In a crowd the downbeat belongs to the drum

A dancer who arrives late at a wedding where the band plays additive metres has to work out which dance it is from whatever bar they walk in on. A dancer who comes in late needs the downbeat marked found that the stream a listener needs is the metre’s landmarks — the starts of its bars and of its long beats — with the first of them marked, and the accent buys two units however loud it is found that in a quiet room the mark only has to be distinguishable, not loud. With ten dances known and an entry at a random step, marking the downbeat adds 23.4 points to the share recognised within the three and a half seconds of a present.

In a loud room the accent has to be loud took the dancer into a room full of talk. Noise of that kind hides soft strokes and lets loud ones through, and an accented downbeat is a loud one; with the room noisy half the time, and the loud strokes always getting through while some soft ones did, marking the downbeat was worth 28.9 points — more than in quiet. But the essay gave each stroke a probability of getting through and asked nothing about where that probability came from. Its last section named the missing piece. A band has more than one way to mark a downbeat — a louder melody note, a bass note an octave below the rest, a drum stroke, a bell — and noise masks by frequency band as well as by level. Talk is concentrated in a particular part of the spectrum, and a mark that lies outside it may cut through where an equally loud mark inside it does not.

Where talk is loud #

The crowd here is talk with the long-term spectrum of speech: in third-octave bands it rises from the bottom of the range to a plateau between about 250 and 400 hertz, and falls about five decibels an octave above it. That shape is the one published averages of speech share, and it holds for a room full of talk as well as for one talker, since many voices only add up a smoother version of the same spectrum.

Against it, four ways of marking a downbeat, each at the band’s own level of 70 decibels. A louder melody note is a tone on G4, 392 hertz, whose partials fall at six decibels an octave. A bass note an octave below is the same shape two octaves down, on G2. A low drum puts its energy in the bands from 63 to 125 hertz. A high bell puts it between 2.5 and 4 kilohertz. The melody’s unmarked strokes are eight decibels under its accent.

A mark is heard when, in at least one band, its level is no more than three decibels under the talk’s level there — about the margin at which a tone in a band of noise becomes detectable — and since the crowd’s level swells and falls, a mark at the margin is heard some of the time and not others, here with a spread of three decibels.

With the crowd as loud as the band, every mark is heard and the melody’s soft strokes are heard 72 per cent of the time. Five decibels louder, the soft strokes are down to 14 per cent and the melody’s accent to 94. At ten decibels over the band the soft strokes are gone and the melody’s accent is heard 47 per cent of the time, while the bass, the drum and the bell are still heard every time. At fifteen decibels over the band the melody’s accent is heard 4 per cent of the time; the bass 90, the bell 93 and the drum 100. At twenty, the drum is still heard 82 per cent of the time, the bell 43, the bass 34, the melody never.

Band by band the reason is plain. The melody’s fundamental sits at 400 hertz, on the talk’s plateau, and its upper partials fall away at much the same rate as the talk does, so there is no band in which it stands clear: at ten decibels over the band the talk is 3.2 decibels above its best band. The drum’s energy is at 63 hertz, where talk is fifteen decibels below its peak, and it clears the talk there by 9.7 decibels. The bell, at 4 kilohertz, clears it by 6.5, and the bass, whose fundamental lies at 100 hertz, by 5.8. A melody is played in the same register as speech, which is part of why it can be sung, and it is exactly the register a crowd fills.

How much louder the crowd can get #

Put as headroom — how loud the crowd can get before a mark is heard only half the time — the four marks spread over thirteen decibels. The melody’s accent gives out with the crowd 9.8 decibels over the band; the bass at 18.8; the bell at 19.5; the drum at 22.7. The melody’s unmarked strokes, eight decibels softer than its accent, give out at 1.8. A drum stroke at the band’s own level therefore outlasts a melody accent as though it were twelve or thirteen decibels louder — more than the whole difference between an accented and an unaccented note.

