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EphemeraPOLES
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A sister instrument to Ephemera

POLES

A Playable s-Plane.

H(s) = k · Π(s − z) / Π(s − p)

Place points on the complex plane. Each one is a decaying tone. The sum is the sound.

Open the s-plane →

Free in browser · strike with the spacebar

nCount9
σDamping198 ms
jωPitch310 Hz
QQ22

A playable s-plane.

H(s) = k · Π(s − z) / Π(s − p)

Poles is the Laplace transform you can strike. Place points on the complex plane - each one is a single decaying tone. Their sum is the sound.

Left to right is σ: how fast a voice fades, from a quick pluck on the left to an endless ring on the right. Down to up is jω: its pitch. That is the whole instrument - two coordinates per voice.

Nothing plays until you strike. Then every pole rings at once, like a struck bell, and decays along the curves you drew.

The board

Left to right is how long it rings. Down to up is pitch.

p = σ + jω

One plane holds the whole instrument. Every voice is a single point on it, and its place decides everything you hear.

The s-planeA complex plane. The horizontal real axis (sigma) runs from decay on the left to growth on the right. The vertical axis (j-omega) is pitch. The amber vertical line at sigma equals zero is the stability boundary - past it, a sound never fades. Cyan stable poles sit on the left in conjugate pairs; one amber pair has crossed the boundary and rings on.σ← decaygrowth →jωpitch ↑σ = 0past here, sound never fadesstable · rings, then fades
  • σ - decay ← → growth
  • jω - pitch ↑
  • σ = 0 - past here, sound never fades

Try it

Drag a voice across the line.

Grab the pole and move it. Left it fades fast; toward the amber line it rings longer; past it, the sound never stops.

σ →σ = 0σ = -4.5 · fades

Drag the dot · or focus it and use the arrow keys · the strike bar follows along

How it works

Three moves. One bell.

01

Place a voice

p = σ + jω

Drop a point on the plane. Its place is the whole sound: left↔right sets how long it rings, down↔up sets its pitch.

02

Strike

x(t) = Σ e^(σt)·cos(ωt)

Nothing sounds until you strike. Then the whole bank rings at once, like a struck bell, and decays along the curves you drew.

03

Reshape

σ → 0⁻ ⇒ τ → ∞

Drag a voice while it rings. Toward the line it sustains longer; past the line it self-oscillates forever, held just in check by a limiter.

What you can do

Six ways to shape a ring.

Every feature is a move on the same plane. Place, strike, and reshape - the math stays visible the whole way.

Strike to hear it

strike → Σ rings

Nothing sounds until you hit it. A strike rings the whole bank at once - like a mallet on a tuned bar - then every voice decays on its own curve.

Poles and zeros

z carves · p rings

A pole is a voice that rings. A zero is its opposite - a notch of silence that carves a band out of the sound. Place both to shape timbre, not just pitch.

Cross the stability line

σ > 0

Push a voice past σ=0 and it stops fading - it self-oscillates forever, a drone that feeds itself, held just in check by a soft limiter.

Couple your voices

kᵢⱼ binds pitches

Tie poles together. A solid thread pulls their pitches into unison; a dashed one pushes them apart. Move one and the others answer.

Exciters and dynamics

v · mallet · bow

Choose what does the striking - a hard mallet, a breath of noise, a sustained bow. Velocity and pen pressure shape the attack of every hit.

Record the motion

p(t) - orbit

Drag a voice while it rings and Poles remembers the path. Replay the motion as a modulation orbit - a sound that keeps moving after you let go.

Presets

Pick one. You’ll hear it.

Each is a real arrangement of poles on the plane. Tap Hear to ring it right here, then open it in the instrument to reshape it.

Bell

inharmonic · Σ pₙ

A struck bell - a cluster of inharmonic partials that bloom bright and fade together.

Open →

Bowed strings

σ → 0 · sustained

Voices held just short of the line - a sustained, breathing string section that never quite stops.

Open →

Glass harmonica

high Q · pure

A few very pure, very high voices - the wet-finger-on-crystal shimmer, almost no overtones.

Open →

Pendulum

low jω · slow

One low, slow voice with a wandering orbit - a deep tone that sways as it decays.

Open →

Cascade

pₙ ladder ↓

A harmonic ladder tumbling down - many partials staggered in pitch, ringing into each other.

Open →

Every preset is just a handful of points. Open one and move them.

“A pole is just a sound that hasn’t faded yet.”

The Poles idea

Try it first, own it later

One instrument, three doors.

Free Web

$0

The full s-plane in your browser. Strike, shape, and share by link. No install, no account.

Launch in browser →

Desktop

$19.99

Native app. Offline. Save and load files, audio + MIDI export, VST3 hosting, lifetime updates.

Get the desktop app →

Ephemera Bundle

Included

Poles ships free with Ephemera Premium and lives as a module inside Dimensional too.

See Ephemera →

One-time purchase · no subscriptions, ever · free forever in the browser

FAQ

Questions, answered.

No. Drag a dot, strike, and listen — that's the whole loop. The transfer function and the σ/jω labels are there if you're curious, but you never have to read them to make a sound.

Strike it yourself.

place · strike · reshape

Free in your browser, no account. Place a few points, strike, and hear the math ring. Then share the plane you made.

Open the s-plane →