against 28 of 31 with no steps [synthetic].

• A chord’s own beating sets a floor of about 1.3 dB under the fold error, so a smeared duck can stay on the grid. On the 76,836 stems, of 9205 ducks that stayed where both reads lock, 654 would have read 1 dB or more less ripple at the fitted period, 2.12 dB on average. A 12 dB duck 1 % slow over 12.3 beats at 96 BPM reads 6.5 dB of ripple on the grid and 1.1 dB at its own period, at fold errors of 1.42 and 1.33 dB [synthetic].

• The shape test can pass a gate. Over 8 phases and 9 to 32 beats, a 12 dB gate 3 % below the tempo at 55 Hz and 174 BPM strips in 4 of 376 runs [synthetic].

• The depth reads shallow, and the bias depends on the shape: an 18 dB duck reads up to 11.8 dB short in the set of Depth bias. On the noiseless chords of the 123,840 signals, on the tempo, with releases of 80 ms or more, it reads a median of 4.9 dB and at most 9.2 dB short [synthetic].

• peak_db compares two notes directly only when they read the same harmonic, so the pool’s level gate can leave out a note that reads a higher harmonic of a timbre with weak upper harmonics [fact].

• A second sound on the beat, such as a kick in the same stem, can read as a beat-locked pump; over fewer than 8 beats it is not stripped [synthetic].

• The search takes the deepest fold, so a second modulation near the tempo can take it [fact]. Under a duck on the tempo, a deeper second duck 0.5 to 2.5 % off took 53 of 64 locks, and a shallower sine, duck or gate took 15 of 623 [synthetic].

• A gate cuts across notes on the beat as a pump does; no test tells the two apart on a read that locks on the grid [fact]. A lock on a level with a duck’s shape off a division, such as a saw tremolo that falls at once and rises over the beat, strips as a duck too. Of 360 saw tremolos each, 266 strip at 3 % above the tempo against 63 with no search on free reads, 232 against 8 at 3 % below, 138 against 0 at 3.5 % above and 10 against 0 at 3.5 % below, and none at 4 to 5 %, on the 123,840 signals [synthetic].

• A heavy tail hides the release, so release_s is null over a median tail_weight of 0.5 [fact].

Sources

• Envelope stages: Xfer Records, Serum 2 manual. Facts only.
• Attack and decay descriptors: Peeters, Giordano, Susini, Misdariis and McAdams, The Timbre Toolbox: extracting audio descriptors from musical signals, JASA 2011. Inspiration only.