Expressive Circles: The Secret Geometry of Music?

Imagine building a musical piece not as a straight line, but as circles chasing and transforming each other. This is the core idea behind "Expressive Circles," a new compositional approach illustrated by the author in his work for piano trio (piano, violin, cello). The inspiration stems from Surrealism in art and the "musique surrealistique" of composer Hanna Kulenty, with nods to Witold Lutosławski and unism theory.

The method relies on three formal models: closed, open, and inverted structure. Each handles the musical theme differently—like doors closing, swinging wide, or flipping upside down on the sound. Dramaturgically, the music seeks a trance state achieved in two ways: "logarithm," which stretches and rarefies time, and "drive," which pushes forward with relentless energy.

The article makes this tangible by showing actual score excerpts and colorful diagrams translating theoretical geometry into concrete notes. A fascinating crossroads of sound mathematics, emotion, and avant-garde proving composition can be pure architecture.

The Expressive Circles concept articulates three distinct structural models. The "closed structure" presents thematic material that returns onto itself, creating perfect circular unity where beginning and end coincide timbrally and harmonically. The "open structure" fragments the theme into cells evolving linearly without recomposing the initial unity, generating a sense of continuous expansion. The "inverted structure" reverses formal parameters: the climax appears at the start and material progressively dissolves toward silence.

Dramaturgically, the two trance types define the temporal experience. The "logarithm" trance relies on golden ratio or numerical series (e.g., Fibonacci) to determine section durations: each episode is shorter than the previous by a constant ratio, accelerating temporal perception toward a point of no return. The "drive" trance uses rhythmic ostinatos, static harmonies, and growing dynamics (continuous crescendo) to induce a hypnotic state through energy accumulation, akin to minimalism but with constantly shifting harmonic tension.

The author highlights parallels with Kulenty's "surconventional deconstruction," where conventional material (scales, chords) is deconstructed to create new syntaxes, and Lutosławski's "controlled aleatoriness," where performer freedom is framed by rigid formal coordinates. The article's color diagrams map parameters like density, register, articulation, and dynamics onto Cartesian axes, visualizing the trajectory of the piece's "expressive space."