Math LabLab v Rhythm

Lab v

Slicing time

A bar of music is a whole pizza. Cut it in halves, quarters, eighths — or threes — and turn each slice on or off while the beat sweeps by.

one bar, five ways to slice it — tap a slice to turn it on

whole1 × 1/1
halves2 × 1/2
quarters4 × 1/4
eighths8 × 1/8
triplets3 × 1/3

read it on a stave — pick a row

One line, one pitch — so the only thing on the page is time. A slice you switched on is a note; a slice you left off is a rest, which is silence written down and counted just as carefully. 4 of the 4 quarters slices are on. The triplets row is missing on purpose: dividing the bar by three needs a tuplet bracket, and we would rather leave it out than write it wrongly.

tempo — how fast the bar goes by100 BPM

one bar lasts 240 ÷ 100 = 2.40 s

Same pizza, different slices

Every row is the SAME bar of time. The quarters row cuts it into 4 equal pieces; the eighths row cuts it into 8. Two eighths fit exactly inside one quarter — that's 1/8 + 1/8 = 1/4, and you can hear it.

Threes are rebels

The triplets row cuts the bar into 3 — and 3 doesn't fit neatly into 2, 4 or 8. Its slices land between everyone else's. That in-between feel is called a triplet, and drummers love it.

3 against 2 = LCM

Press the “3 against 2” button. Halves click 2 times, triplets 3 times — and they only land together at the very start of the bar. They next meet after 6 little slices, because 6 is the smallest number both 2 and 3 divide into: the LCM. Polyrhythm is LCM you can dance to.

For the classroom

Learning goals

  • Fractions with different denominators (1/2, 1/4, 1/8, 1/3) can share one whole — the bar — and be compared by ear and eye.
  • Equivalent fractions become audible: two eighth-note clicks occupy exactly one quarter-note slice.
  • The least common multiple predicts when two rhythm cycles coincide: 2 against 3 realigns every LCM(2,3) = 6 sub-slices.

Try this

  1. 1.Turn on ALL quarters and ALL eighths, play, then ask: how many eighth clicks per quarter click? Now predict for eighths vs halves before trying it.
  2. 2.Load '3 against 2' at 70 BPM. Split the class: half claps with the halves row, half with the triplets. Ask where everyone claps together — then slow it down and count the 6 LCM slices out loud.