Acoustics & Music Theory
why it sounds like that
Concept

Lbdm — where it appears

The local boundary detection model, which scores each gap between two notes by how much the pitch, the length and the rest around it change. It is the boundary detector used here, and it finds a phrase end only where the tune supplies one of the cues it weights.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

The boundaries that survive each amount of smoothing. The local boundary strengths of Twinkle, twinkle read at every scale: the curve is smoothed with a Gaussian of the width on the horizontal axis and the peaks that survive are counted. Small scales give 11 boundaries and large ones give one, and the notation marks 5. The level with that many falls at a width of 2, where the model finds 100 per cent of the notated boundaries and 100 per cent of what it finds is notated — a comparison with no threshold in it, which is what the scale parameter buys.

A boundary at a stated level

A boundary detector run over three tunes agreed with the notation on one and barely at all on another, and left two things owing: a version with a scale parameter, and a version run on performance timings. Both are paid here, and they pay differently — the scale removes a free parameter from the comparison and does not rescue the hard case, while two per cent of rubato does.

form · Phrase Twinkle, twinkle, phrased at the level each tempo selects. The number of boundaries the model finds when its smoothing scale is set by the psychological present rather than chosen, against the tempo the tune is taken at. The scale in notes is the present's 3.5 seconds divided by the mean note length, so a fast tempo puts more notes inside the present and smooths harder. The page's own phrasing has 5 boundaries, drawn as the flat line; the model matches it best at 160 beats per minute, where the present holds 8.2 notes. The same tune at two tempos is read at two levels, which is the prediction and is not a free parameter.

The level the tempo chooses

The boundary detector has a scale parameter and an earlier essay left it free, ending with the sentence that names this one: the scale is in notes and the psychological present is in seconds. The psychological present is two to eight seconds, a tempo converts one to the other, and the level a listener reads then stops being a parameter at all — which is a prediction with teeth, because the same tune at two tempos should be phrased differently at levels the arithmetic names in advance.

form · Phrase

Named alongside it

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

PhraseScale-spaceSegmentationFinal lengtheningGroupingHierarchyNotationPerceptual presentRubatoTempo

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