Fourier Touch has practical applications as a teaching tool besides being a tool to generate tones for use in composition. It’s actually one of several apps by KonakaLabs that are available free, and well worth a look.
One neat feature is that you get a readout of the exact frequency you are generating, and how wave forms interact, though only one waveform type (sine, triangle, saw, square, etc) is playable at one time. Still, it’s enough to inspire interesting sound creation, particularly if you add other processing (like a reverb pedal) afterward.
There are also two accelerometer interactions built in, which can be a bit frustrating at first. One of them is set for volume. Another is set for frequency, so when you stop touching the screen, the program will default to a frequency and volume based on how you hold the device.
This is one app that is less useful when the iPad is mounted in a stand. The best results for experimental tones come from holding the iPad flat, then tilting it in various directions with one or more fingers on the screen so that the resulting combined waves, frequency sweeps and volume changes generate alien radio transmissions.
Here’s a short alien radio transmission: