Evidence — where it appears
Named by 26 essays across 3 fields — each of them below, with the objects they name alongside it.
A count and a correlation
Cadence evidence is a count of ordered pairs and profile evidence is a correlation with a template, and the cadence essay refused to total them because they are not in the same units. Score each against its own chance and they are — standard deviations above chance are the same unit whatever produced them. Then the trouble moves: the obvious null does nothing at all to one of the two, because shuffling the bars leaves a pitch-class histogram exactly as it was.
The passage built to make them disagree
A cadence count and a key-profile correlation have been put on one scale and run on a passage where the two agree, which tells nobody anything. Building one where they disagree — the notes of one key and the cadences of another — measures the exchange rate at about six bars per cadence, and finds something the agreement case concealed: the two statistics cannot be varied independently, because lengthening the profile evidence adds cadence evidence too, for a third key.
A twenty-five is a nine until its last unit
Every account of long additive metres says they are heard as groups of shorter ones, and the metre-induction model had never been pointed at the claim. Pointed at it, the model does not prefer the group — it prefers the long bar outright, and would go on preferring it more the longer anybody listened. What it cannot do is start: the evidence that separates a bar of twenty-five from a bar of nine does not exist until the whole bar has been heard, and at the tempo an unequal metre is best played at the psychological present holds sixteen units.
The chords are a weak witness to the barline
Scaled by its own range, the metre overrules the chords every time the two disagree about where a bar begins. The obvious repair is to score each reading against its own chance — the metre against the same number of notes placed at random, the chords against the passage's notes shuffled across its bars — and add the standard scores. It changes very little: the search finds the barline within six points of where the product found it, and the chords gain the power to move the barline only on passages whose rhythm says nothing, where random notes move it nearly as often. The null's real result is the size of the two witnesses. At the written barline the metre stands up to 5.9 standard deviations above chance, and the chords, with every note a tone of its bar's chord, stand 1.55 above it at best.
The accent buys two units, however loud it is
A twenty-five cannot be told from a group of shorter bars on its onsets until more steps have gone by than a listener's present holds, and the obvious objection is that nobody plays an aksak bar as bare onsets: the long beat is louder, and the bar's first beat is marked. So how loud does an accent have to be? The question has a surprising answer. Loudness is not the variable. The existing accent cue changes nothing, and delays the answer where it changes anything. An accent that a reading has to predict works at any strength at all, and at no strength does more than a fixed amount: on the long beat it buys the two steps of a short beat, and on the downbeat it takes every arrangement to one floor — the bar less its last beat — which no cue carried by the notes can break. The longest bar that can be heard as one moves from sixteen units to eighteen.
The chords mark the barline by changing there
Read bar by bar, the chords stood barely above chance at the barline and broke the metre's half-bar tie two times in three at best. Read instead by where they change — how different the chords are across a candidate's barlines against how different they are across the middle of its bars — the same notes break the tie right on 81 to 96 per cent of passages, and added to the metre they find the barline on up to 89 per cent against 61. The weakness was the question the old reading asked, not the harmony.
The bass errs fast where the content errs slow
Asked how often the chords change, a reading built on pitch-class content names a slower multiple and never a faster rate. Give the passage a bass that states each new root and moves between chord tones inside a chord, and a reading built on the bass's moves errs the other way: it names a faster grid and never a slower one. At two chords a bar the bass is right every time; at a chord every two bars it is never right. Six ways of combining the two readings each trade one end of the range for the other.
The ceiling is thirteen bars with names
The key-finder's two cues stop buying anything at about 93 per cent of scheme bars read right, and the obvious suspect was the chord segmentation feeding it. The reading was never given a segmentation: every bar arrives with its true chord. What the ceiling is made of can be listed instead, and it is thirteen bars of 188 — seven in a bridge of secondary dominants, four in a minor episode whose chords C major also owns, and two at the edges of a modulation. No weight of any cue moves one of them.
A bass that holds through a change marks the barline
At two chords a bar the chords change on the barline and on the half-bar alike, so a reading of where they change is at chance, and the metre ties the two. The bass has one more piece of evidence: a change inside the bar can be voiced over the note already sounding, and a change on the barline is voiced over its root. Hold the bass through one mid-bar change in six and the metre and bass together place the barline in 85 per cent of eight-bar passages; one in three, 97. The convention cannot be stronger than that, and the chord changes, asked first, only get in the way.
