Harmonious dyads, triads, tetrads, and hexads can be constructed by inscribing geometric figures in the 12-hue color circle

Any set of hues is harmonious if the geometric figure connecting their positions on the 12-hue color circle is centrosymmetric (center of the figure at the circle’s center). This produces: (1) Dyads — any complementary pair (diameter); (2) Triads — equilateral or isosceles triangle; yellow/red/blue (equilateral) is the fundamental triad; (3) Tetrads — square or rectangle (two pairs of complementaries at right angles); (4) Hexads — hexagon (three complementary pairs) or tetrad + white + black. These figures can be rotated freely on the circle, generating infinite harmonious combinations. On the color sphere, figures can be inscribed at any tilt and brilliance level, expanding to tints, shades, and mixed tones. The theory does not constrain expression — it guides discovery of new combinations.

Examples

In GLSL: float hue_triad_b = mod(hue + 120.0/360.0, 1.0); float hue_triad_c = mod(hue + 240.0/360.0, 1.0); generates equilateral triad. For tetrad: offsets of 0, 0.25, 0.5, 0.75 of the circle.

Assessment

Construct a harmonious tetrad starting from orange; explain why a trapezoid in the color circle produces simultaneous contrast effects; rotate an equilateral triad by 30 degrees and name the resulting three hues.