Synaesthesia is my favourite music visualization program. I created an updated Windows port and also ported it to Emscripten. The code is on GitHub. Here is a screen shot, but you have to see it in action to really appreciate it.
Click here to run the program. Then start visualization by dragging an audio file from a file browser window on your computer to the web page. No information is sent over the network. The file is played by the web browser and visualized by asm.js running in the browser.
If you find that Firefox can't play MP3 files in Linux, install gstreamer1.0-fluendo-mp3.