Acoustics & Music Theory
why it sounds like that
Concept

Temporal coherence — where it appears

The frequency separation up to which alternating tones can still be held together as a single line, which rises as the sequence slows. It is the upper of van Noorden's two boundaries and it caps how far a fast melody may leap.

Named by 4 essays across 3 fields — each of them below, with the objects they name alongside it.

A 7-semitone sequence at 120 ms a tone. Tones drawn as pitch against time, one bar per tone. The events are the same in both readings of this pattern; what changes is whether a listener assigns them to one line that leaps back and forth or to two lines that each stay put. Nothing in the drawing decides which, and nothing in the sound does either.

The ear builds objects, and sometimes offers a choice

What arrives at an ear is one pressure signal. What a listener gets is a set of separate things — a violin, a voice, a car outside. The assignment is a construction, and the clearest evidence is that it can be flipped by changing nothing but the speed: one sequence of tones is a single line when slow and two lines when fast, with a wide region in between where the listener may choose.

perception · Auditory scene Four voices, placed by the arithmetic. The rules in force are: no parallel octaves; no parallel fifths; no voice crossing; no gap over an octave above the tenor; the leading note is not doubled; the leading note resolves, outer voices; no augmented melodic interval. The four parts are drawn lowest to highest — bass, tenor, alto, soprano. I – vi – ii – V – I in C major, realised in four voices by the cheapest set of voicings obeying 7 rules, at 16 semitones of motion in all. Every gap between adjacent voices narrower than the fission boundary of 5.2 semitones is marked, and below that boundary two parts cannot be heard as two however hard a listener tries.

A voice is a stream, and the ear decides which

Seven earlier essays have assigned voices to notes. Whether a listener follows the assignment is a separate question with laboratory numbers attached, and the numbers are unkind to it: two parts closer than about five semitones cannot be heard as two at any speed, a third of the gaps in the cheapest four-part writing are inside that limit, and in a third of chord changes the ear's own rule for continuing a line does not recover the parts as written.

perception · Voice-leading Ode to Joy as a path. Ode to Joy plotted as 30 notes against the 8 scale degrees it uses, one column per note. Its largest melodic interval is 2 semitones and it spans 7; the mean absolute step is 1.24 semitones. Beethoven, Ninth Symphony, finale, 1824 — the theme as first stated, eight bars.

A melody is a walk, not a set

Nine essays here are about which seven of the twelve a scale takes, and every one of them describes a set. A tune is not a set; it is a path across one, and the path is nearly all small steps. That is not a matter of taste. Above about eight notes a second the ear stops being able to hold a large interval and a small one in the same line, and at sixteen the choice disappears altogether — so a fast passage is scalar because a fast passage that leaps is two pieces of music.

scales · Melody The same steps, counted by the clock. The step distribution of Ode to Joy and Twinkle, twinkle counted two ways: once per interval, which is what every earlier figure did, and once weighted by how long the note it leaves is held. The two disagree because a tune's long notes are not distributed evenly over its interval sizes — in Ode to Joy the 2-semitone step is 55.2 per cent of the moves and 60.0 per cent of the time. Which of the two a claim about melodic motion means has never been stated here, and the answer matters most exactly where a tune slows down, which is at the ends of its phrases.

The note that has a length

Every melodic figure so far reads a table where each note is a pair — a pitch and a duration — and throws the second number away. A step between two minims and a step between two quavers have been one event in every histogram it has drawn. Weighting the same statistics by time moves the step distribution by up to seven points, changes forty-four of a hundred and one contour signs, and turns up an off-by-one in the one figure that did use the durations: it took the length of the note arrived at where the time between two onsets is the length of the note left.

rhythm · Melody

Named alongside it

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

StreamingAuditory scene analysisFission boundaryContourMelodic intervalBistabilityCompound melodyDurationFusionGroupingInter-onset intervalNull model

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