Permanent magnet manipulation of a piano string:
Experiment with Matt Choboter and Jenny Graf Sheppard Feb. 6th 2024

A flat 38 x 8 mm neodymium magnet was placed above a piano string (D4) at different fractions of the string length and with the magnetic pole pointing down towards the string.

We tried four different points: 1/5, 1/4, 1/3 and 1/2 of the string length (setup as seen in the video below).

Multiple solenoids along the string. The solenoids are 12V push/pull solenoids bought for another purpose, and they are not ideal because they have a groove in the core. Yet, by placing the string just at the edge of this groove a clearly audible change in pitch was achieved.

When plugged the string vibrates in two dimensions simultaneously. Therefore I made a wheel of six electromagnets to impact the string equally from all directions. The effect was too little to evaluate because the magnets were too weak to have an obvious impact.

The spectral analysis shows that the tone splits.
Each overtone splits in a diffenrent way: They split more when the magnet moves towards their respective anti-nodal points and not at all when the magnet is at their nodal points.

We had the perception when playing the tones that something was sounding an octave below the fundamental. The spectrogram does show energy in the low register (below 200 hz), but not at an octave below. As the magnet moves towards the center of the string the tone F3 a major sixth below the fundamental seems to become stronger. Yet, this tone is very weak and unstable, so it may just be noise in the room, noise in the recorder or maybe a resonant frequency of the piano frame.
 
I did expect that the frequencies would be dependent on the amplitude. But that doesn’t seem to be the case.

The two vidoes at the right shows a string activated by an e-bow. An electromagnetic coil is towards the other end of the string (both at about one third of string length).

When I apply current to the coil the eigenfrequency of the string changes.

In the left video the tone drops by a major second, in the right only by a semitone.

Magnetic impact on a string (Documentation)

Electro-magnetic manipulation of a mono-chord:
Experiment at KKT Feb. 5th 2024

These two pdf-files contain spectral analysis of various sound examples. Analysis and comments made by William Sethares.

Relatively tensed string bending down about a major second

Model of field lines: Row of fields

Anticipated shape of the magnetic field: Circle of fields. Model made with javalab

Recoding of the same four tones as the video shown at the left.

The spectrogram shown underneath the audioplayer corresponds to the audio recording.

 Full spectrogram analysis of the four piano tones. Spectrograf made with Spear software

Zooming in on the partials. Spectrogram annotated with cent diviations. Also annotated with "Nodal point"/"Anti-nodal point", refering to the placement of the magnet relative to wave pattern of each overtone. For the nodal points the spectrogram is also coloured red.

Nodal point

Row of solenoids

Magnet placed above the following fraction of the string length:

1/5                          1/4                           1/3                          1/2

1/5                          1/4                           1/3                          1/2

                   Magnet placement (fraction of string length)

Video

Nodal point

Anti-nodal point

Same string, more loosely tensed. Bending down about a semitone

Right side

Nodal point

Full top view: A guitar pickup were mounted at the end for recording

Anti-nodal point

Anti-nodal point

Nodal point

Nodal point

Anti-nodal point

5th partial

4th partial

Fundamental

2nd partial

3rd partial

Left side