The division, not a second sky
For integer n, Hn multiplies a natal longitude by n and wraps it around 360°. If two source positions differ by any whole multiple of 360° ÷ n, their Hn positions coincide. The table below lists useful examples, including the aspect name commonly attached to the first step. It does not assert that all multiples have identical interpretations.
| Chart | One division | Natal separations that meet in the derived chart |
|---|---|---|
| H2 | 180° | Opposition; exact natal conjunctions also remain together. |
| H3 | 120° | Trines at 120° or 240°. |
| H4 | 90° | Squares at 90° or 270°, and opposition at 180°. |
| H5 | 72° | Quintile-family divisions at 72°, 144°, 216°, or 288°. |
| H6 | 60° | Sextile, trine, and opposition multiples of 60°. |
| H7 | about 51.43° | Septile-family divisions in sevenths of a circle. |
| H8 | 45° | Semisquare, square, sesquisquare, and opposition multiples. |
| H9 | 40° | Novile-family divisions in ninths of a circle; 120° trines also meet. |
| H10 | 36° | Decile-family divisions; a 72° quintile also meets. |
The additional H9/H10 rows here follow the same explicit 360° ÷ n arithmetic; they are not claims that one house style or interpretation is universally accepted.
Why an H6 conjunction needs a natal check
Take two invented natal points at 10° and 130°. Their 120° separation is a trine. H6 sends them to 60° and 780°, which wraps to 60°: a conjunction. The same H6 chart could also join points 60° or 180° apart. Only the source natal difference tells you which angular relationship folded together.
Higher harmonic numbers
H11 through H36 are available in the free calculator, but the finer divisions amplify small source uncertainty. A three-degree orb in H30 admits an original separation only about one tenth of a degree from a multiple of 12°. Birth-time errors may be much larger than that for the Moon and especially the angles. Use an exact recorded time where those points matter. Derived sign labels can change sharply under tiny corrections near a wrap boundary; the source longitude and distance are more informative than a single isolated sign label.
See the aspect arithmetic guide for the modulo rule and a worked H7 example.