In 1911-12, Scriabin composed piano sonatas six and seven, the first large-scale post-Prometheus attempts at wresting sonata form from moorings of traditional tonality. Though important scholarship has emerged since Cheong first identified Scriabin’s octatonic “referents”, I believe the minute workings of his octatonic techniques are still underappreciated. A preoccupation with cycles along the ic3 axes underpinned Scriabin’s approach to local harmonic motion, and the relationship of these octatonic-derived axes to each other enabled his repurposing of sonata allegro form. The proof-of-concept work for using these techniques as an approach to sonata form was Scriabin’s Poème-Nocturne (op.61), composed concurrently. By comparing the Poème-Nocturne and the sixth and seventh sonatas, we witness a remarkably unique technique in evolution. I also introduce a notation for harmony in Scriabin’s most octatonic music, charting movement between the three octatonic “keys”, as well as individual referents within, at both chord and phrase levels.

Scriabin’s penchant for rotating harmonies along ic3 and ic4 axes of transposition was rooted in old Russian harmonic tricks. In his most octatonic works, adherence to a single strict orthographic form of each transposition (a “referent”) afforded him at least four discrete spellings of each octatonic zone. In the Poème-Nocturne, sixth sonata, and seventh sonata, these zones function similarly to keys, allowing Scriabin to reconcile a new harmonic vocabulary with the traditional harmonic departure and return of sonata form. Chord progressions within those octatonic zones shows Scriabin at his most impressive. Scriabin either satisfies or thwarts expectation of mediant cycle completion in remarkably subtle ways: a harmonic alchemy in which chords of repeating pitch classes spiral, sidle, and shapeshift. This paper attempts to elucidate those techniques in detail, further elucidating Scriabin’s eccentric creativity, and the precision of his most constructivist music.

Most scholarship focused on Xenakis centers around the composer and his work with mathematics. This also applies to published analyses of his compositions for percussion, including Okho (1989) for three djembes. Tom De Cock’s analysis of Okho presents Xenakis’s sketches that employ sieve sequences for structuring rhythm, continuing the research initiated by scholars such as James Harley, Nouritza Matossian, Dimitrios Exarchos, and Anne-Sylvie Barthel-Calvet.

While there are abundant discussions regarding Xenakis and mathematics, his parallel interest in classical Greek literature has rarely been addressed, even though his fascination with classical antiquity is referenced in numerous interviews and publications. There has not yet been an investigation of how his literary interest intersects with his compositions in structural terms. Scholarly examination of classical Greco-Roman literature reveals a frequently used rhetorical structure prevalent among well-known authors. Known as chiasmus, this structure emphasizes the centermost clause surrounded by parallel clauses stated in reverse order.

An analysis of Okho through symmetrical structures unveils a cohesive narrative centered on the contrast of stability and chaos, achieved through the construction and deconstruction of palindromes and chiasmi. These processes evolve over time; smaller chiasmi initially embedded within a single bar expand into larger multi-measure structures constructed through Fibonacci sequences. Finally, the chiastic structure is systematically diminished and dismantled as the piece approaches its conclusion.

The once elusive connection between Xenakis’s mathematical processes and Greek literature comes to light through the intersection of rhythmic sieves with palindromic and chiastic structures. By seamlessly integrating sieves into his chiastic structures, Xenakis effectively forges a link between mathematics and literature, harmonizing the worlds of modernity and classical antiquity.

The Nigerian composer Akin Euba (1935-2020) is known for coining the term “African Pianism,” as well as creating solo piano works that define that style. According to Euba (2005), African Pianism is “a style of keyboard composition and performance that is influenced by African traditional practices (as found, for example, in the music of drums, xylophones, and ‘thumb pianos’).” Scholars such as David Bolaji (2019) and Bode Omojola (2001) have associated the rhythmic elements of African Pianism with African drum ensemble traditions (for Euba, Yoruba drumming tradition is central). Pitch elements, on the other hand, have been associated with Western art music, and considered less crucial to defining the style. For this reason, existing analyses of Euba’s piano music focus on tracking its rhythmic motives as they recur in different juxtapositions, and as they create polyrhythmic patterns with each other or with the frequent ostinati. Comments about pitch are usually limited to mentioning that the piece is “atonal” or based on a twelve-tone row.

My presentation, then, aims to add to the analytic discourse about Euba’s piano music by doing a closer reading of a piece’s pitch language, showing how it parallels and enhances the rhythmic language. I chose the first movement of Scenes from Traditional Life, which Kofi Agawu (2005) suggested as a model for African Pianism. A pitch-class set analysis of this piece reveals that motives recur and juxtapose in various combinations not only at pitch, but also as set classes. Moving the analysis to this higher level of abstraction reveals numerous interlocking patterns that project the work’s form, which I understand as ABA’, as well as giving it harmonic continuity.

Euba’s harmonic approach has features in common with “block” structure in Stravinsky works such as the Rite of Spring—but it is more likely that his inspiration came not from Stravinsky, but from the musical language of the Yoruba people. In this way, Euba successfully captures the African identity in music.