An argument for Schoenberg’s serialistic style being an extension of classical tradition could be made in various ways, I don’t presume that this will be an exhaustive list; they are merely thoughts that have surfaced in my study. One possibility is regarding the mathematics involved in 12 tone composition, it is completely feasible that one would be capable of composing a piece of music without “hearing” it at all, they could simply follow the agenda for churning out “chords and melody” until the row is used a specific number of time. The same could be said of western common practice harmony where chords move through stages of stability and instability based on their tonic, subdominant, and dominant relationships. There is also the more robust influence of science on music in the classical period. Common ideas regarding music’s influence on the human state were being changed from the “affections” of the Baroque period to an emphasis on complex relationships in the classical period. Dr. Margaret Hanning (the author of Concise History of Western Music) has argued that this stems from the emphasis for empirical study and scientific reform. Again, with the technological age advancing during the lifetime of Schoenberg, it was easy to see various classical ideas creeping up in the beginning of the 20th century. From these vantage points, the music of Debussy is considerably more “modern” than that of Schoenberg. Therefore, the music of the post WWII composers could be seen as a logical extension of the Schoenberg tradition in that there was frequently a mathematical basis for the compositional style, there seemed to also be a distancing of the general emotional state which was often attempted to be conveyed. This is not to say the pieces were devoid of any aesthetic purpose, it’s just that the pieces represented a much more intellectual aspect than the Romantics.
With serial-note composition being so fertile for compositional innovation, it was only a matter of time before other aspects of music was to become numbered. In the music of Messiaen and Boulez not only pitches were serialized but also rhythms, dynamics and articulations. This gave way to exciting passages full of variety in sonic possibilities but also came with a great deal of rhythmic complexity. The music of Stockhausen was something of a departure from the strict serialism of the above mentioned composers as he began thinking in terms of “whole” sounds made up on individual parts that would become another whole, Stockhausen did offer some classical input as he often sought contrast which Morgan likened to the practice of writing antecedent and consequent phrases. Milton Babbitt was a composer who did a great deal of work with rhythmic values in serial composition, creating disjointed rhythms which added small segments to otherwise pulse-driven music, an example of this kind of complexity can be seen in the Quartet No. 3 which is pictured in the textbook on page 353. Morgan notes that this kind of hyper-serialism was somewhat short lived, but its influence would be felt for generations, especially in younger composers.
It might be that the greatest aspect of serialism’s validity in the classical tradition was its adoption by Igor Stravinsky as a compositional tool. Morgan notes that with Schoenberg’s passing serialism belonged to the past and therefore was fair game as inspiration for the composer who always seemed to draw from folk traditions and venerated musical styles. In this respect, serialist came full circle, from being a revolutionary idea based on continuation of classical functional techniques, to being adopted and revised as a legitimate compositional method, to being studied “post-mortem” by music historians as a style that belonged to a valid past.