CHORD PAINTING

In the chord space system, chords are represented as quantized color spectra, which are mapped onto specific geometric structures (membrane-string) to generate chord space. Its essence is a priori quantized spatial structure, and painting is its empirical phenomenon. It also exists in the framework of Euclidean geometry and membrane-string theory.

Core Mechanism: Spacetime Mirror Symmetry

Chord encoding (quantized spectrum) is the unified basis for spacetime generation: it unfolds as music in the time domain and condenses into painting in the spatial domain. The two exhibit an inherent mirror symmetry: -7, -4, 0 ↔ 0, 4, 7 (mod 12). This symmetry makes music and painting two ways of unfolding the same chord system.

The Geometric Semantics of Chord Encoding

Chord encoding not only describes frequency ratios but also carries geometric semantics (membrane -strings), thus determining the spatial structure:

Open String: Corresponds to a minor triad (−7,−3,0) mod 12, representing a faceted structure;

Closed String: Corresponds to a major triad (−7,−4,0) mod 12, representing a contour structure;

Membrane: Corresponds to symmetrical chords, such as diminished seventh (0,3,6,9), whole tone (0,2,4,6,8,10), augmented third (0,4,8), and chromatic chords (0,1,2,3,4,5,6,7,8,9,10,11) mod 12, representing continuous surfaces in nonlinear space.

Chord Geometry Framework:

Triads (open and closed chords) define the boundaries of symmetrical chords (membrane), i.e., the generating lines of space. Thus, the chord geometry framework is established: the geometric semantics of a chord () determines the spatial structure, while the spectral semantics of a chord (the chord itself) defines its tonal relationships. Together, they constitute the Chord Space—a unified structural field connecting music and painting.

Experimental Verification

These results are not theoretical assumptions, but rather stem from independent observation and experimentation in painting. The discrete distribution of color and the spatial arrangement of forms repeatedly verify the aforementioned chordal geometric characteristics. Therefore, *Chord Painting* is not only an art monograph, but also an experimental report on chordal space.

It demonstrates how to measure the geometric structure of music visually, and how to use painting as an observational instrument to reveal the tonal order of life and the universe. Painting is redefined here: it is no longer a subjective representation of perception, but a visible generation of chordal structures.

Each work is a spatial unfolding of the spectrum; every line, every color plane, is a geometric manifestation of a chord in space and time. *Chord Painting* thus becomes one of the pillars of the chordal language system—it provides a visual foundation for observation, verification, and application, allowing chords to transform from the temporal flow of music into the spatial form of painting.

Li, X. H. (2020). Chord Painting. ResearchGate.

https://www.researchgate.net/publication/340492620_Chord_Painting

Li, X. H. (2024). Chord Language. Zenodo.

https://zenodo.org/records/11817631

Li, X. H. (2020). Chord Painting. ResearchGate.

https://www.researchgate.net/publication/340492620_Chord_Painting

Li, X. H. (2024). Chord Language. Zenodo.

https://zenodo.org/records/11817631