Beep.js really isn't a synthesizer, it's more of a step-sequencer. You might want to check out WAD.js, which is more concerned with synthesizing sounds than scheduling them (it has filters, LFOs, other effects, etc). https://github.com/rserota/wad. Full disclosure, I wrote WAD.js.

and btw it's totally possible to make well-timed music with web-audio. I've got a midi keyboard hooked up to web-audio based looper, and that's what I use as my primary instrument these days for practicing. It works fine for me.

Impressive. Though your demo works (for me) only in Chrome (no error and no audio in FF & IE11).

Certain features that I depend on (particularly midi input) are only available in chrome as of right now, so I honestly only test it in chrome, though most of the basic functionality ought to work in other browsers.

This is the point where I stop and say "oh well, wait another year and maybe then..."

"Evergreen browsers only" is reasonable to ask for lots of sites; but "This site only works properly in the Chrome browser" gives me unpleasant flashbacks to when this notice was everywhere, but the browser was "IE5".

Failing that, it could also be interesting to explore the possibilities of making sounds and music that aren't so dependent on timing. Eventually consistent tunes, if you will. :)