A walking bass marks the bar by the note it is on
The reading that finds a barline from where the bass moves collapses to twenty per cent when the bass moves on every crotchet, and the bass the last essay called busiest moved twice a bar, because its beat was the half-bar. Given one that really walks, the same computation with sounds the chord's root in place of moves rises from nothing to a whole note a bar exactly as the other falls, and the two are equal at a bass moving on three crotchets in eight. Neither places a barline alone: the root is still sounding on the quaver after it. The metre, which cannot tell a barline from a half-bar, tells it from the quaver after it at once.
A texture in which nothing says where the bar begins
Two chords a bar over a bass that moves inside the chord is the one arrangement in which every witness this account has stands together at the metre's coin toss. The metre ties the barline with the half-bar, the chords change at both, and the bass states a root at both and walks between both — at every busyness, and whichever question the bass is asked. The only thing that breaks the symmetry is the voicing convention, and what it is worth falls from 98 per cent to 90 as the bass fills in, not because fewer changes can be held but because the motion around them is evidence for nothing. Chasing five points of residue above the toss found a defect that had been flattering the reading since it was written.
The leap at the barline is a fact about register
A bass leaps to a root at the barline and steps inside the bar, and no reading of pitch classes can see it — so the essay that named it recorded it as a limit. Given octaves and the size of every motion, it is worth nothing: realised at least motion the reading tracks whether the bass moved at all and ends 0.87 semitones on the wrong side of zero, because a line that always takes the nearest octave has no leaps to take. Play a stated root at the bottom of the compass instead, and the same sixteen notes in the same order turn a margin of minus 1.67 semitones into plus 1.67 and hold at 90 per cent where the move reading has fallen to 20. The barline is not where the bass moves furthest. It is where the bass goes back down.
The bridge is not a labelling problem
Seven of the key-finder's thirteen remaining misses are the thirty-two-bar song's bridge, and the essay before this one proposed that they might be an argument about labels rather than a failure: relabel the eight bars with the keys their dominants point at, and the reading's E and D majors might turn out to be right. They do not. The reading gets one bar of eight under either label, because four of the eight are read as the chord's own root taken for a tonic — a dominant seventh heard as a chord in its own right. And one of the bars the relabelling could have bought is unwinnable in principle: an applied dominant is the same four notes in the major and the minor of the key it points at.
Looking ahead rescues the relative minor, not the bridge
A key-finding reading that scores each bar by its own notes cannot hear an applied dominant, whose meaning is in the bar after it. Given one cue about a pair of bars — a dominant earns credit when the next bar is rooted on its key's tonic — the thirty-two-bar song's bridge is read as the chain of dominants it is, each chord both the arrival of the last and the departure to the next. But the same cue hears a blues's opening tonic seventh as the dominant of its own IV, and at the setting that read the listing best it costs five bars for three. The cue earns its place only in a reading reluctant to change key, and there what it rescues is the rondo's episode in the relative minor.
A crowd costs a late dancer the silences, not the steps
A dancer who hears only the landmarks of an aksak rhythm — the heads of bars and long beats — recognises it from a late entry better than one who hears every onset, as long as everything played is heard. Let a share of what is played be lost in a crowd and the lead goes, but not for the reason expected. Most of the cost arrives before a single landmark is missed: a listener who allows that one might be can no longer treat a silence as proof, and the landmark stream is built almost entirely of silences. At one lost onset in ten, the caution alone takes 25 points from the landmarks and 5 from the full stream.
A melody marks the barline by where it lingers
At two chords a bar over a walking bass, every harmonic witness stands at the metre's coin toss about where the bar begins. Give the passage a melody with a habit — long notes that prefer the downbeat — and the barline comes back: with a long note in half the bars and four in five of them on the downbeat, in 91 per cent of passages. The count of long notes barely matters; the preference is everything, and at even odds no number of long notes helps. A phrase end held through its bar is the strongest single cue. And a listener who adds the bass's readings to the melody's does worse than one who ignores the bass.
A syncopated melody needs its phrases to land
Put a melody whose long notes all fall on the half-bar over a harmony that changes once a bar and a walking bass, and a listener adding up the evidence hears the bar begin in the wrong place three times in four. The harmony knows where the bar is, but only through one witness: the bass's root votes for the barline in every passage, and the bass's motion never does — a walking bass lands on each new root by step, so it moves less at the barline than inside the bar. One syncopated voice ties the root, and the motion breaks the tie its way. What rescues the barline is not the harmony but the melody's own phrase ends: hold half of them from the downbeat and the reading finds the bar in 86 per cent of passages.
Two bars of drum hold the barline; a dozen bars of bass do not
A listener who settles where the bar begins and then holds it hears a syncopated tune against the bar only if the ground before it built enough confidence to spend. Read bar by bar, a walking bass under one chord a bar is worth less than half a vote a bar for the barline, and a syncopated bar takes an eighth of a vote back, so a tune needs about twelve bars of that ground to be heard against the bar nine times in ten. A drum on the downbeat makes each bar of ground worth a vote and a half, and two bars are then enough — but only for a listener who can bank more than four votes of confidence.
