Acoustics & Music Theory
why it sounds like that
Concept

Silence — where it appears

A gap in the sound that the music is doing something with, as against the absence of a performance. What a listener is given during one is set by how quickly loudness decays and by how long the room keeps ringing, so the same written rest is a different event in a dry hall and a wet one.

Named by 7 essays across one field — each of them below, with the objects they name alongside it.

A rest is a diminuendo, and a long one. How far a listener's running impression of loudness falls during a silence, converted into the diminuendo that would have taken it the same distance. Half a second of nothing is worth 3.2 decibels, a second and a bit is worth 8.1, and two and a half seconds is worth 17. The marked line is three and a half seconds, which is where a gap starts to be heard as an ending rather than as a pause: at that length the reference has fallen by 24 decibels, which is more than a fortissimo to a pianissimo. A tempo swept over a factor of ten, a deceleration over a factor of three and a gesture length over a factor of forty-eight all returned the same reading to four significant figures. This one moves it by twenty-four decibels.

A rest is a diminuendo

Three parameters swept over factors of ten, three and forty-eight returned the same reading to four significant figures. The one manipulation left unswept moves it by twenty-four decibels: a silence. A listener's running impression decays at the loudness smoother's two-second release, so a general pause is a diminuendo nobody wrote, and at the length that makes a gap an ending it is worth more than any marking a composer has.

form · Closure A general pause of a bar is worth 4.9 decibels in a hall and 8.1 in silence. What a rest is worth as a diminuendo, in rooms with different reverberation times. The upper curve is the earlier figure, which assumed the sound stops when the players do; each curve below it lets the hall go on sounding, falling sixty decibels in its own reverberation time until it reaches the background. At the bar of silence a general pause usually is — about 1.2 seconds — the dry value is 8.1 decibels, shoebox concert hall keeps 60 per cent of it and gothic cathedral keeps 22. At 3.5 seconds, where a gap stops being a pause and becomes an ending, the same hall keeps 86 per cent. A long silence outlives any hall's tail and a short one does not, which is why the room costs the device most at exactly the length a composer writes it.

A rest needs a dry room

The twenty-four decibels a general pause is worth assume the sound stops when the players do. Put a hall under it and a bar of silence keeps 60 per cent of its value in a shoebox concert hall and 22 per cent in a cathedral, while a three-and-a-half-second one keeps 86 and 45 — because a hall's tail has a length and a rest either outlives it or does not. A written bar of silence is worth half its dry value at 2.76 seconds of reverberation, which falls between the concert hall and the stone church.

form · Closure A bar of silence is worth 13.1 decibels written last and 6.0 written first. Four closing gestures, drawn against how many seconds of silence each contains. All four hold the same 12-part texture, write the same 6.0-decibel diminuendo over 4 seconds, and differ only in what order the diminuendo and the silence are written in. The quantity is how far the listener's running impression has fallen when the final chord arrives, in decibels of equivalent diminuendo. Written with the silence last, a general pause of a bar is worth 13.06 decibels and one of three and a half seconds is worth 28.3. Written with the silence first, both are worth 6.00 — exactly the diminuendo's own depth, because the music resuming after the silence puts the reference back at its own level. The silence written first is worth less than the silence written with no diminuendo at all, which reads 8.12 at a bar: a diminuendo placed after a general pause takes 2.12 decibels away and adds nothing.

A general pause is spent by the note after it

Whether a composer should write the pause before the diminuendo or after it looks like a question about how big the ensemble is. It is not. Forty decibels of ensemble are worth one decibel of silence, and the order is worth seven — because a running impression rises twenty times faster than it falls, so half a general pause is spent by ninety-seven milliseconds of sound.

form · Closure A final chord stands above the impression for a fraction of a second. How far a final chord at the tutti's own level stands above the listener's running impression at the instant it is released, against how long it lasts, for four ways of arriving at it. Straight out of the tutti it stands above nothing at any length; after 1.2 s of silence the impression is 8.1 dB down, and the chord stands highest, 5.14 dB, when it lasts 54 ms; after 3.5 s of silence the impression is 23.7 dB down, and the chord stands highest, 14.42 dB, when it lasts 28 ms; after a 6 dB diminuendo the impression is 5.0 dB down, and the chord stands highest, 3.18 dB, when it lasts 42 ms. Every curve is level again by half a second, because the impression's attack of 99 ms catches the note's attack of 22 ms, so a held chord is released at the impression's level whatever preceded it.

A final chord stands out for a twentieth of a second

A general pause drives a listener's running impression down, and the final chord that follows is supposed to cash the fall in. It cashes in at most two thirds of it. The note's own loudness rises with a 22-millisecond constant and the impression with a 99-millisecond one, so after a bar of silence the chord stands furthest above the impression 54 milliseconds in, by 5.1 of the 8.1 decibels the silence bought, and after 206 milliseconds the two are within a phon of each other. A short stamp spends most of its life standing out; a chord held a second and a half spends a seventh of it.

form · Closure A louder final chord stands higher and still stands for a fraction of a second. How far a final chord stands above the listener's running impression at the instant it is released, against how long it lasts. The chord is a struck six-note tonic; "a step louder" is the hammer velocity doubled, which raises its loudness 7.12 phons above the tutti's. At the tutti's level, after 1.2 s of silence, the impression is 8.09 dB below the chord and the chord stands highest, 5.14 dB, at 54 ms; a step louder, straight out of the tutti, the impression is 7.12 dB below the chord and the chord stands highest, 4.51 dB, at 36 ms; a step louder, after 1.2 s of silence, the impression is 15.21 dB below the chord and the chord stands highest, 9.46 dB, at 38 ms. Every curve returns to zero by half a second: the impression climbs to whatever level the chord is played at, so a louder mark is not a stand that lasts but a deeper fall to climb out of, and a silence and a mark add as depths.

