I spent a while learning English change ringing, on specially mounted church bells. It is basically an exercise in combinatorics: the "change" is applying the pattern so that the bells ring through all possible sequences that the pattern can do. At first it sounds like noise, but after a couple of years, you do start to notice a certain musicality to it. As I understand Schoenberg, one of his ideas was that you cannot re-use a note until all the others have been used, which is essentially the same requirement that change ringing has. (The bells are heavy and are swinging through their full arc, so you cannot change their order very quickly.) After realizing this, I listened to some Schoenberg and found it much more listenable than I did in college.
12-tone/serialism was a seriously dire period in modern art music. After Romanticism ran its course and maxed out the tonal possibilities of music that attempted to convey emotion, 12-tone came along to provide a rigid intellectual structure to music that had existed in the baroque and classical periods, but had been blown away by the Romantics and post-Romantics.
Unfortunately it also made listening to music a purely intellectual exercise as well, and a painful one for folks who expect tonality to be a part of any music they want to sit through.
Thankfully folks like Steve Reich, Terry Riley, and Philip Glass came along to embrace the rigid structure and intellectual design approach, but to return tonality as a core principle with Minimalism. Art Music was listenable again.
This is a pretty simplified and inverted way to look at it in my opinion.
In many ways serialism was the inevitable direction that late 19th century Romanticism was moving in, with increasingly ambiguous tonality expressed by composers like Wagner and Mahler. In the early 20th century there was an explosion of new approaches and techniques which started from this basis and pushed tonal approaches to the breaking point and beyond. Composers including Ives, Stravinsky, Schoenberg, and others were all trying new things within the domain of "atonality" and while we tend to look back and shove history into narrow movements and philosophies I don't think there was necessarily such a "serialism period" so much as there was the Second Viennese school along with a bunch of other composers trying things out at the same time. And even within that group the approaches were distinct; Berg is known for being a bit more "loose" and romantic in his usage of 12-tone technique vs. the rigid formalist Webern, for example.
Leaving aside the dubious assertions of what is or is not listenable, the reality is that art music in the 20th century became more and more fragmented as the entire music scene changed around the world. Minimalism was just one thing that happened after serialism. Even if we exclusively focus on music labeled "European Art Music" the 20th century was a period of incredible experimentation and exploration with many different approaches to tonality (and atonality) introduced.
I mostly listen to minimalism but I wouldn't call 12-tone/serialism "dire." Like all periods, there's good and bad. On the other hand, I've lost my taste for Germanic 19th century music.
Matter of taste: the second Viennese school, Bartok & Shostakovitch is pretty much the only classical I can tolerate, the "mimsy" stuff leaves me cold. Horses for courses.
Bartok never wrote using the 12-tone serial method. He wrote dense harmonies, especially in his middle period (e.g. the sonatas for violin and piano), but in terms of how he devised those harmonies he has more in common with Glass than Schönberg.
Especially Bartok’s late works are more approachable (Concerto for Orchestra, Piano Concerto no. 3) and while they don’t slam home a tonal key like the end of Beethoven’s Fifth, the harmonies are plenty recognizable.
If ever a blog post could have done with some playable media.
Here’s an example: Schönberg’s Variations for Orchestra (1928): https://www.youtube.com/watch?v=g7wefv98lvo
12-tone serial music always sounds to me like it belongs in a film soundtrack — it works well as background because the serial method suppresses the creation of recognizable melody as a foreground element.
For those of you who want to experience 24-tone composition, listen to Angine de Poitrine: