musicians of old

Chapter 889 Atonality Analysis!
"Op. 11, Three Piano Pieces, composed by Schoenberg in 1909-1910, is hailed as the 'birth certificate' of his atonal inspirations."

"Just look at the first three bars of the first song."

Fan Ning waved his hand in mid-air, directly "grabbing" the notes and lines in the musical score and imprinting them onto the blackboard behind him.

"Here, the first three measures directly constitute the 'set of pitches' that unifies the entire piece! Of course, if you want to use traditional expression, you can call it the 'theme,' and if you want to use Schenker analysis, you can call it the 'basic structure,' which means the same thing."

“Look at the high-pitched melody, starting from the B note, which contains a minor third, a major third, and a semitone. The left-hand chord is also a B note plus a minor second, and then it is shifted once.”

"By arranging the 'interval vectors' of the melody in the most compact and leftmost manner and extracting their identifying features, we obtain a very simple 'basic form'."

"0, 1, 3"

Fanning's chalk danced, making only a few strokes.

"Following the classification rules, we name this set of pitch levels the (3-3) set!"

"Undoubtedly, every corresponding functional segment in the entire piece is an expansion and variation of this (3-3) set. In terms of melody, Schoenberg expands the entire piece by reorganizing, expanding, splitting, and overlapping the three elements in the 'interval vector'. In terms of rhythm, the theme initially adopts an anacrusis iambic form, and all subsequent appearances follow the iambic form, with the unifying element running through the entire piece. The same applies to rhythm, with the values ​​of quarter notes, eighth notes, dotted eighth notes, and thirty-second notes being firmly bound to other elements."

"Logic! This is what logic is!"

"It's like an embryo of life. The various parts of the music gradually develop from this embryo into buds, and then continue to grow and multiply, eventually forming a complete 'living entity'!"

“Starting in 1923, Schoenberg took his work a step further and began to use the ‘twelve-tone’ technique.”

"Twelve-tone music is a further development of atonal music. Previously, his inspiration could only guide small works, while large works required more complex concepts and techniques. Twelve-tone music solved this problem. Ultimately, whether it's called 'atonal,' 'twelve-tone,' or 'serialism,' it's all a specific organizational logic of pitch set theory! Schoenberg abandoned tonality, but that doesn't mean he chose 'end' or 'chaos'! He never abandoned unity! He simply replaced the traditional dominant-subordinate relationship with this deep network of kinship!!"

Fan Ning's concluding remarks were forceful, and he casually pulled out two sheets of woodblock printing paper from his briefcase once again.

“If Schoenberg was building a network, then Webern was carving a diamond.” His tone was full of admiration. “His Concerto for Nine Instruments is extremely short, but extremely dense. Every note carries a structural responsibility. Here, he mainly plays with another of the five basic types: ‘complementary’ relationships!”

Fanning, referring to the musical score, connected the twelve marks on the dial to each other, dividing them into four triangles.

“Triangle,” he repeated the word “triangle” meaningfully.

It seems to be a metaphor for "the path" or something else.

"The four tone groups, each containing three notes, exhibit certain patterns among themselves, such as '0, 1, 4' or '7, 10, 11'. These groups act as 'seeds,' giving rise to more 'subsets' of four- and five-note tones! These 'subsets' are distributed throughout the various instrumental parts, echoing each other and forming an extremely refined and highly self-consistent miniature world!"

The chaotic atmosphere in the classroom gradually solidified into an orderly atmosphere.

“I know that some people here will think that this theory is too ‘sharp’ and abandons the past works with style!”

"But no, that still applies!"

The third movement of Fanning's "Symphony No. 7," which was "made on the spot," had been paused at some point, but now it has suddenly resumed playing.

