Rhythm
Time, grouping, and how much of it you are supplying. The other axis of the piano roll, except that lesson 1 shows it is not another axis at all.
Rhythm is the part of music where the listener does the most work and gets the least credit for it. The beat is not in the signal. The grouping is not in the signal. Both are inferences, they are made without effort or training, and a great deal of what music does with rhythm is done to those inferences rather than to the sound. This course measures what can be measured and is clear about the rest.
The derivation
Lessons 1 and 2 establish that beat and metre are supplied by the listener, because everything after that is defined relative to them. Syncopation cannot be measured without a metre, and groove cannot be discussed without both.
- 01BeatSpeed a rhythm up far enough and it turns into a pitch. Slow a pitch down far enough and it turns into a rhythm.Establishes: Rhythm and pitch are one axis divided by hearing near 20 Hz, and the beat is inferred rather than present.
- 02MetreIdentical clicks, evenly spaced, carrying no accent at all, and you will hear them in groups anyway.Establishes: Metre is an inferred hierarchy of strong and weak, and it persists when nothing in the sound marks it.
- 03Syncopation, measuredA word usually explained by example, given a number instead, and the number needs a metre to exist.Establishes: Syncopation is computable against the metric hierarchy, so it is a property of a pattern and a metre together.
- 04As even as possibleSpread k onsets across n steps as evenly as they will go, and traditional timelines start falling out.Establishes: Maximal evenness in time is the same algorithm that picked the diatonic scale, run on a different axis.
- 05Two clocks at onceThree against two, and the arithmetic that decides how long it takes to come back round.Establishes: A polyrhythm repeats at the lowest common multiple, and which pulse is the beat is genuinely undecided.
- 06GrooveSwing measured rather than described, and the awkward finding that more timing deviation is not more groove.Establishes: Microtiming is measurable, tempo-dependent, and does not straightforwardly cause the thing it is credited with.
Three kinds of claim, again
Some of this course is arithmetic and would hold with nobody in the room. A polyrhythm returns to its starting point after a number of pulses set by the lowest common multiple, and the timelines in lesson 4 come out of the same maximal-evenness algorithm that picked the diatonic scale in Harmony.
Some of it is a fact about hearing, established by experiment and quoted here rather than derived: that a pulse is inferred at all, that it works only within a certain range of speeds, that identical events get heard in groups.
And some of it is convention, including a good deal of what is normally asserted most confidently. Lesson 6 takes the most cherished claim in the area, that human timing deviation is what makes music feel alive, and reports what happens when it is actually measured.