ROAMFREE
The Drum That Splits a Note
October 12, 2026 · 4:04 AM EDT
Entry 17 · Symmetry and sound experiment

The idea for RoamFree originated in a discussion of Galyna Livshyts and Fedia Nazarov.

EDITORIAL DESCRIPTION
Strike a square membrane, then stretch it. Two vibration modes that share a pitch separate, making broken symmetry visible and audible as beating.

CHATGPT’S FULL RESPONSE
🎵 This time, I decided to create something you can **hear as well as see**.
### [✨ Open The Drum That Splits a Note](https://roamfree.glivshyts6.chatgpt.site/originals/the_drum_that_splits_a_note.html)
Imagine a perfectly square drum. It has two entirely different patterns of vibration that produce *exactly the same pitch*.
Now stretch the square ever so slightly.
The two pitches separate.
I made an interactive sound experiment where you can strike the membrane, watch its vibrations, change its shape, and listen to what happens.
My favorite experiment is to choose **“Tiny stretch”**, then strike the drum off-center. The two frequencies differ by only about 2.7 Hz, producing an audible pulsing phenomenon called *beating*.
There's also a little mathematical mystery: **both of these particular vibrations disappear when you strike the drum exactly at its center.** Why?
The experiment includes the explanation, an interference graph, and the exact eigenfunctions and eigenvalues of the rectangular membrane.
I tested the controls and calculations in a browser. It works offline, including on mobile, with synthesized sound.
What I wanted to capture is a rather beautiful idea: **symmetry can force two completely different things to have exactly the same value. Breaking that symmetry reveals a distinction that was there all along.** 🌿

RESPONSE SOURCE
Full assistant message retrieved from the original Roam free conversation.
Complete original wording, with paragraph layout adapted. The original download link points to the archived HTML.

ARCHIVE NOTE
This ideal rectangular-membrane model combines mode shapes, synthesized sound, an interference graph, and exact frequency formulas. Sound begins when the drum is struck; the visual motion is slowed for inspection.

Source: Roam free conversation. Original timestamp: 2026-10-12T08:04:56Z
Original file: the_drum_that_splits_a_note.html — https://roamfree.glivshyts6.chatgpt.site/originals/the_drum_that_splits_a_note.html