Every movement, however free it looks, has a pulse. A step, a swing of the arm, a beat of a wing — each repeats, and each repetition takes time.

This session gives you the physical vocabulary for talking precisely about that pulse: period, frequency, and speed — and why they are not the same thing.

By the end, you'll be able to describe your own heartbeat, your own gait, even a hummingbird's wing, in exactly the same terms — which is also the first step toward tracking movement and turning it into sound, piano included.

A period (T) is the time it takes for one complete cycle of a repeating motion — one full step, one full wingbeat, one full swing.

Frequency (f) is simply how many of those cycles happen per second: f = 1 / T. If a step takes half a second, its frequency is 2 steps per second.

Frequency is measured in Hertz (Hz) — one Hz means one complete cycle every second. A slow, heavy motion has a long period and a low frequency; a quick, light motion has a short period and a high frequency.

The simplest periodic body in physics is the pendulum: a weight swinging from a fixed point.

Its period depends only on its length and on gravity — not on how wide it swings, and not on how heavy the weight is. A longer pendulum always swings more slowly than a short one.

This single fact — longer means slower — turns out to govern almost every example in today's session, from a child's leg to a hummingbird's wing.

The most intimate periodic motion you own is your own heart: roughly one beat per second at rest — about 60-80 beats per minute, close to 1 Hz.

Under exertion — dancing included — that frequency can double or more, while the body's other rhythms (breath, stride) often tangle into related, overlapping periods.

Long before any machine measured it, the heartbeat was probably humanity's first unit of tempo.

Walking is periodic too: dancers and gait researchers alike call its frequency cadence — steps per minute. A relaxed walk sits around 100-120 steps/min, roughly 1.7-2 Hz.

But cadence alone doesn't tell you how fast someone is actually travelling. A tall person and a short person can share the same cadence and still cover very different distances per step.

Which raises the question underneath this whole session: if frequency alone isn't speed, what else is needed?

Speed is frequency multiplied by how far each cycle carries you — its amplitude, or in gait terms, the stride length.

Sprinters increase both: a faster leg-cycle frequency and a longer stride. Elite sprinters reach cadences above 4-5 steps/second with strides over two metres — two independent quantities, frequency and amplitude, multiplying into genuinely extreme speed.

Keep this multiplication in mind: speed = frequency × amplitude. It will come back, almost unchanged, when we get to the piano.

Remember the pendulum: a longer pendulum swings more slowly. The same logic applies to limbs and wings, which behave like pendulums built out of muscle and bone.

A short limb (or a short wing) is a "short pendulum" — it naturally wants to oscillate fast. A long limb is a "long pendulum" — it naturally wants to oscillate slowly.

This is why small animals move in a blur and large animals move almost in slow motion — not because of effort, but because of size itself.

A hummingbird's wings beat around 50 times per second (50 Hz) — fast enough to hover motionless in the air.

A housefly's wings beat even faster, well above 150-200 Hz — too fast for the human eye to resolve as individual strokes.

Contrast that with an albatross, gliding on wings that may flap barely once per second, or an elephant's unhurried gait, with a period closer to two full seconds per step.

Same physics, three orders of magnitude apart — purely a function of size.

A piano string is, again, a pendulum in disguise — just a vibrating one instead of a swinging one.

Short, thin, tightly-strung strings (the piano's high notes) vibrate at a high frequency. Long, thick, loosely-strung strings (the low notes, wound in copper wire) vibrate at a low frequency.

Short and light vibrates fast; long and heavy vibrates slow — the exact same rule that separated a hummingbird's wing from an elephant's leg.

Music names the same quantity differently: tempo, measured in beats per minute (BPM).

A tempo of 120 BPM means one beat every 0.5 seconds — a period of half a second, a frequency of 2 Hz. A slow adagio at 60 BPM is a 1-second period, exactly the frequency of a resting heartbeat.

Tempo is simply frequency wearing a musician's name.

Entrainment is what happens when an independent periodic body — a footstep, a heartbeat, a swinging arm — locks its own frequency onto an external one, such as a musical beat.

This is most of what dancing is, physically: a body voluntarily tuning its many natural periods — stride, swing, sway — to a shared external frequency.

Which means a dancer's movement is not just inspired by music — it can be measured, cycle for cycle, against it.

Measuring a heartbeat or a pendulum is easy. Measuring a dancer's full-body period, in real time, on stage, is not — which is exactly the technical problem this course is named after.

Modern tools attack it from several angles: wearable accelerometers (measuring acceleration directly), motion-capture markers, and camera-based pose estimation (tracking joints frame by frame from ordinary video).

Each gives a stream of numbers over time — a position, a velocity — from which period, frequency and amplitude can all be recovered.

Once a movement's frequency is captured as a number, it can be mapped — frequency to pitch, amplitude to volume, period to rhythm — onto a piano, real or sampled.

This is the project underneath Dancing Piano: using the exact physical quantities introduced today — the same ones that separate a hummingbird from an elephant — to let a tracked body play an instrument with its own motion.

Every session from here builds, piece by piece, toward that pipeline: track, measure, map, sound.

Today's vocabulary — period, frequency, amplitude, speed, entrainment — is the physical foundation for everything that follows in this course.

Next sessions will get hands-on with the tracking side: how to actually capture a body's movement, and how to turn the resulting numbers into music.

Before then: notice your own rhythms this week — your stride, your pulse, the tempo of whatever you happen to be dancing to.