The problem with solutions based on tracking where we are in the music, then inferring the correct action, is that it still encodes assumptions about when the page should be turned, which is great... until it's wrong.
I think the most natural is a pedal, which has actually been implemented.
Grandparent's suggestion of ambient audio seems rather inadequate. Pianists don't turn pages always at the very end of the page. They read ahead, and how much they read ahead depends on the particular passage.
Yes, I implicitly added a requirement for myself that I not merely duplicate off-the-shelf tech, because that would be boring. One characteristic of that solution is that it requires additional hardware, whereas head tracking (and maybe eye tracking) could be done with the same setup pictured in the article. But I would totally agree that given a pedal, that will be the superior solution on almost every level. Truly, nothing else speaks with the input clarity and precision of a simple button.
However, I worked on the prototype for a music app that does polyphonic pitch detection for a greater effect than page turning. It listens and follows along note by note as you play your (real) guitar and, as you hit the notes properly, actually uses the master tracks of rock songs to give you a very cool sensation of playing the real song. It's called Rock Prodigy: Guitar and is free with per-song IAPs if you want to try it out.
People will want to play the first few measures over and over, try something again after messing it up, stop and take it from the top and so on. If you turn the page too soon or scroll the music the user is playing off the screen, the customer reviews are going to look like Armageddon has come.
The only way I see that works understandably and well enough is to recognize when the last measure of the last staff is completed. Even that may be incompatible with some music, but it should work well enough in general.
Even better if the App was able to match the scrolling speed to the playing speed automatically.
I also heartily agree with the commenter who noted that continuously-scrolling music would be disorienting in real use.
They have yet to experience the pain of a thousand cuts that (that my team and I have gone through) that is working with the music publishing industry.
The thing with these apps is that people who don't really understand them group them all together. "Oh, another music-y app for fancy music people!"
While their app now is not remotely a competitor, if they actually get some real funding, they could pivot in a number of ways to compete against apps like mine, because they've been able to position themselves well in the "music app startup" slot by presenting at TC.