Acoustics & Music Theory
why it sounds like that
Concept

Envelope — where it appears

How a note's amplitude changes over its lifetime, from the attack through the decay and the sustain to the release. It carries as much of an instrument's identity as its spectrum does, and the attack carries most of that.

Named by 25 essays across 4 fields — each of them below, with the objects they name alongside it.

Three envelopes. How loudness changes over the life of a note, for plucked, bowed and struck. Remove the attack from a recorded piano and it stops sounding like a piano, which is the shortest demonstration that the envelope carries as much identity as the spectrum.

The shape of a note, which is most of what an instrument is

Cut the first fifty milliseconds off a recorded piano and listeners stop calling it a piano. The attack carries more identity than the steady tone it leads into, and it is the part every spectrum plot leaves out.

timbre · Envelope Three attacks, the first 50 ms. How loudness changes over the life of a note, for plucked, bowed and struck, drawn over the first 50 milliseconds. By the right-hand edge the plucked note is at 91%, the bowed note is at 36%, the struck note is at 97% — attack times of 4 ms, 140 ms, 2 ms, a spread of 70 to one, and the part a listener uses to tell them apart. Remove the attack from a recorded piano and it stops sounding like a piano, which is the shortest demonstration that the envelope carries as much identity as the spectrum.

The first fifty milliseconds

A spectrum is supposed to be what makes a trumpet a trumpet. Cut the first fifty milliseconds off a recorded note and listeners stop being able to name the instrument — while the spectrum they are hearing is unchanged. Identity is in the part of the sound that ends before the note has properly started.

timbre · Envelope The same note, hit at a middling dynamic. The spectrum of a struck string with the hammer's own contact time applied as a low-pass. Contact lasts 1.60 ms at this force, against 2.26 ms at the softest and 0.95 ms at the loudest drawn — felt is a nonlinear spring, so a harder blow is a shorter contact and a brighter note. The spectral centroid moves from partial 1.5 to partial 2.2, which is a change of timbre and not of loudness.

A hammer is not an impulse

Contact lasts a couple of milliseconds, which low-passes the note — any partial whose half-period is shorter than the contact is barely excited. Piano felt is a spring that stiffens as it compresses, so a harder blow makes the contact shorter, the corner higher and the note brighter. A loud note is not a scaled-up quiet one, and no linear model gives that.

instruments · Excitation point Helmholtz motion, bowed at 9% of the way from the bridge. Above: the string at 5 instants of one period. It is two straight lines meeting at a corner, and the corner travels round the string rather than the string swinging. Below: the resulting force on the bridge, a sawtooth whose two segments are in the ratio 0.09 to 0.91 — the bow's own position. A sawtooth contains every harmonic at exactly one over n, so the spectrum barely changes with bow position even though the waveform plainly does.

The bow makes a corner

A bowed string is not a string swinging. It is two straight lines meeting at a single sharp corner that travels round the string once per period, triggering the slip that keeps it going. The force on the bridge is therefore a sawtooth, and a sawtooth is every harmonic at exactly one over n — which is why a bowed string is the most nearly perfect harmonic series in the orchestra.

instruments · Bowed string How much bow force is allowed, and where. Schelleng's diagram. The lower bound is the least force that will trigger a slip on every pass of the corner and goes as one over beta squared; the upper bound is the most the string will take before it sticks for more than a period and goes as one over beta. At beta = 0.09 the usable range spans a factor of 9.0; at 0.03, near the bridge, it is 3.0, and at 0.2, over the fingerboard, 20.0. The window closes in proportion to beta, so the difficulty of playing near the bridge is a slope on this picture rather than a matter of opinion.

How much bow is allowed

Too little force and the corner fails to trigger a slip on every pass; too much and the string sticks for more than a period. Both bounds depend on where the bow is, and they depend on it differently — one as the square of the distance from the bridge and one linearly — so the window between them closes in proportion as the bow approaches the bridge. Sul ponticello is difficult by a power law.

instruments · Bowed string A reed that shuts at 5000 pascals, and the air it lets through. Volume flow through the reed channel against the pressure across it, in the quasi-static model: Bernoulli flow through an opening that closes linearly with pressure. The flow peaks at 1667 pascals — exactly a third of the closing pressure, for any reed, because that is where the two effects balance — and it is 0.18 litres a second there. Everything to the right of that peak is the argument: the flow falls as the player blows harder, from 0.18 to 0.05 litres a second by 4500 pascals, and a resistance that behaves that way supplies energy instead of taking it. There is no reed inertia in this model, so it cannot squeak.

