TIL my piano simulates resonance

Since I can’t keep tuning a physical piano, I bought a digital one. Today I was playing a song with sustain pedal, and I noticed that the low notes sound different when the pedal is pressed.

The (physical) pedal works by releasing the damper from all notes when pressed. Normally (when not pressed), the damper holds the strings that aren’t being played so that they don’t vibrate (or stop vibrating).

First without pedal, then with pedal

I’ve noticed that the digital piano simulates the strings’ sympathetic vibration from a physical piano.

If you don’t know what resonance is, it’s when an object, in this case the piano string, is subject to a force, in this case the air pressure, that varies at a frequency similar to the object’s resonance frequency.

If the object were a swing chair, it would be akin to apply a force every time it gets near a given point. The swing swings more. If the force is applied in different times, the swing doesn’t swing as much.

In this case, the low notes’ frequencies divide the frequencies of the higher notes. For a more precise prediction of which notes divide which, take a look at the harmonic series. In the swing’s case, it’s like pushing every nth swing: it swings less, but still swings quite a lot.

This was the input for the above audio:

Sheet music with 2 low Cs in octave, played twice. In the second time, the pedal is pressed and released
Generated by computer to minimize my hand’s variations

I personally find this intersection between physics and music very interesting.