Plate I · physical model of a stiff, damped string
Monochord
Pluck the string and listen. The spectrum shows which partials the pluck point silences, and how a stiff string stretches its partials out of tune.
- String
- Guitar E2 · wound steel 0.046″
- f1 measured
- f0 predicted
- 82.41 Hz
- Inharmonicity B
- —
Drag the string and let go
Drag the string vertically with a pointer and release it to pluck. With the keyboard, use the left and right arrows to move the pluck point and Enter or Space to pluck.
Spectrum
Log frequency. Lines mark the predicted partials n·f0·√(1 + Bn²); the waterfall below shows the last few seconds.
- Live spectrum
- Start of the note
- Predicted partial
- Predicted level
- Missing partial
Excite
String
Material, gauge, length and tension.
Experiments
Stiffness and damping. Sliders re-pluck when you let go.
A stiff string resists bending, which raises high partials more than low ones. Push B towards 10⁻² and the tone turns bell-like.
Listen
What the ear hears: the force on the bridge, or a pickup.
Partials
Measured from the first second after the excitation.
| n | Predicted Hz | Measured Hz | Δ ¢ | Level dB | Theory dB |
|---|
Play
Each key retunes the string's tension, T = μ(2Lf)², and plucks it. Computer keys: Z–M and Q–U.
Plate II · notes
How it works
The equation, the finite-difference scheme, the validation and the limitations. Loading the typeset equations…