A scene filled with ghosts and the world of yesterday continues to unfold from the middle section!
Fanning's improvised themes of "Shadow," "Lament," "Waltz," and "Country"—various materials exaggeratedly distorted yet naturally blended, the shrill timbre of the treble woodwinds, the somber roar of the double bass, the ominous roll of the timpani—all these elements constituted a sonic nightmare! "For example, continue to dissect yourselves." Fanning's gaze slowly swept across from left to right.

"This scherzo, written on the spur of the moment, has already revealed my creative intentions to you directly through the Schenker analysis I just performed. Now, I will continue to demonstrate the effectiveness of the scale theory, illuminating for you those ghostly sonic details that writhe on the edges of tonality!"

Fanning pointed to the musical score scrolling on the blackboard: "This recurring D note can be ignored for now; it's a 'remnant' of tonality. But those dissonant sounds attached to it, like that sharp, impactful chord between the viola and bassoon..."

Its pitch was quickly written down by Fanning: F, A#, C, G#.

"Convert to numbers, sort by interval vector, find the 'basic type', and the set is classified as (4-18)!"

“Now, pay attention to this 4-18,” Fanning’s voice was filled with a sense of both fear and joy in the discovery of knowledge. “It is not a random passerby. Here, where the French horn and violin converse, this ghost reappears, only with a displaced mask. And the clarinet’s strange glissando lines, its core notes also belong to a subset of this set!”

“I’m standing right here!” Fanning pointed to himself. “I’m demonstrating how to have one foot on the boat of tonality while the other plunges into the torrent of atonality. This new structural glue, ‘Pitch Set Theory,’ can be used to glue together those bizarre transitions and color interludes that tonal logic can no longer fully explain! Here, the Schenker system and set theory are not mutually exclusive, but complementary. One describes the shape of the riverbed of the main stream and tributaries, namely the ‘background’ and ‘middle ground,’ while the other analyzes the most turbulent and eddy-filled complex waters in certain areas, namely the ‘foreground details’!”

Fanning threw the chalk back onto the table.

"Therefore, even atonal music still has its own artistic order! The theory of pitch sets shows us that this order exists in Schoenberg's decisiveness, Webern's condensation, Babbitt's precision, and even in the ghostly nightmare I just described!"

"Crackling—crackling—"

As soon as he finished speaking, outside the classroom corridor, the hundreds of millions of stretched black shadows that were pressed against the distorted windows began to stir violently like never before!
They no longer merely peered greedily, but convulsed wildly like living creatures thrown into boiling oil, their outlines sometimes blurring into a writhing mass of color, and sometimes sharply highlighting countless empty and thirsty eye sockets!

Inside the "lecture hall," Fan Ning walked to the front of the stage, placed her hands on the lectern, and leaned forward slightly.

"Look, don't overreact to a theory that has limitations."

His gaze swept over every face that was absorbed in the moment.

Does this still have limitations?
For the first time, the amused smiles on the lips of those "gentlemen" in the front row, all wearing identical top hats and sporting upturned mustaches, froze.

"The advantage of the theory of pitch class sets is that it is good at classification and good at tracing origins."

Fan Ning stood in front of the podium, his fingertips tapping the wooden tabletop, producing a rhythmic, soft sound, as if welcoming the further revelation of higher mysteries!
"It tells us what music 'is,' just as biologists classify species, we also use the theory of pitch sets to map atonal nebulae. But can simply pinning musical specimens in a display case reveal the secrets of art's brilliance?"

Fanning suddenly raised her voice: "No!"

"Music is alive. It breathes, it pulsates, it transforms. We are not only concerned with 'what it is,' but also want to ask 'how it became!'"

Fanning whirled around and wrote new terms on the blackboard again, adding exclamation marks with sharp, decisive strokes—

"Generalized Theory of Intervals and Transformations!"

“Keep your temper on those isolated chords and tonal sets,” Fanning sneered, waving his hand as if drawing an invisible net in the air. “In the context of transformation theory, every musical object exists only in its dynamic relationship with other objects; music is an eternal journey of ‘becoming’!!.”