EIGENMODE.

Circular membrane · Bessel eigenmodes

Eigenmode The notes a shape can hold

A clamped drumhead can only vibrate in a fixed alphabet of shapes — its eigenmodes. Step through them in the order the drum hears them: concentric rings and radial diameters, each ringing at its own inharmonic pitch.

Mode 03 / 10 J₂₍₁₎ Two diameters cross the head — a four-lobe clover of antinodes.
Nodes 2 diam · 1 circ
Ratio ×2.136
Pitch 205Hz

← → step · space sound

Reading the drum

Every circle keeps the same alphabet

01 — The alphabetStrike a taut circular membrane and it cannot move however it likes. The wave equation, clamped at the rim, permits only a discrete set of standing shapes. Each is a Bessel function Jm in the radius times a sinusoid around the angle.

02 — Two numbersEvery mode is named by two integers. m counts the straight nodal diameters that split the head; n counts the still nodal circles nested inside the rim. The pair (m, n) fixes the shape exactly.

03 — InharmonicThe pitches are set by the zeros of the Bessel functions, which are not whole-number multiples. That is why a drum sounds like a drum and not a flute — its overtones ring at 1.59, 2.14, 2.30… never a clean octave.

04 — What you seeGold lobes push toward you, violet lobes push away, and the dark seams between them are the nodal lines that never move. The bright rim is clamped: pinned flat while the interior breathes.

#ShapeαRatioDescription