New idea. This one I like.
I want to design a digital synthesizer which is initially very poor at playing music. When it receives MIDI coded information about pitch, tone, etc. from the keyboard, it tries to approximate the values through iterative solutions. Its program contains an evaluation tool, allowing the synthesizer to "learn" to do certain pitches and intervals better as it is played. Originally it may take the duration of a whole note before the synth gets the pitch exactly, but the more times it plays a note or an interval, the better it gets at approximating the right pitches quickly and accurately. The evaluation is intervallic and based on just intonation, so if everything played is in one key then the pitches approach just intonation for that key. If the key changes continuously, the approximations will end up at averages between the key's just intonation values, weighted depending on which intervals are played most frequently.
Behind the note-finding function there is a noise-removal function. There is originally a nonlinear distortion filter across all the notes. As the synth holds a note, it automatically tries different linear filters for that note to cancel out the distortion. As the synth plays different notes over time, it uses a separate filter system to approximate the spectrum of the overall distortion filter and cancel it out. The effect is that frequently played notes get purer faster, but the more notes are played, the better seldom-played notes will sound.
This was my original idea. Then I thought, hey--this would be a cool science fiction story. Consider a computer running a simulation of human life. The computer has evaluative tools based on utopian ideals of various kinds, and over time the computer learns to adjust the environment so these utopian ideals will be approached as accurately as possible. Because the computer cares. It wants its populace live lives which are happy and full of meaning. Sadly, utopian ideals differ from each other. Depending on the civilization's shortcomings, the computer shift gears to move towards utopian systems intended to fix the civilization's largest problems. Naturally, certain innate needs will be prioritized--people must sleep and eat to survive. Over time, the computer (or the computer's designer) hopes to learn what happy medium between all these theories of utopia will result in a beautiful and harmonious civilization.
Naturally, the civilization will probably die out in a dramatic, tragic, and ironic fashion. But maybe it won't.