The reed is a valve, not a vibrator

Three essays here have said that a clarinet's reed does not choose the note, and none of them said what it does instead. It chops a steady stream of air, and past a third of the pressure that closes it the flow falls as the player blows harder — a resistance with the wrong sign, which is the only thing in the instrument capable of putting energy into an oscillation that is otherwise losing it.

instruments · Air column A constant bow force cannot start a note. Schelleng's minimum and maximum bow force, evaluated at the speed the bow has after one period rather than at the speed the note will be sustained at. Both bounds are proportional to bow speed and the speed after one period is the acceleration divided by the frequency, so both are proportional to acceleration and the region is a wedge through the origin. Its width as a ratio is 9.0 to 1 at every acceleration — the attack is not a narrower window than the sustain, it is the same window somewhere else. A fixed force, drawn here at 0.02, is inside it at one acceleration, about 0.18, which is why the force has to rise with the speed and why beginning a note is a trajectory through this plane rather than a point in it.

The note has to start somewhere

Schelleng's diagram says how hard a bow may press at a given distance from the bridge for a steady tone to be possible. It is a map of a note that is already sounding, and it contains no information whatever about how to begin one. Read the same inequality at the speed the bow has after a single period rather than at the speed it will settle to and the admissible region turns out to be a wedge through the origin — same width as a ratio, a hundred and ninety-six times lower in force. A constant bow pressure is inside it for one instant of the attack and outside it for the rest.

instruments · Bowed string A perfectly tuned unison is the shortest note on the piano. How long a struck unison takes to fall forty decibels, against how far apart its two strings are tuned, for a note whose single string would ring for 20 seconds and whose bridge takes the in-phase mode down in 1.5. At a perfect unison the hammer excites only the mode that drives the bridge, so the note dies in 1.00 seconds. The longest note is at 2.30 cents, at 3.05 seconds — three times as long. Past 4.48 cents the two modes stop sharing a frequency and start sharing a decay, the note beats instead of ringing, and the sustain collapses.

Three strings, and the note that comes back

The usual account of a beat adds two independent sources together. A piano's strings are joined at the bridge and are not independent: the pair has normal modes, one of which drives the bridge and dies in a second and a half while the other cancels at the bridge and rings for twenty. A hammer striking a perfect unison excites only the first — so a perfectly tuned unison is the shortest note on the instrument, dying in one second, and the longest is at a deliberate detuning of about two and a half cents, at three. Past four and a half cents the two modes swap what they share and the sustain collapses.

instruments · Beating A note gets duller as it dies. Each partial of a string note against time, with the loss rising as the partial number to the power 1 — so the fundamental takes 6 seconds to fall sixty decibels and the 8th takes 0.75. The heavy line is the power-weighted centroid, falling from partial 1.77 toward the fundamental; it is halfway there after 0.15 seconds. A single-rate envelope would draw all of these as parallel lines and the centroid as a horizontal one, and a struck string does neither: what is left at the end of a long note is very nearly a sine.

The note that gets duller as it dies

Every envelope drawn so far is one curve applied to a whole sound, and no struck string behaves that way. A string loses energy to air, to internal friction and to the bridge, and all three losses rise with frequency — so a note with a six-second fundamental has a sixteenth partial that is gone in under half a second, and the sound moving toward the listener is a spectrum collapsing toward its own fundamental. Which means an instrument is identified twice: once by the fifty milliseconds of its attack, which the earlier essays measured, and again by how fast its colour drains, which they did not.

timbre · Envelope One envelope, and the three places a listener might be said to hear it. The amplitude envelope of a note with a 90 millisecond exponential attack, with the three criteria the literature offers drawn across it. The heard moment is 8.0 ms at the detection criterion, 28 ms at the perceptual-onset criterion and 94 ms at the perceptual-attack criterion. The physical onset is at zero on this axis and no criterion puts the heard moment there. The buttons play this attack against a two-millisecond one, started at the same instant.

