…because some thoughts are worth remembering
Twelve-tone music gets a bad rep with even the die-hards of classical music fans. It’s similar to how people respond when you say “logarithmic function“: mostly “huh?”, a few furrowed eye brows, or even fewer exclaiming, “beautiful!”
My first encounter to twelve-tone music happened about the time when I was studying linear algebra. Equations can be represented as a matrix (though Neo never makes an appearance here, nor is there a blue pill option). Its lingo includes rows and columns to easily refer to the elements in the matrix, and how one can have an inverse of the row, or rotate the elements. I doubt Arnold Schoenberg, the inventor of the twelve-tone technique, studied matrix algebra or was inspired by it. My struggles in linear algebra helped me embrace the approach Schoenberg chose to elevate classical music to the next level, and somehow what I can only describe as clunkiness of twelve-tone music helped me digest the fundamental theorems of linear algebra.
So what is twelve-tone music, you ask? It’s best to travel in time before its birth to put it in context: what is tonal music? I have not read anything more beautifully stated than this passage by Milan Kundera:
This is what my father told me when I was five: a key signature is a king’s court in miniature. It is ruled by a king (the first step) and his two right-hand men (steps five and four). They have four other dignitaries at their command, each of whom has his own special relation to the king and his right-hand men. The sort houses five additional tones as well, which are known as chromatic. They have important parts to play in other keys, but here they are simply guests.
Since each of the twelve notes has its own job, title, and function, any piece we hear is more than mere sound: it unfolds a certain action before us. Sometimes the events are terribly involved (as in Mahler or—even more—Bartók or Stravinsky): princes from other courts intervene, and before long there is no telling which court a tone belongs to and no assurance it isn’t working undercover as a double or triple agent. But even then the most naive of listeners can figure out more or less what is going on. The most complex music is still a language.
~Milan Kundera “The Book of Laughter and Forgetting” Part Six, The Angels, Section 17
Classical giants like Beethoven and Brahms populate their musical scores like graphic artists use the color wheel: compatible but fundamentally different notes seldom juxtaposed by a contrasting note with a pattern that makes you crave to hear that one resolving key. Not so in twelve-tone music. But it needn’t be bland. Check out how Vi Hart, a mathematical artist, explains twelve-tone music (and more, including the transformation of Mary Had A Little Lamb tune converted to twelve-tone).
And if you prefer the eloquent prose of Kundera, here’s the continuation of his character’s thoughts:
This [Edit: passage quoted before this] is what my father told me. What follows is all my own. One day a great man determined that after a thousand years the language of music had worn itself out and could do no more than rehash the same message. Abolishing the hierarchy of tones by revolutionary decree, he made them all equal and subjected them to a strict discipline: none was allowed to occur more often than any other piece, and therefore none could lay claim to its former feudal privileges. All courts were permanently abolished, and in their place arose a single empire, founded on equality and called the twelve-tone system.
But all good things come to an end, as Kundera writes:
Perhaps the sonorities were more interesting than they had been, but audiences accustomed to following the courtly intrigues of the keys for a millennium failed to make anything of them. In any case, the empire of the twelve-tone system soon disappeared. After Schönberg came Varèse, and he abolished notes (the tones of the human voice and musical instruments) along with keys, replacing them with an extremely subtle play of sounds which, though fascinating, marks the beginning of the history of something other than music, something based on other principles and another language.
I am intrigued by the idea Kundera presents that the paradigm shift that took place in tonal music by the twelve-tone technique seen as progress, also quickened the travel to its end:
People fascinated by the idea of progress never suspect that every step forward is also a step on the way to the end and that behind all the joyous “onward and upward” slogans lurk the lascivious voice of death urging us to make haste.
In the days when Arnold Schönberg founded his twelve-tone empire, music was richer than ever before and intoxicated with its freedom. No one ever dreamed the end was so near. No fatigue. No twilight. Schönberg was audacious as only youth can be. He was legitimately proud of having chosen the only road that led “onward.” The history of music came to an end in a burst of daring and desire.
Kundera in his own novel romanticizes the journey of classical music accelerated by the twelve-tone technique, which then abruptly faced a dead-end. In my mind, however, with hints of linear algebra still tangled with my introduction to twelve-tone music, I saw continuing progress. If not progress, a variation, when looped enough, morphed to offer another option that enriched our understanding of our world, like quantum mechanics, as our physical world also faced uncertainly and questioned the status quo with World War II.
It can’t be a coincidence these events took place around the same time.
Photo: Santa Fe, New Mexico