Thirteen decibels is a large number in a room. A crowd’s talk rises as people speak up to be heard over the band and over each other, and the step from a crowd as loud as the band to one ten decibels louder is the familiar step from a reception to a party. Across that step the melody’s accent goes from always heard to heard half the time, and the drum does not notice.

What it is worth to the dancer #

The earlier essay’s account of recognition takes the chance a marked stroke gets through and the chance an unmarked one does, and returns what marking the downbeat adds to recognising the dance. Here the crowd covers half the time in stretches of sixteen steps, as there, and the two chances come from the band arithmetic above.

With the crowd at the band’s level every mark adds 28.9 points: the soft strokes are thinned, the marks all get through, and the dancer is in the situation the earlier essay found most favourable to the accent. As the crowd rises the soft strokes vanish, and even a mark that always gets through is worth less — 22.1 points at five decibels over the band, 19.8 at ten. That fall is the same for every mark and is a cost of losing the unmarked strokes, which carried the rest of the landmark stream.

The marks part company where they start to be lost. At ten decibels over the band, the drum, the bell and the bass add 19.8 points each and the melody’s accent 14.7. At fifteen, the drum still adds 19.8, the bell 18.2, the bass 18.0, and the melody’s accent 11.6 — two-fifths less than a drum would at the same level, and half what it was worth in quiet. At twenty, the drum adds 17.3 and the melody 11.3, by which point the melody’s accent is not heard through the talk at all, and what it still adds comes entirely from the downbeats that happen to fall in the quiet half of the time.

The choice of mark matters more the longer the crowd talks. With the crowd ten decibels over the band and covering a tenth of the time, the melody’s accent adds 22.2 points against the drum’s 23.3 — nearly the same, because most downbeats fall in quiet stretches anyway. Covering half the time, 14.7 against 19.8; three-quarters, 7.4 against 12.8. In a room where talk never lets up, the melody accent’s worth halves again while the drum’s falls only with the loss of the soft strokes.

Why the soft strokes go first, and what they were doing #

The fall common to every mark, from 28.9 points to 19.8 between a crowd as loud as the band and one ten decibels louder, deserves its own account, because no choice of mark can buy it back. The melody’s unmarked strokes are eight decibels softer than its accent and sit in the same band, so they are the first thing the talk takes: heard 72 per cent of the time at the band’s level and almost never at five decibels over it. A late dancer needs the landmarks, not the rhythm found that the landmark stream — bar starts and long-beat starts — is what recognition runs on, and the unmarked strokes are most of those landmarks. With them gone, a dancer is recognising the dance from its marked downbeats alone, one stroke a bar.

That turns out to be worth something — the 19.8 points, close to the quiet room’s 23.4 — because a downbeat that recurs at a dance’s own bar length already distinguishes most of the ten dances from one another; the dances that share a bar length are the ones it cannot separate. It also explains why the earlier essay found the accent’s worth peaking when some soft strokes still got through: the marked downbeat tells the dancer where the bar starts and the surviving soft strokes tell it how the bar divides, and the combination beats either alone. A crowd that hides bars is kinder than one that hides onsets found the same preference from the other side: what a listener needs from a damaged stream is the structure, not the count.

A band could protect the soft strokes too, by moving them out of the talk’s register — playing the inner beats on a low instrument as well — but that is the same remedy as for the downbeat, and it costs the same thing: the dance’s rhythm would then live in the drums and bass rather than the tune. Many dance bands in loud venues have arrived at exactly that division of labour, and the arithmetic of one sound hiding another is one reason it works.

How much of this depends on the shape of talk #

The headroom figures rest on the speech spectrum’s shape, and that shape varies with the talkers, the room and how loudly people are speaking: raised voices put more energy into the upper bands.