A louder final chord is a deeper silence and a brighter sound

A final chord marked a step louder than the passage was supposed to stand above a listener's running impression for as long as it sounded, since the impression can climb no higher than the chord. It climbs exactly that high, and the stand closes in half a second as it always did. What a louder mark actually buys is depth — about seven phons, the same depth a second of silence buys — and a spectrum whose balance point sits most of a whole tone higher, which, unlike the stand, lasts for the whole chord.

form · Closure A rest can balance a louder stamp only if the stamp is shorter than a ninth of a second. The level a final chord a step louder than the tutti, 7.12 phons, leaves the running impression at, in phons over the tutti, against the length of the rest before it, for stamps of 50 ms, 70 ms, 100 ms, 120 ms, 200 ms. 50 ms: 0 s +2.21, 0.25 s +0.16, 0.5 s -0.92, 0.75 s -1.91, 1 s -2.83, 1.5 s -4.46, 2 s -5.84, 2.5 s -7.00, 3 s -7.95, 4 s -9.38, 5 s -10.30, 6 s -10.89, balanced by a rest of 0.29 s; 70 ms: 0 s +3.16, 0.25 s +1.47, 0.5 s +0.67, 0.75 s -0.05, 1 s -0.71, 1.5 s -1.84, 2 s -2.76, 2.5 s -3.51, 3 s -4.12, 4 s -5.00, 5 s -5.55, 6 s -5.89, balanced by a rest of 0.73 s; 100 ms: 0 s +4.27, 0.25 s +3.07, 0.5 s +2.55, 0.75 s +2.08, 1 s +1.67, 1.5 s +0.97, 2 s +0.42, 2.5 s -0.02, 3 s -0.37, 4 s -0.87, 5 s -1.17, 6 s -1.35, balanced by a rest of 2.47 s; 120 ms: 0 s +4.83, 0.25 s +3.88, 0.5 s +3.48, 0.75 s +3.12, 1 s +2.81, 1.5 s +2.29, 2 s +1.87, 2.5 s +1.55, 3 s +1.30, 4 s +0.94, 5 s +0.72, 6 s +0.59, and no rest brings it to the tutti; 200 ms: 0 s +6.14, 0.25 s +5.76, 0.5 s +5.60, 0.75 s +5.47, 1 s +5.35, 1.5 s +5.16, 2 s +5.01, 2.5 s +4.89, 3 s +4.80, 4 s +4.68, 5 s +4.60, 6 s +4.56, and no rest brings it to the tutti. Past a stamp of 115 ms no rest is long enough: the stamp lifts even a fully fallen impression past the tutti.

No rest balances a louder chord held past a ninth of a second

A rest before a final chord leaves the passage quieter than the tutti and a louder mark on the chord leaves it louder, so the two together can leave it exactly where it was, while the chord stands out by both at once. They can — but only for a stamp. A chord a step louder and longer than 115 milliseconds lifts even a listener's fully fallen impression past the tutti, so no rest of any length balances it; two steps louder, the limit is 67 milliseconds, and three, 45. The balanced ending exists, and it is decided by the release, not by the rest.

form · Closure In a hall the balanced ending is a louder chord, and the hall sets how much louder. The gain over the tutti, in phons, that a final chord held after no rest needs for the listener's running impression to finish exactly at the tutti's weight when the chord's tail has died into the silence, against the hall's reverberation time, for chords held half a second, one second and two. 0.5 s: 0.2 s 0.7, 0.3 s 1.2, 0.45 s 1.9, 0.6 s 2.7, 0.8 s 3.9, 1 s 5.0, 1.25 s 6.6, 1.5 s 8.2, 1.75 s 9.9, 2 s 11.7, 2.25 s 13.7, 2.5 s 15.8, 3 s 20.4. 1 s: 0.2 s 0.7, 0.3 s 1.1, 0.45 s 1.9, 0.6 s 2.7, 0.8 s 3.8, 1 s 5.0, 1.25 s 6.5, 1.5 s 8.1, 1.75 s 9.9, 2 s 11.7, 2.25 s 13.6, 2.5 s 15.7, 3 s 20.4. 2 s: 0.2 s 0.7, 0.3 s 1.1, 0.45 s 1.9, 0.6 s 2.7, 0.8 s 3.8, 1 s 5.0, 1.25 s 6.5, 1.5 s 8.1, 1.75 s 9.9, 2 s 11.7, 2.25 s 13.6, 2.5 s 15.7, 3 s 20.4. The dashed lines are one dynamic step, 7.12 phons, and two; a one-second chord a step louder balances in a hall of about 1.34 s and two steps louder in one of about 2.32 s.

In a hall the balanced ending is a louder chord

In a dry room a rest before a final stamp a step louder can leave a passage finishing exactly at its tutti's weight, but only for a stamp shorter than a ninth of a second. The prediction was that a hall would make it impossible: its tail fills the rest and lengthens the stamp. That is right for a small room and wrong for a hall. Read when the chord's tail has died, a live hall pulls every ending below its tutti, and the ending that finishes at its own weight there is a held chord marked louder than the passage — five phons louder at a second of reverberation, a whole step at about 1.3 seconds, two at 2.3.

form · Closure

Named alongside it

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

ClosureDynamicsLoudnessIntegration windowTemporal integrationCadenceNotationReverberationBrightnessCritical bandwidthMusical formOrchestration

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