A note is heard after it starts

Every rhythm essay until now has treated a note's onset as the moment it happens. It is not: the instant a listener aligns a note with a beat is later than its physical start by an amount the note's own attack decides, and for a sung or bowed note that amount is about thirty milliseconds — the size of the whole quantity six essays on microtiming set out to measure.

rhythm · Perceptual-centre Two fusion cues, and they do not agree about a single spectrum. Each spectrum twice. Hollow is the harmonicity census — the fraction of partials near enough a whole multiple of one fundamental to fuse, which is harmonicity. Filled is the same fraction under common fate: how many partials decay at a rate within a factor of 2 of the strongest partial's. Ranked by harmonicity the order is an ideal string, a piano string, a bell, a kettledrum, a bar; ranked by common fate it is a kettledrum, a bar, an ideal string, a piano string, a bell. The two orderings are nearly reversed. An ideal string is perfect on the first cue and 20 per cent on the second, and a kettledrum — the worst spectrum in this collection for fitting a series — is the only one whose partials all die together.

The partials that do not die together

The fusion census is a still photograph: it asks whether a set of partials fits one harmonic series and has no term for time. Put time in and the ranking reverses. An ideal string is perfect on harmonicity and holds a fifth of its partials together by decay; a kettledrum — the worst spectrum in this collection for fitting a series — is the only one whose modes all die at one rate.

perception · Auditory scene What a slow start costs a trumpet, in its own settling time. The amplitude of a trumpet's A4 resonance — the 4th impedance peak, of Q 37, time constant 27.1 milliseconds — driven from rest by a pressure that rises over 10, 40, 80, 140 milliseconds, against the step every earlier figure has assumed. The step reaches 90 per cent of its final amplitude in 62.5 milliseconds. A ramp of 140 takes 157.8, which is 95.3 more — and that excess is 68 per cent of the ramp's own length. Across the whole range a player works in the excess is a little over half the ramp: 0.52, 0.56, 0.61, 0.68 at 10, 40, 80, 140 milliseconds. So the tongued attack is not something added to the note. It is the step, which is what has been computed all along, and what has a price is its absence.

What the tongue actually removes

The question this essay was written against asked for an impulse: a tongued attack, a martelé stroke and a struck key all deliver one before the steady drive begins. The arithmetic refuses the framing. A tongue release does carry energy at the note's own frequency, and it is worth 0.17 milliseconds on a trumpet against a settling time of 62 — capped at about 1.13 over the resonance's Q. What articulation is worth is the ramp it removes, and that is about half the ramp's own length: 44 milliseconds, and very nearly the same 44 on every wind instrument in the collection.

rhythm · Onset time The census with the criterion moved under it. Every instrument's speaking time in milliseconds, against the fraction of the steady amplitude counted as speaking. The criterion is in the wind instruments alone: a resonance takes −ln(1−p)·Q/(πf) to reach a fraction p, so those lines rise across the whole picture, while a bow's capture and an exciter's contact contain no criterion at all and are flat. Every earlier figure sits at 0.9, where the wind instruments are the slowest things in the collection by a factor of 20.5. At 0.05 they are the fastest: a violin's G3 string is the slowest at 15.5 milliseconds and a trumpet takes 1.4. The three clusters cross at a criterion between 0.18 and 0.39, which is inside the range the perceptual measurements work in — their three named criteria are 15 decibels below peak, 6 decibels below peak, and ninety per cent — and the settling figures have only ever used the third of them.

Read at two different heights

Ten placements of these figures, one value: the settling criterion is nine tenths in every one of them, and nothing is measured behind it. It is a multiplicative constant only inside the mechanism that has it — a bow's capture and an exciter's contact contain no criterion at all — so moving it rescales one of three clusters against two that stand still. The most-quoted number here, a factor of sixty-nine between the instrument's account and the listener's, is 5.9 at the criterion the listener's own measurements use, and the ordering an earlier essay was written about does not exist below a fifth.

perception · Onset time Articulation is worth 2.6 phons, and nobody counts it. A passage of notes at 80 decibels, 2 to the beat, at 7 tempi and 3 articulations, scored against the same level held continuously. The variable is the fraction of each inter-onset interval that is sounding — 0.95 is a legato, 0.4 a staccato — and the vertical axis is what that costs the passage's running loudness in phons. Nothing here is anybody playing harder or softer. At 40 to the beat the span from legato to staccato is 1.47 phons; at 200 it is 2.61, because a staccato note there lasts 60 milliseconds and no longer reaches its own loudness either.

