Beat, tempo, metre, rhythm · From Zero to Mozart

Four words get thrown around loosely and mean four different things. Sorting them out now saves a lot of muddle later, because almost every rhythm problem is really a confusion between two of them.

Beat — the pulse you'd tap your foot to. Steady, even, usually felt without counting.
Tempo — how fast that pulse goes. Measured in beats per minute: 60 is one beat a second, 120 is twice that.
Metre — how the beats group. Music leans harder on some beats: a march goes "one-two, one-two"; a waltz goes "one-two-three". That pattern of leaning is the metre.
Rhythm — the actual pattern of longs and shorts you play on top of the beat. The tune's own shape in time.

The beat is the grid. Tempo is how fast the grid scrolls past. Metre is how the grid is grouped. Rhythm is what you draw on it.

Same beats, faster and slower — that's tempo

60 bpm

Eight plain beats. Play it at 50, then drag the tempo to 150. Nothing about the rhythm changed — same eight equal beats. Only the speed of the pulse moved.

Same speed, grouped differently — that's metre

100 bpm

Eight beats grouped in twos — a march. Lean on every 'one'. Feel the strong–weak, strong–weak.

100 bpm

The exact same pulse speed — now grouped in threes, a waltz. Lean on 'one', let 'two' and 'three' fall away. Same beat, different metre; the accent moved.

The rhythm is not the beat

The beat keeps marching underneath while the rhythm does whatever the tune wants on top — sometimes matching the beat, sometimes not.

72 bpm

Tap a steady four with your foot. Now clap this rhythm on top — a long note, then quicker notes, then a held one. Your foot doesn't change; the hands do. That's the rhythm living over the beat.

The usual mistake

Saying "faster" when you mean "more notes." Playing eighth notes instead of quarters is not a faster tempo — it's the same beat, cut into smaller pieces. If a passage feels like it's getting away from you, check first: did the pulse actually speed up, or did you just hit a busier rhythm and start to panic? Nine times out of ten it's the second one, and the fix is to keep your foot steady.

Try

Set a metronome to 80 and tap along in plain beats. Now, without touching the metronome, fit two claps into each click, then three, then four. The tempo never moved. You were subdividing — a rhythm question, not a speed question.