CHORD PAINTING

Chords consist of two types: Pitch Chords and Color Chords. These two are mirror-symmetric: {n₂,n₁,0} ↔ {0,-n₁,-n₂} mod 12, serving as reciprocal (anti-)chords that express time and space respectively.

Space-time quantization originates from geometric quantization; different Color Chords (quantized chromatic spectra) map to different geometric structures, producing Chordal (quantized) Geometry, and generating figure-ground, faceting, and other spatial structures.

Geometric Semantics of Chordal Encoding: Color Chords encode geometric semantics and determine spatial structures:

Note: Corresponds to single frequency (x) mod 12, forming  Point Space.

Open String: Corresponds to the minor triad (-7,-3,0) mod 12, forming **faceting lines**;

Closed String: Corresponds to the major triad (-7,-4,0) mod 12, forming **contour lines**;

 Membrane: Corresponds to **Symmetrical Chords**, such as diminished seventh (0,3,6,9), whole-tone scale (0,2,4,6,8,10), augmented triad (0,4,8), and chromatic chord (0,1,2,3,4,5,6,7,8,9,10,11) mod 12, constituting continuous surfaces of non-linear space.

Chordal Geometric Framework: Triads (Open String, Closed String) define the boundaries of Symmetrical Chords (Membrane): Major triads (Closed Strings) generate contour lines, producing closed surfaces; Minor triads generate faceting lines (curvature lines); Major-Minor triads together constitute "volume," from which chordal space is generated; all chords can be decomposed into Notes: points.

When chordal spectra are shielded by the observer, chordal geometry transforms into non-chordal (atonal) geometric elements: points, lines, surfaces, and volumes.

Painting is the application of geometry; Chordal Geometry (space) takes color painting as the foundation of observation, first-person visual experimentation as the research methodology, and experimental illustrations as the experimental report.

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