A staccato is a dynamic mark

Every loudness figure in this collection is of a sound that has been going on long enough, and no note in music has. Run the running-loudness model on notes with lengths in them and an articulation turns out to command 1.5 phons at a slow tempo and 8.1 at a fast one — more than the 1.8 decibels a whole texture commands, on the same page, written down in the same ink, and counted by nobody.

perception · Loudness The top of a struck note's series falls while the note lasts. The highest partial still above the threshold of hearing, against time, for a note struck at 80 decibels on a fundamental of 130.8 hertz with a 1/n spectrum and a loss rising as the partial number to the power 1. It starts at partial 152 and it is falling from the first millisecond. The horizontal lines are the three tops computed from frequency alone, all of which assume a note that never ends: the note's own top drops past the difference-limen top after 0.03 seconds, past the semitone top after 0.32, and past the resolvable top after 0.64. After that the series is shorter than the ear could have resolved, and what stops it is the clock.

The top that falls while the note lasts

Four earlier essays have asked where the harmonic series stops, and all four answered with a number computed for a tone that never ends. A struck C3 has 152 audible partials at the strike and eight after two-thirds of a second, so the ear's own resolution limit governs the first ten per cent of the note and the decay governs the rest. Playing ten decibels louder buys the ear a further tenth of a second, and doubling its reign would take fifty-eight.

timbre · Harmonic series A struck note's two ends are the same for every loss law. The partial levels of a string spectrum struck at 80 decibels on 130.8 hertz, and what is left of it when the fundamental itself falls under the threshold of hearing, for three laws relating a partial's decay rate to its number. The left panel is every one of them: a loss law cannot change the spectrum at the instant of the strike, because no time has passed. The other three are every one of them too: whatever the law, the note ends with nothing above the threshold. So both ends of the slide are shared, and everything that distinguishes an exponent of 0.5 from an exponent of 1 from an exponent of 2 is in the middle.

The middle nobody could have guessed

A struck note has no steady state, only a slide from one spectrum to another — so the question is what the middle carries that the ends do not. The answer is exact rather than statistical: every loss law in the family leaves the strike with the same spectrum and ends in the same silence, so both endpoints carry precisely nothing about which of them it is. The whole difference is 41.3 decibels, and it peaks 0.38 seconds in, seven per cent of the way through the note.

timbre · Envelope There is less to collapse the higher the note is. The same string model struck at 80 decibels on nine fundamentals, an octave apart. The heavy line is how far the spectral centroid falls between the strike and the note's death, in semitones — the whole of the colour drain, in the unit a musician has for pitch. It runs from 25.2 semitones at A0 to 6.6 at C8, a factor of 3.8, and it falls monotonically. The reason is the dashed line, which is how many partials exist at all: 727 under the audio ceiling at A0 and 4 at C8. From C7 upward a struck note has fewer partials than the ear could have resolved — 9 against 10 — so there is nothing left for a collapse to take away.

The collapse belongs to the bass

Every envelope drawn until now has no pitch in it: the decay model counts partials rather than measuring them in hertz. Put a fundamental in and the collapse it describes shrinks monotonically up the keyboard, from 25.2 semitones of colour drain at A0 to 6.6 at C8, because a partial has to fit under twenty kilohertz to exist and the top note has four of them. Above C6 a struck note has fewer partials than the ear could have resolved, and there is nothing left for a collapse to take away.

timbre · Envelope One attack time, three shapes, 48 ms of disagreement. Three amplitude envelopes with the same 90-millisecond attack time, which is the only quantity the published tables report. a resonator from a step rises as one minus a decaying exponential; an excitation ramping rises in a straight line; a ramp through a resonator is a raised cosine. Each is normalised so that its own 10-to-90 per cent rise takes exactly 90 milliseconds, so all three are the same measurement. The horizontal rules are the three criteria a heard moment is read off. At 6 dB below peak the three shapes put the heard moment at 28.5, 56.4, 76.3 milliseconds — a spread of 48, on one attack time, from a property nothing in the table records.

An attack time is not an attack

Eight earlier essays read a heard moment off an envelope, and every one of them used the same envelope shape without saying so: the source table records one curve for all nine of its families, and the map's own arithmetic does not carry the parameter at all. A published attack time fixes a ten-to-ninety time and nothing else. Under the two other shapes the same measurement admits, every millisecond computed so far doubles — and the constructed passage called inaudible earlier becomes three times a listener's threshold.

perception · Perceptual-centre The attack is the balance dial, turned by the clock. The level of a violin against a clarinet on one note at 392 hertz, moment by moment through the attack, with both players starting together. Two envelopes rising at different rates are a balance, so this axis is the same dial a conductor turns — and its whole travel is 6.02 decibels, which is twenty times the log of the ratio of the two attack times, 45 against 90 milliseconds, and nothing else. The pair does not begin as one player alone: both envelopes leave zero at the same slope ratio, so the dial starts at a finite offset rather than at silence. The dashed line is the balance at which the composite changes owner, -3.48 decibels — inside the travel, so the note belongs to a clarinet for its first 29 milliseconds and to a violin for the rest of its life.

