In mathematics, the Gibbs phenomenon, discovered by Henry Wilbraham (1848) and rediscovered by J. Willard Gibbs (1899), is the peculiar manner in which the Fourier series of a piecewise continuously differentiable periodic function behaves at a jump discontinuity: the nth partial sum of the Fourier series has large oscillations near the jump, which might increase the maximum of the partial sum above that of the function itself. The overshoot does not die out as the frequency increases, but approaches a finite limit.
These are one cause of ringing artifacts in signal processing.
The basic issue with Carter is that the ultra-complex structures that appear in the scores aren't actually understandable to the ear. I can play time signatures like 5 against 3 quite accurately - this probably puts in 1% of 1% of the world (it isn't particularly hard to do, a days' dedicated study will get you 3 vs 4, 3 vs 5 and 4 vs 5, but how many people spend a day studying polyrhythms) but I've sat through Carter string quartets looking at the score with the complex polyrhythms all spelled out - and it just sounds like a lot of notes at the same time.
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