Quite a few years ago, I did some research into the problem of pitch recognition. As it turns out, traditional methods (based on Fourier AnalysisI) don't give very good results: they aren't accurate enough, and you can't apply them in real time. So I did some mathematical research, and Master Tuner™ was born.
I went to a couple of the big trade shows, and completely failed to sell thousands of copies, although it was enthusiasticaly received by musicians. So I gave up on it ... upon which the trade magazines said nice things about my product, and it went on to make money.
It turns out that I was the first person to take the mathematical approach that I did - the next person to publish anything on the subject was a Judith Brown of MIT, who published a paper a couple of years later. So, years later, I did an MSc based on my original research, plus some of the ideas which had been published in the intervening years.
Now I'm completing a PhD in the Faculty of Interdisciplinary Studies at the University of Calgary, trying to push the boundaries further. My research is in the area of real-time pitch and tempo analysis of musical performances. The intention is to create another commercial product, which will make musician's practice time much more effective. If you've got great ideas for an education game to teach musicians to play better, I'd love to hear from you!
Academia is also about publishing. Here's a journal paper, jointly submitted by my supervisor and me.