Steepen or flatten the talk’s fall above 400 hertz, from three decibels an octave to eight, and the four marks behave very differently. The bell’s headroom swings from 17.4 decibels to 32.5: on a flat-sloped crowd it is no better than the bass, on a steep one it beats everything. The drum’s moves only from 23.2 to 21.7, and the bass’s from 19.3 to 17.7, because both lie below the talk’s peak, where its shape was not changed. The melody’s accent stays near ten decibels until the slope reaches six an octave, when its upper partials begin to stand clear and its headroom climbs to 17.9 at eight.

So the drum’s advantage is the robust one. It comes from talk being weak at the bottom of the spectrum, which is true of every talker, and not from how talk falls off at the top, which depends on who is talking and how loudly. A bell is an excellent mark in a room of quiet conversation and an ordinary one in a room of shouting. A drum is a good mark in both.

What the arranger’s choice is #

The earlier essay’s lead called this the arranger’s version of the player’s question. The player’s version was whether to accent the downbeat harder; the answer was that in a loud room the accent has to be loud enough to get through, and everything else about it stops mattering. The arranger’s version is which instrument should carry the downbeat, and on this arithmetic the answer is the one band traditions in loud places have usually reached: the downbeat goes to the lowest instrument, and to a drum before a bass. A melody line can carry the dance in a quiet room, and does, but at a party it has to be doubled underneath.

There is a familiar exception that points the same way. Where a band does carry the downbeat high — a bell, a cowbell, a high clap — it is usually with a sound whose energy sits above three kilohertz, beyond the talk’s plateau, rather than in the register of the tune. The arithmetic says that works while the crowd’s talk falls off steeply, and that it is the first such mark to fail as people raise their voices.

The model the figures rest on #

The crowd is a fixed spectral shape at a stated level. Real talk fluctuates in time and in spectrum, and a crowd’s level is not independent of the band’s: people talk louder when the band plays louder. The figures report the crowd relative to the band for that reason.

A mark is heard in its best third-octave band if it stands above the talk’s level there by more than −3 dB, with a three-decibel spread in the crowd’s level. That counts masking within a band and ignores masking spread from one band to the next. Upward spread of masking from the talk’s loud plateau is strongest at high levels and falls on the bands above it, so it would cut into the bell’s headroom in a loud crowd and leave the drum’s alone, since the drum lies below the plateau.

The marks are idealised. A real drum has energy well above 125 hertz in its attack, and a real bell has partials below 2.5 kilohertz; each would carry some of its mark in bands where the talk is louder. The melody’s accent is modelled as a single louder note, and a real melodic accent may also be longer, higher or ornamented, any of which changes its spectrum.

Recognition is the earlier essays’ — ten known dances, a random entry, a listener who hears the noise and counts a silence only where the room was quiet, odds of nineteen to one asked before naming the dance.

What these figures cannot show #

How a dancer weighs a drum against a melody. The figures count a marked downbeat as a marked downbeat whichever instrument carries it. A listener might trust a mark in the tune more than one in the drum, or the reverse, and a crowd costs a late dancer the silences, not the steps found that what a listener does with what it cannot hear matters as much as what it can. The band arithmetic says which marks arrive; it does not say how much each is believed.

And bodies in the room. At a wedding the dancer can also see other dancers, feel the floor and watch the drummer. A dancer who hears the crowd can trust the quiet kept to sound alone, and so does this.

Still open: a mark that is felt as well as heard #

A low drum in a room is not only heard. At sixty hertz and below, at the levels a kick drum produces near a stage, the floor and the body vibrate, and that vibration is a channel talk does not mask at all. If the downbeat carried by a drum reaches a dancer through the floor as well as the air, its survival in a crowd is not a matter of decibels over the talk: it is close to certain wherever the dancer is standing, and the worth of the mark under the loudest crowd is the worth of a mark that always gets through. The computation is this one with a second channel for the drum that depends on distance from the stage and not on the crowd, and it would say how far from the band the advantage the figures give the drum turns into one no other mark can approach.