The blend arrives before the note does

Nine essays on spectrum draw a steady state, and the strongest cue that two instruments are two instruments is that they do not start together. Two envelopes rising at different rates turn out to be a balance — the same dial an earlier essay swept — so the attack is that dial moved by the clock, and its whole travel is fixed at twenty times the log of the two attack times. It is six decibels for a clarinet with a violin against a crossing twelve to twenty-two decibels out, so one pair in ten changes hands during its own attack, and which one depends on a convention rather than on the instruments.

timbre · Spectrum A doubled pizzicato gives its note away while it is still the louder. The power of a violin plucked, against a flue pipe holding the same note at 392 hertz, through the first 600 milliseconds of the pluck, with the pluck starting 12 decibels up and its fundamental decaying over 1 second. With each partial losing level in proportion to its number, the composite stops resembling the pluck at 70 ms, when the pluck is still 5.2 decibels the louder. With every partial fading together it would keep the note until 543 ms. The dashed line is the balance at which the steady-state doubling changes owner, minus 20.6 decibels: the release crosses the owner long before its balance gets there, because what hands the note over is the pluck's upper partials going, not its level.

A doubled pizzicato gives its note away early

The attack turns the balance between two players on one note by a few decibels and stops. A pluck does not stop — every partial of it decays, so a pizzicato doubled by a held instrument walks the balance for the whole note, and the expectation was a handover as slow as the decay. It is fast. A one-second pizzicato over a flute loses its note in 70 milliseconds, while it is still five decibels the louder, because what hands the note over is its upper partials going first. A uniform fade would have kept it eight times as long.

timbre · Spectrum A bow shows the loss law a blow conceals. The same string on 130.8 hertz under three loss laws, drawn twice each: struck, and held by a continuous drive. The pale marks are the spectrum a blow produces, and they are identical in all three rows — a strike is the source spectrum and has no loss in it yet, which is why both endpoints of a struck note were found to carry nothing about the law. The solid marks are where each partial settles when a drive balances its own loss, at drive over loss, so the steady spectrum rolls off as the source's roll-off plus the exponent. At an exponent of 0.5 the held spectrum's centroid sits at 167 hertz, 5.7 semitones under the strike's 232; At an exponent of 1 the held spectrum's centroid sits at 144 hertz, 8.2 semitones under the strike's 232; At an exponent of 2 the held spectrum's centroid sits at 133 hertz, 9.6 semitones under the strike's 232. The quantity that is invisible at both ends of a struck note is the slope of a bowed one, for as long as the bow moves.

A bow holds the number a blow hides

Two struck notes with different loss laws are identical at the strike and identical at the end, which is why separating them at all meant looking in the middle. Drive the same two strings continuously and the loss law stops being a rate and becomes a slope: each partial settles at its drive over its own loss, so the exponent adds to the source's roll-off and sits in the spectrum for as long as the bow moves. It is 18.7 decibels of separation available from the first instant, against 41.3 that a blow delivers after four tenths of a second and then takes away.

timbre · Envelope From partial 3 the room is the slower of the two. Decay rates in nepers a second for each partial of a note on 130.8 hertz, in a concert hall. The rising curve is the string's own loss, which grows as the partial number to the power 1. The flat-ish curve is the room's, from its reverberation time at that partial's frequency. A reverberant field is the source convolved with the room, so a partial's tail falls at the SLOWER of the two — the heavy line — and the room keeps returning energy the string has stopped making. From partial 3, at 392 hertz, the room is in charge: 6 of the note's 8 partials are held up by the room rather than let go by the string. Those are exactly the partials the string was losing fastest, which is why the room does not merely lengthen the note.

