Another excerpt from Curtis Roads' recently-published book, Composing Electronic Music: A New Aesthetic (Oxford, 2015):
[Gérard] Grisey based his rhythmic theory on perception, rejecting approaches based purely on simple mathematical abstractions such as prime numbers, Fibonacci series, and so on. He did not reject mathematics, but he felt that algorithms needed to take perception into account. As he pointed out, in Stockhausen’s Gruppen (1957) for three orchestras, the work’s rhythmic structure is highly organized in terms of tempi but unfathomable to the listener:
The tempi have great structural importance. Who perceives them?
Grisey took issue with rhythmic abstractions promoted by the integral serialists, who were strongly influenced by Messiaen’s book Technique de mon langage musicale (1944). One of the techniques described by Messiaen was non-retrogradable rhythm, or rhythmic palindrome (figure 6.4). He defined these as follows:
Whether one reads them from right to left or from left to right, the order of their values remains the same.
Messiaen’s student Pierre Boulez experimented with related methods of generating symmetric and asymmetric rhythmic figures by transformation of rhythmic cells. For example, he created figures that were the rhythmic inverse of another figure (i.e., notes replaced by rests and vice-versa).
As Grisey (1987) pointed out, these kinds of rhythmic abstractions (i.e., permutational and symmetrical note relations) make absurd assumptions about perception:
Such a distinction, whatever its operational value, has no perceptible value. . . . What a utopia this spatial and static [notion] of time was, a veritable straight line at the center of which the listener sits implicitly, possessing not only a memory but also a prescience that allows him to apprehend the symmetrical moment at the time it occurs! Unless, of course, our superman were gifted with a memory that enabled him to reconstruct the entirety of the durations so that he could, a posteriori, classify them as symmetrical or not!