Groove

Start with the part that is a number

Swing divides a beat into a long and a short instead of two equal halves. The ratio between them is the whole of it, and notation has no way to write it down: triplet feel implies 2:1, a dotted eighth and a sixteenth implies 3:1, and players sit between and around both.

So swing is a quantity that notation rounds to the nearest available symbol, which is a good enough reason to measure it instead. And when people did, the result was not the one you would guess.

The ratio is an output, not a setting

The obvious model is that a player has a swing ratio, somewhere near 2:1, and applies it at whatever tempo. Hold the ratio in that figure and sweep the tempo to hear the problem: the short note has nothing holding it up. Set 3:1, the swing a dotted eighth and a sixteenth notates, and by 300bpm the short note is down to fifty milliseconds - half the length drummers were actually measured producing, at any tempo.

Friberg and Sundstrom measured jazz drummers' ride patterns across tempos around 2002 and found that what stays roughly constant is the short note, at something near a tenth of a second, while the beat contracts around it. Switch the figure to that model and the ratio falls out on its own: past 3:1 near 150, 2:1 near 200, and straight eighths by about 300, with nobody deciding to stop swinging.

That is a satisfying result because it replaces a stylistic constant with a physical one and explains a fact every player knows, which is that fast tempos swing less. It is also, so far, the last comfortable thing in this lesson.

The explanation everybody gives

Ask why programmed music sounds stiff and you will be told, more or less universally, that it is because the timing is perfect. Human players are slightly early and slightly late, that variation is what makes it feel alive, and this is why sequencers ship with a humanise button.

It is a good story. It has a mechanism, it matches the intuition that machines sound mechanical, and it has been repeated for forty years. It also makes a clean empirical prediction: add timing deviation, get more groove. That is testable, and it has been tested.

What the testing found

Broadly, it found the opposite. Fruhauf, Kopiez and Platz put drum patterns to listeners in 2013 with timing deviations of varying size and reported that the quantised versions were rated highest for groove, with ratings falling as deviation grew. Work by Madison and colleagues on microtiming in real recordings similarly failed to find the effect the folk account requires.

The fair summary is not that microtiming does nothing. The literature is genuinely mixed, some studies find small effects for particular instruments and styles, and systematic timing relationships between parts are a different proposition from random jitter. What is not supported is the strong version: that deviation as such is the source of groove, and that more of it gives more. The humanise button is not doing what its name says.

Being clear about what the figure above can and cannot do. It presents the stimuli and lets you form an impression; it does not measure anything, because groove is a rating and one reader is not a sample. What it can honestly show is that the deviation is real and audible - at forty milliseconds it is a quarter of a step - so if you find yourself preferring the quantised setting, that is not because the effect was too subtle to notice.

What does predict it

The better predictor turns out to be something this course already made computable. Witek and colleagues found in 2014 that the urge to move tracks syncopation in an inverted U: patterns with little of it are dull, patterns saturated with it are hard to move to, and the maximum sits in the middle.

That is the ladder in the figure, and it is why all five rungs have exactly six onsets. Event density predicts groove ratings on its own, so a ladder that got busier as it got more syncopated would have confounded the two. Only the syncopation moves, and the scores beside each rung come from lesson 3's measure.

And that closes the course, because of what syncopation turned out to be. Syncopation belongs to a pattern and a metre together, never to a rhythm on its own, and the metre is supplied by the listener. So the best available account of groove says it is not in the recording at all. It is a measure of how hard the music is making your inference work, and the sweet spot is where the inference is being challenged without being broken.

The shape of the whole course

Lesson 1 found the beat was not in the signal. Lesson 2 found the same of grouping. Lesson 3 showed syncopation is measured against the metre and therefore against something the listener brought. Lesson 5 found that which pulse is the beat has no answer in the audio at all.

Lesson 4 is the exception that makes the pattern worth stating. Maximal evenness is pure arithmetic, it accounts for a startling number of the world's timelines, and it is completely indifferent to who is listening. It also cannot explain the clave, or say why anybody should want evenness in the first place.

Which is the honest position for a course on rhythm to end in. There is real arithmetic here and it goes further than you would expect. It stops well short of the thing people actually mean by rhythm, and the gap is filled by a listener doing continuous unconscious work that the music is written to exploit.