This problem has been bothering me ever since I learned about Fourier transforms and the frequency domain as an undergraduate who loves music. Unlike in electrical engineering and physics, where frequency is a *linear* scale, and an entire bounded spectrum can be translated up/down in frequency using mixing converters, 12-tone music uses a *log* frequency scale, and I'm not aware of any simple Fourier formulae that work on a log frequency scale. The ultraviolet catastrophe shows that the amount of information encoded in higher musical octaves grows enormously, so any invertible Fourier translation of standard 12-tone scales is going to have to throw away this extra information. Is anyone here aware of any interesting papers or theorems which involve *linear* time and *logarithmic* frequency? Or perhaps there are Fourier-like theorems that involve *logarithmic* time and *logarithmic* frequency? Or *exponential* time and *logarithmic* frequency?