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All three edges
Original Atlas graph rule: select h and a transformed orb t. Add edge XY when its transformed residual r(XY) ≤ t. A triangle requires AB, BC and AC. AB plus BC with no AC is a connected chain, so label it as two qualifying pairs rather than a partial triangle. Always print h, t, each residual and the three body names.
David Cochrane, The First 32 Harmonics · printed p. 25 / PDF physical p. 31 ↗
Realizable calculation
Original Atlas math example: use H5 positions A=0°, B=5°, C=10° and t=10°. The three circular separations are 5°, 5° and 10°, so all edges qualify; it is a triangle. These correspond to natal positions 0°, 1°, 2°. For a chain, use H5 positions 0°, 7.5°, 15° with t=10°: AB and BC qualify at 7.5°, while AC fails at 15°.
Test symmetry separately
Cochrane gives a midpoint symmetry example but says triangles need not be symmetrical. In this atlas, do not infer a midpoint from clique membership. Compute it in the selected coordinate frame, state its tolerance, and report symmetry as a second finding.
David Cochrane, The First 32 Harmonics · printed p. 25 / PDF physical p. 31 ↗
Keep geometry, hierarchy and interpretation apart
Cochrane discusses added harmonic contacts and a separate H15 triangle. In this atlas, preserve every selected factor, residual and reduced order; do not decide which layer dominates. A triangle is not his chart-ranking score, and its presence alone does not authorize a factor-theme reading.
David Cochrane, The First 32 Harmonics · printed p. 25 / PDF physical p. 31 ↗
Word origin · etymology
Middle English through Anglo-French, from Latin triangulum, neuter of triangulus ('triangular'), from tri- plus angulus ('angle').
Harmonic modifies this geometric word to name a pattern in a selected transformed circle.
How we know · epistemology
Declared angular-threshold graph; source-specific reading
The clique is reproducible geometry. Cochrane records symmetry as variable; interpretation remains qualitative.
David Cochrane, The First 32 Harmonics · printed p. 25 / PDF physical p. 31 ↗
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