Acoustics & Music Theory
why it sounds like that
Concept

Final lengthening — where it appears

The systematic slowing of the last notes before a phrase boundary in performance. It is the most reproducible expressive-timing effect there is, and it makes a boundary detector's own resolution a function of where in the phrase it is looking.

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 A ritardando does not spend the diminuendo. The arrival reading under a deceleration into the ending, from no ritardando at all to a final tempo 30 per cent of the starting one — which stretches the closing bars from 12.0 seconds to 20.2. The expectation was that it would matter: a ritardando lengthens exactly the bars the gesture is happening in, so a diminuendo that would have been absorbed at a steady tempo gets more of the smoother's own time to be absorbed in. It moves the reading by 0.00 per cent. Every line here is flat to within the thickness of the line, which is the second time a tempo parameter has been swept here and found to do nothing.

The reading was a step response

Sweeping the tempo found it did not decide the answer. This one sweeps the deceleration across a factor of three and finds a null to five figures, and then sweeps the length of the closing gesture across a factor of forty-eight and finds it moves the reading by eight per cent — but not as a function of seconds. Sorted by seconds the twelve runs scatter; sorted by how many bars the instruction covers they fall into three tight groups. One sentence explains the null and the not-null together.

form · Closure

Named alongside it

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

CadenceClosureDynamicsLbdmLoudnessNotationPhraseRitardandoRubatoScale-spaceSegmentationTempo

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