Untitled

In Schoenberg's Op. 25, the row is consistently segmented into 4-note groups known as tetrachords.
Important observations:
- One form of the row leads into another; for example, P-0 ends on B-flat, which is the starting pitch of I-6.
- In the Minuet, the presentation of the tetrachords appears to take precedence over the order of the series.
This work exemplifies the principles of 12-tone composition.

Combinatorial rows are those that can overlap, producing new 12-tone sets through the hexachords.
Instances of combinatoriality are found in rows P-0 and I-5 in both Op. 33A and Op. 37, along with R-0 and RI-0.
A new row that arises from combining row forms is referred to as a derived row.
Transitioning to a derived row can create a sense of modulation.

Began studying under Schoenberg in 1904 and progressed towards free atonality and 12-tone serialism.
Berg's compositions remain closely tied to the sound and spirit of Romanticism, even within a fully serial context.
His opera, Wozzeck (1925), is recognized as the most successful free-atonal work of its time, continuing to be performed regularly.
Wozzeck is noted for its complexity and length among free atonal works.

Utilizes pitch collections as Leitmotivs; for instance, the sequence 0148 represents the title character, Wozzeck.
Composed in three acts, each containing five scenes, interludes connect these scenes.
Each act follows a structural archetype borrowed from the past:
- Act I: Structures reminiscent of a Baroque suite.
- Act II: Follows a symphonic format.
- Act III: Comprises a series of “inventions” based on musical structures.
Noteworthy scenes:
- Act III, Scene 2: Built around the pitch B without tonicizing it.
- Act III, Scene 3: Exhibits a saturation of rhythm as showcased in the examples.

Compared to Schoenberg and Webern, Berg's 12-tone works are more likely to evoke the sounds of tonal music.
In the Violin Concerto, Berg employs a tone row that features both major and minor chords along with a segment of a whole-tone scale.
This structure incorporates the Bach chorale “Es ist genug.”

Webern received the most traditional musical training within the Second Vienna School, attaining his PhD in musicology in 1906, with a dissertation focused on Henricus Isaac.
He exhibited an obsession with abstraction and internal musical unity, striving for the utmost relatedness among all components of his compositions, leading to a trend of shorter pieces.
Webern viewed 12-tone composition as a necessary evolution of earlier musical styles.
Like Schoenberg, he drew upon concepts from prior music, such as canons, though he did not evoke their sound as Berg did.

The second hexachord of Webern’s Op. 21 is the retrograde of the first, transposed by a tritone.
Circled pitch pairs in many row forms remain adjacent.
The canons present in his works are abstract structures where the listener emphasizes details of instrumentation and texture.

Stravinsky was born into a musical family; his father was a bass vocalist in the St. Petersburg Opera.
He began piano lessons at the age of 9 but never attended the conservatory.
Stravinsky studied privately under Nicolai Rimsky-Korsakov.
In 1909, Sergei Diaghilev commissioned him to write three ballets, all premiering in Paris with the Ballets Russes: Firebird (1910), Petrushka (1911), and Rite of Spring (1913), leading to his international acclaim.

Russian Period (1909-1918):
- Works influenced by Russian music and folk elements.
- Musical influences from Rimsky-Korsakov present.
- Characterized by large ensembles, block textures, diatonic and octatonic materials, fragmented melodies, and ostinatos.
Neoclassical Period (1918-1951):
- Shift towards smaller ensembles.
- Utilization of classical forms (e.g., Octet) and recompositions of 18th-century material (ex: Pulcinella).
- Continued usage of block textures, diatonic and octatonic materials, fragmented melodies, and ostinatos.
Serial Period (1951-1971):
- After Schoenberg’s death, Stravinsky adopted the 12-tone system in compositions such as Threni and In Memoriam Dylan Thomas.
- His application of serialism highlighted the similarities his music had always shared with this style.

The narrative centers around a love triangle among puppets animated within a Russian circus setting.
Scene 1:
- Presented as diatonic but non-functional set on D.
- Features an ostinato pattern in the horns, clarinets, and cellos (D-A E-G).
- Displays a repetitive structure with ascending fourths in the flute alongside the repetition of its line.
Scene 2:
- Constructed from an octatonic collection:
  $[C, D-flat, E-flat, E, F extsharp, G, A, B-flat]$
- From this collection, Stravinsky forms two tritone-related major chords on C and F extsharp, often referred to as the Petrushka chord, which first appears in the clarinets.
- The intricate piano part mirrors Stravinsky's original intent to utilize this music for a piano concerto.

Stravinsky’s Rite of Spring extends the innovations observed in Petrushka both pitch-wise and rhythmically.
The narrative reflects an ancient sacrificial ritual, drawing on the concept of Primitivism, characterized by driving rhythms and relentless music.
Collaborated with Nicholas Roerich on the plot, which is purportedly based on real ceremonies; Roerich also designed the ballet's costumes and sets.
Choreographed by Vaslav Nijinsky, the dance reflected unconventional ideas parallel to the innovative music.
The choreography has been reconstructed for performances by the Joffrey Ballet.

Opens with an extremely high bassoon solo, evoking sounds from ancient tribal instruments of the Russian steppes.
Dominance of solo winds during the introduction leads to a textural growth that becomes increasingly chaotic.
No clear tonal focus is present, alongside a lack of chord resolution.

The break from tonal conventions is exemplified in the “Dance of the Young Girls,” underpinned by superimposed F-flat major and E-flat-7 chords, both also forming an octatonic collection.
Much of the pitch material shifts within layered blocks of ostinatos when this