Acoustics & Music Theory
why it sounds like that
Concept

Forward masking — where it appears

The raising of a listener's threshold for a sound by one that has just stopped. It decays over about two hundred milliseconds from a level ten decibels below the masker, which is why it hides a quiet successor and cannot hide an equally loud one.

Named by 5 essays across 3 fields — each of them below, with the objects they name alongside it.

The threshold before, during and after a burst. The level a brief probe needs in order to be heard, plotted against when it happens relative to a 70 dB burst that occupies the shaded band. To the right is forward masking, which decays over about 200 milliseconds. To the left is backward masking: the threshold is raised for a probe that has already finished before the masker begins.

A sound hides what came before it

Masking does not stop when the masker does. A loud sound raises the threshold for about a fifth of a second after it ends, which is unremarkable, and for several milliseconds before it begins, which is not. The auditory present is a window rather than an instant, and inside the window the order of events is not the order they arrived.

perception · Masking Nothing at all until fifteen decibels, and then it depends on the tempo. The fraction of a line's partials that stay above threshold, over how fast the line moves and how much louder everything before each note is. Darker is more lost. The whole left-hand side is white: at equal levels a note cannot be masked by its predecessor at any tempo, and that is a proof rather than a measurement — forward masking leaves a threshold at most ten decibels below the masker, and a note's own partials mask each other from the same components at full level. The boundary is between twelve and eighteen decibels, and beyond it the loss grows with the tempo: at 280 to the crotchet and 36 decibels of contrast, 26 per cent of the line's partials are gone. Fifteen decibels is about the gap between a forte and a piano.

An equal note cannot be masked

Three earlier essays are about one instant, and forward masking lasts two hundred milliseconds — longer than a note at any brisk tempo. So a fast line should be a sequence of events hiding each other, and it is not: a note masks itself ten decibels harder than its predecessor can, at any speed. What does hide a line is dynamic contrast, and the boundary is fifteen decibels.

perception · Masking What the chord before takes out of the chord after. Five chords at 1.2 seconds each, with the roughness each one has on its own — its simultaneous masking and the threshold of hearing already applied — and the roughness it actually has once the chord in front of it has raised the threshold. Four of the five are untouched. The fifth, i, two parts, follows the only step in this passage that falls more than fifteen decibels, and it arrives into a hole: it is entirely below threshold for its first 13 milliseconds and takes 240 to get all of itself back. Masking can only remove partials, so it can only lower a roughness — and the chords it can reach are the ones a written dynamic has just made quiet, which are already the smooth ones. Across the passage the dissonance contrast goes from 3021 to 3113: the mask widens it by 3.0 per cent rather than eating it.

A soft chord has to fade in

Forward masking sits between the two integration times already in play — two hundred milliseconds against a thirty-seven millisecond roughness window and a two-second loudness release — and it was owed as the term that might eat the dissonance contrast. It does not. It widens it, by three per cent at a chorale's pace and fifty-nine at four chords a second, because it can only ever remove partials and it can only reach the chord a dynamic has already made quiet. What it does instead is stranger: one chord in the passage is entirely inaudible for its first twelve milliseconds and takes a quarter of a second to arrive whole.

form · Orchestration One doubling, held down a phrase. Where a single held arrangement of 4 players on 3 notes stands among the 36 at each chord of a 5-chord passage, best at the top, with what each chord would rather have named along the bottom. The held answer is flue pipe · trumpet · clarinet+violin, and it is the chord's own first choice at 4 of 5 of them. Holding it costs 16.2 per cent of the passage's roughness against re-scoring every chord — which is 2.4 per cent of the range the choice actually spans, since the arrangements at one chord differ by a factor of 7.8 on average. The cost is not spread over the passage: 1 chord carries nearly all of it.

An orchestrator doubles a line, not a chord

Three earlier essays made the objective a functional over a passage and a later one went back to holding one chord still. Put the doubling back into time and the retreat turns out to have been cheap: one arrangement held down a five-chord phrase is that phrase's own best answer at four of its five chords and costs 2.4 per cent of the range the choice spans — while the forward mask named earlier as the third temporal constant reaches for twenty milliseconds rather than two hundred, and cannot change the answer at any pace at all.

instruments · Orchestration With 4 of six required at the end, the best schedule hands parts over. Six parts entering, leaving and re-entering a five-chord passage over four sounding players, in the walk through all 64 sets of sounding parts that makes the least audible entrance as audible as possible, with no memory of the chord before and at least 4 of the six sounding at the last chord. I, open: clarinet on G4 enters at 0.6 dB; vi, close below: oboe on E4 enters at 0.3 dB, and clarinet leaves; IV, close above: brass on E3 enters at -0.7 dB, voice on C5 enters at 2.2 dB, and oboe leaves; V, bracketing: violin on G5 enters at 7.2 dB; I, hollow: flue pipe on C6 enters at 4.0 dB. The least audible entrance is -0.72 dB against -2.65 for the best schedule in which nobody leaves; the walk has 2 exits and 6 entrances.

An exit is worth nothing until the tutti is given up

Six parts entering a five-chord passage have a best schedule when each enters once and stays, and letting parts leave and come back was supposed to improve it. Searched over every set of sounding parts at every chord, it improves it by exactly nothing, with or without the chord before still masking — as long as all six must be playing at the end. Let one part be missing from the final chord and the weakest entrance gains 1.4 decibels; let two be missing and it gains 1.9, by a relay in which the parts with least room come in, are heard for one chord, and give way.

form · Orchestration

Named alongside it

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

MaskingOrchestrationDynamicsEnumerationIntegration windowPartialRoughnessAudibilityBackward maskingCritical bandwidthDoublingLoudness

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