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Metronome
Emma

创建者

Emma

20. 八月 2026SE
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Metronome

A pendulum that beats slowly without being long. An ordinary pendulum's period depends on its length, so a comfortable 60 beats a minute needs about a metre of swing — no use on a piano. The trick is to put a second weight ABOVE the pivot. That raises the whole system's centre of mass toward the pivot point, which weakens the restoring force and stretches the period, so a pendulum barely 20 centimetres long can be made to tick as slowly as you like. Slide the upper weight to change the tempo. Dietrich Nikolaus Winkel in Amsterdam built this double-weighted pendulum around 1814. Johann Nepomuk Maelzel saw it, added a graduated scale, patented the result in 1815 and put his own name on it — which is why tempo markings still read M.M. today.
初学者
45 minutes

说明

1

Show the length problem

Establish why an ordinary pendulum will not do.

  1. Hang a simple pendulum 20 cm long and time twenty swings.
  2. Convert to beats per minute.
  3. Calculate the length needed for 60 bpm.
A 20 cm pendulum runs fast — well over 100 beats a minute. Reaching 60 needs close to a metre. A musician's desk cannot hold a metre of swinging brass, and that constraint is the entire reason the metronome is built the way it is.

此步骤所需材料:

Steel RulerSteel Ruler1
StopwatchStopwatch1
2

Pivot a rod in the middle, not the end

Build the double-weighted pendulum.

  1. Pivot a light rod so that a good length projects both above and below the pivot.
  2. Fix a heavy weight low on the bottom arm.
  3. Fit a second, sliding weight on the upper arm.
The lower weight supplies the restoring force that brings it back; the upper weight works against it. The two are in tension, and the tempo is set by their balance rather than by the rod's length.

此步骤所需材料:

Brass RodBrass Rod1 length
Digital Kitchen ScaleDigital Kitchen Scale1
3

Slide the upper weight and map the tempo

Now calibrate it, which is exactly what Maelzel added to Winkel's mechanism.

  1. Set the sliding weight low and time twenty beats.
  2. Move it up in steps, timing at each position.
  3. Mark the rod with the beats-per-minute you measure.
Raising the weight makes it SLOWER — the opposite of what most people predict. Notice too that the scale is not evenly spaced: the beats crowd together at the fast end, which is why a real metronome's numbers are printed unevenly.
4

Find the point where it stops working

Push the adjustment to its limit and watch the mechanism fail.

  1. Keep sliding the upper weight higher.
  2. The beat slows further and further.
  3. Eventually the pendulum will not return at all and simply falls to one side.
Past that point the combined centre of mass has risen above the pivot, and the rod is an inverted pendulum — an unstable system with no restoring force. The slowest tempo on a metronome is set by how close its designer dared approach that limit.
5

History and context

Dietrich Nikolaus Winkel, an Amsterdam mechanician, built the double-weighted pendulum around 1814. Johann Nepomuk Maelzel — showman, mechanician, and the man behind the touring chess-playing automaton the Turk — visited him, saw the device, and in 1815 patented a metronome using the same principle with a graduated tempo scale added. Winkel took the dispute to a commission of the Netherlands Royal Institute, which found in his favour and recognised him as the inventor. Maelzel had the name, the patent in other countries and the distribution, and it is his initials that ended up in the repertoire.

Beethoven adopted the device enthusiastically and went back to add M.M. markings to earlier symphonies. Many of those markings strike modern performers as implausibly fast, and there is a long-running argument about why — a faulty metronome, a misread scale, a different convention for what counts as a beat, or simply that he meant it. No explanation has settled the matter, and performances still differ enormously as a result.

What it did to music is worth stating carefully. Before the metronome, tempo words like allegro carried meaning that was regional, traditional and negotiable. A number is not negotiable. Composers gained precise control over something they had previously had to trust performers with — and performers have been arguing about whether that was a gain ever since.

材料

4

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