Whole, half, quarter, eighth. Build a bar, and every new pattern you invent gets collected. There are 56 in all — go hunting.
A bar in 4/4 needs four beats — no more, no less. But there are loads of different ways to get there. Build one, and it goes in your collection.
build a bar — it collects itself when it hits 4 beats
empty — add a note value below
your collection
You have found 0 ways to make 4 beats — out of 56
Nothing collected yet. Build a bar above and it lands here — tap any one to hear it again.
what exactly are we counting?
We are counting ordered patterns — the order you play them in. ¼ + ½ + ¼ and ½ + ¼ + ¼ use exactly the same blocks, but they are different rhythms, so we count them as two. Mathematicians call an ordered list like this a composition.
ordered patterns making 4 beats = 56
If you only cared which blocks were in the bag and not what order they came out, there would be far fewer. Then ¼ + ½ + ¼ and ½ + ¼ + ¼ are the same handful of blocks — one answer, not two.
different sets of blocks = 10
Both numbers are correct — they answer different questions. Always say which one you mean. Everything on this page counts the ordered kind, using the whole, half, quarter and eighth notes.
a smaller puzzle you can finish
Throw away the whole note and the eighth. Now every bar is built from halves (2 beats) and quarters (1 beat) only. Try to find them all before you press the button — there are exactly 5.
a pattern worth spotting
1, 2, 3, 5 — each number is the two before it added together. It happens because a bar either starts with a quarter (leaving 3 beats to fill) or with a half (leaving 2), so ways(4) = ways(3) + ways(2) = 3 + 2 = 5. Those are the Fibonacci numbers, hiding in a rhythm exercise.
From the NSM syllabus
For the classroom