Eigendrum - draw a shape and hear it as a real drum
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tag and the other only in a dialog: which host is<br>canonical, and how to reach the developer. Everything here is true and is said<br>somewhere visible too. -->
Eigendrum is hosted at eigendrum.com. The older address<br>baselashraf81.github.io/eigendrum is a mirror that redirects there, so eigendrum.com<br>is the canonical URL to link to and to cite. For advertising and partnership<br>enquiries, contact the developer, Basel Ashraf, at [email protected].
Hosting usage is close to its monthly limit less than a day after this went up.<br>If Eigendrum is worth a coffee to you, it keeps the lights on:<br>Ko-fi<br>PayPal<br>Liberapay
An interactive drumhead. Press Enter or Space to strike it at the marked point, and use<br>the arrow keys to move that point. While drawing is switched on, drag with a pointer to<br>trace a new outline.
tap the drum
building the mesh
where the overtones fall
pushed one way
nodal line, never moves
pushed the other way
Every mode is a standing wave this outline permits, and no other. Tap anywhere: the<br>modes with a nodal line under the mallet stay silent, which is why the same drum sounds<br>different depending on where you hit it.
forms
draw your own
from an equation
from an equation
polar<br>parametric
r(t) =
x(t) =
y(t) =
t sweeps one full turn, in radians. Size does not matter: every drum is scaled to<br>the same area, so only the shape is audible.
hear it
Everything below still describes the previous drum.
can one hear the shape of a drum?
hear the other one
modes
press any row to hear that mode by itself - or a key. Modes 1 to 16, in order:
123456789QWERTYU
advanced stats
what you can and can't change
The shape sets its real pitch and overtone pattern. The reference pitch slider names<br>the note a same-area circle would make, so your shape may land higher or lower. Ring-out<br>controls how quickly it fades.
reference pitch
130 hz
ring-out
balanced
mallet
medium
show the mesh
copy link
sound
image
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Site
Built by Basel Ashraf. Free to use. Source available, non-commercial licence.
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Eigendrum is free and has no account, carries no advertising, and stays up on<br>voluntary support alone. If it was worth something to you, that is the way to<br>say so.
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how it works
A drumhead clamped at its rim can only vibrate in certain shapes, at certain frequencies.<br>Those shapes and frequencies are the solutions of
−∇²u = λu inside the shape, u = 0 on the edge
Each solution u is a mode, a standing wave, and each λ gives a frequency<br>proportional to √λ. This is an eigenvalue problem, and for almost every shape it has no<br>formula. So Eigendrum solves it numerically: it covers your shape with a mesh of<br>triangles, builds the finite element stiffness and mass matrices, and finds the smallest<br>eigenvalues of Kφ = λMφ.
why you can trust the numbers
A few shapes have spectra that can be written down exactly, and the solver is tested<br>against them on every change. A circle's frequencies are the zeros of Bessel functions; a<br>rectangle's are π²(m²/a² + n²/b²). The solver reproduces both to<br>better than a tenth of a percent, and because a conforming finite element method minimises<br>energy over a restricted space, its answers are guaranteed slight<br>overestimates, never under. The measured error is in “the numbers”.
where you strike it matters
Striking a spot drives each mode in proportion to how much that mode moves there. Hit a<br>line where a mode stands still and you cannot excite it at all. That was not programmed<br>in; it falls out of projecting the mallet onto the modes.
So a strike is never one mode: it is every mode at once, in a mixture set by where your<br>mallet landed. The rules along the mode list are that mixture, and the modes marked with a<br>square were the ones your mallet could not reach. Pressing a row instead plays that single<br>mode alone - something no mallet can do, and the only way to hear what one<br>frequency of a shape actually sounds like.
drums from equations
Besides tracing an outline you can write one. r(t) gives the<br>radius as t sweeps one full turn, so<br>1 + 0.3cos(5t) is a five-lobed flower; a parametric<br>x(t), y(t) pair reaches the closed curves polar cannot, like a<br>nephroid or an egg. This is not a shortcut for drawing. It reaches shapes no hand traces<br>accurately - eleven even lobes, a superellipse partway between a circle and a square - and<br>it makes a shape something you vary: change one number and hear what moved.
A written shape travels as its own text. The link for a formula holds the formula, so it<br>is something you can read and retype rather than a few hundred characters of encoded<br>outline, and editing it in the address bar works. Anything too thin to mesh honestly is<br>refused rather than answered, because a sliver would still return numbers and they...