I started with a webapp, but it couldn't run in the background, so I (or, well, little helpful shoggoths: Claude, Gemini, & Codex) built a native iOS app instead. The core functionality is simple: every few seconds (configurable), it makes a subtle cue sound, and one second later, it plays a short sound coming precisely from the direction of North using spatial audio (headphones required). After a couple of weeks, I found I could instinctively sense North, including when the app wasn't running. It's definitely not magic: if I teleport somewhere (i.e., use the tube), I normally need to look at the compass once to start tracking it again; but it still feels like I've acquired a new sensory modality.
The app also supports vibration mode (for discreet haptic pulses when you're facing North), runs unobtrusively in the background without affecting your music or podcasts, and can be calibrated to offset the phone being at an angle in your pocket.
I now usually know the direction of North instantly without actively thinking; navigation feels genuinely easier and more intuitive. It's probably most beneficial in areas without strict street grids (like most of Europe) than in the US, though.
The source code of the app is on GitHub, and the app is on the App Store.