The modulo rule
Let the two natal tropical longitudes be A and B, each measured eastward from 0° Aries. In Hn their derived longitudes are (n × A) modulo 360° and (n × B) modulo 360°. They coincide when n × (B − A) is a multiple of 360°. Equivalently, their natal separation lies on a whole multiple of 360° ÷ n. The circular distance uses the shorter arc, so a derived 358° and 2° are four degrees apart, not 356°.
Worked H4 example: a square
Suppose two example bodies are at 15° Aries and 15° Cancer, absolute longitudes 15° and 105°. Their natal separation is 90°. H4 gives 4 × 15° = 60° and 4 × 105° = 420°, which wraps to 60°. They meet at 0° Gemini in the H4 wheel. An opposition at 15° and 195° would also meet there: 780° wraps to 60°. A close H4 conjunction is therefore a prompt to inspect the original 90° or 180° relationship, not to erase that difference.
Worked H7 example: a seventh division
One seventh of a circle is 360° ÷ 7, approximately 51.428571°. Let A = 12° Aries and B = 63.428571°, or about 3.428571° Gemini. Multiplying by seven gives 84° and approximately 444°. Subtract 360° from the latter and both land near 84°, or 24° Gemini, in H7. Rounded input degrees can leave a small visible residual; the underlying result is exact only for the unrounded one-seventh angle.
What an orb means after multiplication
If a pair lies one degree away from an exact H4-folding natal separation, the H4 derived points are about four degrees apart. The calculator's 3° derived conjunction orb would omit it. In H7, that same 3° derived limit corresponds to roughly 0.43° from a seventh-division angle in the natal chart. This division only describes the nearest exact folding; it is not a statistical significance test. A pair near the circular wrap should be measured with the shorter arc.
Interpretation and record limits
Symbolic readings of H5 creativity or H7 insight are interpretive choices, not consequences of the formula. The transform cannot predict an event or validate a trait.
Start with a reliable birth record if using the Moon, Ascendant, or Midheaven. The Moon changes through the day; angles need an exact time and place. The independent harmonic calculator withholds those points for an unknown birth time. It does not generate harmonic houses, which would require a separate stated house convention. Read the step-by-step guide before assigning an interpretation to any derived conjunction.