Squares Table

tHz & nm Analysis — Harmonic Wavelength Symmetry

Structure

The 12 columns are arranged into 3 squares, each containing 4 columns × 10 rows = 40 elements. Within each square, 19 elements share the same positional class across all 3 squares simultaneously. The remaining 21 do not share. Total: 19 + 21 = 40 (the fundamental square width).

Results

Square 1

Square 2

Square 3

Overall (all 120 elements)

Key Findings

1. Grand average is exactly 540/540

As in the Opposites and Triangles tables, the grand average of all 120 elements remains exactly 540.0 tHz / 540.0 nm — the precise midpoint of the visible spectrum. This holds without exception across every geometric arrangement examined.

2. Shared averages step by exactly 30

Shared tHz averages step down by exactly 30 per square: 544.8157... → 514.8157... → 484.8157... This +30 step pattern has now appeared in every table examined.

3. The fractional component 31/38

Every shared average carries the same fractional part: 31/38 = 0.81578947...

• 38 = 2 × 19 (twice the shared count per square)
• 31 is the nuclear mass of Aluminum (element 13) and the atomic number of Gallium (element 31, N column)

4. Square 1 non-shared average is exactly clean

Square 1 non-shared averages are exactly 478.5 tHz / 601.5 nm — whole number multiples of 1.5 with no fractional component. 478.5 / 1.5 = 319 (exactly); 601.5 / 1.5 = 401 (exactly).

5. Squares 2 and 3 share exact fractions involving 14

Squares 2 and 3 have identical non-shared averages: tHz = 619 + 13/14; nm = 460 + 1/14. The fractions complement perfectly: 13/14 + 1/14 = 1. The 14 in the denominator connects directly to the Triangles table (14 non-shared elements per triangle) and the formula: Triangle Δ = SK × 30 / 14.

6. Square 1 asymmetry

Square 1 has a positive tHz Δ (+66.316) while Squares 2 and 3 share a negative tHz Δ (−105.113). This asymmetry — one square opposing two — mirrors the structure seen in the OE/OO rod analysis, where one asymmetric axis anchors an otherwise balanced system.

7. The 19/21 split

• 19 + 21 = 40 (square width)
• 19 × 2 = 38 (denominator of fractional component)
• 21 = 3 × 7 — the 7 may connect to the 7 steps to reach the first symmetry point of the 2 2 4 3 1 3 3 1 3 4 2 2 sequence

Cross-Table Comparison

Open Questions

• Does the squares asymmetry (Square 1 opposing Squares 2 and 3) have a geometric explanation in the circle code wheel?
• Is the 31/38 fractional component connected to element 31 (Ga, N column) or nuclear mass 31 (Al), and does this relate to the first symmetry point of the 2 2 4 3 1 3 3 1 3 4 2 2 sequence?
• What formula, if any, expresses the squares Δ values in terms of SK, 19, 21, and 30?
• Square 1 non-shared average (478.5 tHz) is the exact tHz of element 113 (Nh). Is this meaningful?

Documented: June 8, 2026 · See also: Opposites & Triangles Tables, Odds/Evens Table, Combined Summary