William R. Everdell, in his fine book The First Moderns, identifies five central aspects of Modernism. The first four are 1), the idea that truth lies in the statistical regularities of any given phenomena (probability vs. determinism), 2), "multiple perspective", that is, that every idea or fact implies the perspective from which it was observed, 3), that objectivity is no more reliable than radical subjectivity in the observation, description, or expression of reality, and 4), that any system contains enough self-reference or recursiveness to undermine the system itself.
The fifth aspect, one that subsumes all the others, is ontological discontinuity. This discontinuity can be seen as the central mode of thought and expression in the Modernist era (Mr. Everdell doubts that the Modernist era has ended, in fact). It exists in the space between atoms and in the distance between whole numbers. Binary digitality itself ("0" and "1") is an expression of discontinuity because there is an infinite number of numbers between zero and one, and space between each of them.
The art of the 20th century, including the music, is no exception. All of the pieces on the 101 list embody one or another of these aspects of 20th centruy thought, as well as the traits of the postmodern listed by Jonathan Kramer. This overlap of Modern and postmodern thought leads Mr. Everdell to conclude that the postmodern is reall a continuation of the Modern, with different emphases.
As we explore the compositions on the list, and I attempt to explain why they are there, we'll come back to these aspects of the Modern and see (hear) how they inform 20th century art, thought, and life.