A crowd that hides bars is kinder than one that hides onsets
A dancer joining an additive-metre dance in a noisy room loses some of what is played, and the essay before this one lost it one onset at a time. A crowd does not. It hides stretches — a burst of laughter covers a bar. The prediction was that a stretch as long as a bar would hurt the stream of landmarks most, since it could remove every landmark in a cycle, and that long bars would survive best. Holding the share of time lost fixed, longer stretches help every stream, help the full stream more than the landmarks, and leave long bars as hard to place as ever.
A listener who weights its witnesses needs eight bars of bass, not twelve
A syncopated tune over a walking bass needed about twelve bars of ground before a listener with a memory heard it against the bar nine times in ten, with every witness given one vote a bar. Let the listener weight each witness by how often it has agreed with the reading it holds and the root earns a second vote, the bass's motion loses half of one, and the syncopation loses almost all of its. Eight bars are then enough, a tune that syncopates every bar becomes hearable against the bar at all, and reading the syncopation backwards buys nothing that ignoring it does not.
A listener who knows the style needs no introduction
A listener who weights each witness to the barline by its record needed eight bars of walking bass before a syncopated tune was heard against the bar nine times in ten, and with no introduction at all it learned the syncopation's lesson instead. Finer records — one for each side a witness takes, one for each section — change nothing. What changes everything is arriving with the style's habits: a listener who already gives the bass's motion and the melody's long notes no vote hears the tune against the bar 93 per cent of the time from its first bar, and 94 per cent for a tune that syncopates every bar. The root need not be trusted more. The others need to be trusted less.
A dancer who hears the crowd can trust the quiet
A late dancer in a noisy room who cannot tell noise from silence has to treat every silence as weak evidence, and that caution was the largest cost in every figure before this one. A dancer who hears the laugh that covers a bar knows which silences to discount and can trust the rest. Losing a quarter of the music, that dancer recognises more metres than one who loses nothing but must allow for losses — and the landmarks, which a noisy room had made the worse stream to follow, lead again once the noise comes in bursts. The quiet has to be trusted to one onset in nineteen.
In a loud room the accent has to be loud
A late dancer who hears the crowd as noise ignores everything played under it. Real noise is not that thorough. It hides the soft strokes and lets the loud ones through, and an accented downbeat is a loud one. Let the noise pass loud strokes and some soft ones, and marking the downbeat is worth more to the dancer than in a quiet room: with half the time under noise, 29 points of recognition against 23. Noise that swallows the accent halves its worth. In a quiet room no amount of loudness bought an accent anything extra; in a loud one, loudness is the whole of what the accent is for.
In a crowd the downbeat belongs to the drum
In a loud room a marked downbeat is worth more to a late dancer than in a quiet one, so long as the mark gets through. Whether it does depends on where its sound lies, because talk is not loud everywhere: it is loudest from 250 to 400 hertz, exactly where a melody's notes are, and fifteen decibels quieter at the bottom of a drum. A louder melody note is heard half the time through talk ten decibels over the band; a low drum survives a crowd twelve decibels louder than that. With the talk fifteen decibels over the band, a downbeat marked in the melody is worth two-fifths less to the dancer than one marked by the drum.
A felt drum reaches only where the heard one already does
A low drum near a stage is felt in the body as well as heard, and talk cannot mask a vibration. Given that second channel, a drum-marked downbeat always arrives — and is then worth 19.8 points to a late dancer, exactly what an always-heard drum was worth, because the crowd has already taken the soft strokes that made a mark worth more. The felt channel pays only under crowds twenty decibels over the band. And it is driven by the drum's own level, which in a reverberant room is high enough to be felt only where the drum is already loud enough to be heard.
The felt channel carries the inner beats, not the downbeat
A low drum felt in the body gets the downbeat through any crowd, and is then worth less than it was in a quiet room, because the crowd has taken the soft strokes between. Put a kick drum on every landmark of the dance and let all of it be felt, and in a crowd thirty decibels over the band a late dancer recognises the dance in seventy per cent of entries against thirty-seven for the felt downbeat — with no felt accent at all. The accent, felt or not, is worth about ten points on top. The worry that a stream felt alike has no downbeat turns out to be the small half of the arithmetic.
Named alongside it
The objects these essays reach for when they reach for this one.
DownbeatMetreHarmonic rhythmInferenceAdditive metreAksakPerceptual presentChord segmentationKey-findingMelodyModulationSegmentation