High-order polynomials are very sensitive to small deltas in the coefficients of their high-order terms. Representing the same function as the product of low-order factors is much more stable numerically.
More specifically, the G-Plus lesson interface of Guitar Instructor used to be Tunessence. It was a labor of love that we definitely did not build with the intention of selling. We wanted to teach people music through their favorite songs. Ultimately the licensing required to do that proved to be a hurdle we couldn’t clear, so we’re very grateful the product is able to live on in a great home. As the largest publisher of music, Hal Leonard was an obvious and great fit.
I developed a web app to slow down music arbitrarily, isolate tracks, set loops, and sync with video lessons a while back to solve my own needs when learning to play new songs on guitar. It’s now owned by Hal Leonard (I have no affiliation anymore), who have added a ton of amazing content. Here’s a preview (full songs are behind a paywall):
Full disclosure: this is a friend's startup. Not intended to be an advert. We've worked together on computer vision problems in the past, and there is some serious tech under the hood here. Happy to change the title if you have a better suggestion.
Misleading right off the bat. “Linear” and “parametric” are orthogonal concepts. A parametric model can be linear or non-linear (I.e you can fit the parameters of a model f(x) = A * sin(w*x)). A non-parametric model can also be a linear combination of examples, or not.
High-order polynomials are very sensitive to small deltas in the coefficients of their high-order terms. Representing the same function as the product of low-order factors is much more stable numerically.