Detect a Change in Duty Cycle
Those pulse width changes are so slow, that I think I can see them happening on a video. That suggests they may last more than one field time. I.e. they last, maybe 1/25th or 1/30th of a second. That might take several cycles (as the cycle appears to be 10ms).

My 'knee jerk' is to use small microcontroller (e.g. an ATtiny85, like a digispark). I would tend to choose this path because it is a time-based signal, which may have more variability than the scope shows, and so may need some flexibility in how it is treated. Something which can use an Arduino IDE is likely to have some other people who can help you when you get stuck.

Also, though there appears to be a single input signal and one output, an LED, you might think of other things which you'd like to observe. An an MCU is handy for this.

I believe reaction time better than 1/20th of a second is unusual, so that might be 'instantaneous' enough, though I am willing to be corrected when it comes to music.

If you have a bit more money to spare, I'd probably use an ordinary Arduino, as it can talk to the host PC, which would help with testing and debugging.