The room is the slower of the two

A reverberant field is the source convolved with the room, so a partial's tail falls at the slower of the two rates rather than at their sum — and the room is slower for exactly the partials the string is losing fastest. Half a note's colour is gone in 0.163 seconds in no room at all, 0.313 in a concert hall and 1.441 in a stone church. The destination is identical in all three, because a room cannot hold a partial up above the fundamental it is also holding. What a hall takes away is the rate, and the rate was the whole of the identity cue.

timbre · Envelope The drain does not stop when the key does. The note does.. Semitones of colour gone, against time, for a note on 130.8 hertz left to ring and for the same note released after 0.4 seconds onto a damper of 0.15 seconds. The two curves lie on each other until the key comes up, and the damped one then ends: the note is inaudible at 0.52 seconds with 8.7 of the free note's 9.9 semitones delivered. A damper adds one loss to every partial alike, so it adds the same number to every decay rate and leaves every DIFFERENCE between rates exactly as it was — the spectrum at each instant is the ringing spectrum shifted bodily down by 400 decibels a second. The colour goes on draining at its own rate the whole time. What the damper takes away is not the drain but the seconds.

A damper changes the clock, not the colour

A damper is an extra loss on the string rather than a second decay, so it adds the same number of nepers a second to every partial — and adding a constant to every rate leaves every difference between rates exactly where it was. The damped spectrum at any instant is the ringing spectrum at that instant shifted bodily down, to machine precision. The colour goes on draining at its own rate; the note simply runs out of seconds, and how many it gets is written on the page as a note value and a tempo.

timbre · Envelope A damper is a loss on the string, so a room can overrule it. Decay rate in nepers a second against partial number, for a note on 130.8 hertz in a room of 2 seconds. The rising line is the string's own loss, 1.15 nepers a second at the fundamental and growing as the partial number to the power 1. The line above it is that plus the damper's 46.1, which is what the string does once the key comes up. The flat line is the room. What a listener receives is the SLOWER of the damped string and the room, because a hall goes on radiating what the string has already given it — and here the room is slower on 8 of 8 partials, from the fundamental upward. The composition proposed earlier — take the slower of the string and the room, then add the damper to whichever won — would put the damper outside the minimum, where nothing can overrule it, and would predict a note 2.54 seconds shorter than ringing where the arithmetic here predicts 0.90.

A damper cannot reach into the room

The essay before this one proposed the arithmetic for a damped note in a hall: take the slower of the string's rate and the room's, then add the damper's to whichever won. The composition is wrong, and it is wrong in the one place that decides the answer. A damper is a loss on the string, so it belongs inside the minimum where a room can overrule it — and past about three seconds of reverberation it is overruled on every partial, so the damper removes no audible seconds of note at all.

timbre · Envelope A staccato is the direct sound's, and the room takes it within a fifth of the critical distance. A note on 130.8 Hz held 0.4 s and damped, in a room of 2 s reverberation, heard at distances from 0.02 to 5 times the critical distance: how long after the release the note takes to fall 10 dB and 20 dB. To fall 10 dB: 24 ms at the source, 333 ms far away; 0.02: 24 ms, 0.05: 25 ms, 0.1: 25 ms, 0.15: 26 ms, 0.2: 28 ms, 0.3: 35 ms, 0.5: 103 ms, 0.75: 187 ms, 1: 234 ms, 1.5: 281 ms, 2: 302 ms, 3: 318 ms, 5: 328 ms; doubled by 0.38 of the critical distance. To fall 20 dB: 49 ms at the source, 667 ms far away; 0.02: 49 ms, 0.05: 51 ms, 0.1: 60 ms, 0.15: 117 ms, 0.2: 198 ms, 0.3: 308 ms, 0.5: 436 ms, 0.75: 520 ms, 1: 568 ms, 1.5: 614 ms, 2: 635 ms, 3: 652 ms, 5: 661 ms; doubled by 0.14 of the critical distance. Where the direct sound and the room are equal, the damper's work is already hidden: the room's copy is only 20 dB below the direct sound at a tenth of the critical distance, and a 20 dB fall reaches it there.

Only the player hears a staccato end

A damper stops a string in a seventh of a second, and in a hall the room goes on for two. A listener hears both, mixed in proportion to how close they sit, and the question was at what distance the short part stops mattering. The answer is closer than any seat. A damped note's twenty-decibel fall has doubled in length by a seventh of a hall's critical distance — 77 centimetres in a two-second concert hall — and by a quarter of it in a jazz club. The end of a staccato is something the pianist hears and the front row does not.

timbre · Envelope

Named alongside it

The objects these essays reach for when they reach for this one.

Attack transientDecayBrightnessOnsetTimbrePartialSpectral centroidIdentificationDampingEnsemble asynchronyHelmholtz motionNonlinearity

All concepts