Begin with the natal degree
Read across one row of the position matrix. The first value is an apparent geocentric tropical longitude for the recorded birth instant. The next nine values are derived by multiplying that longitude by 2, 3, and so on through 10, taking the remainder after division by 360°. These later values do not place a planet in a second physical sky. They show how one natal angle appears under nine mathematical scales.
Take two invented natal longitudes, 43° and 115°. Their separation is 72°. In H5 they become 215° and 575°; reducing the latter by 360° gives 215°. The two marks meet as a derived conjunction. The 72° natal interval is one fifth of a circle, so this is an exact fivefold relationship. The example is arithmetic, not a birth-chart claim.
Read a pair in both directions
A listed pair is close in a harmonic wheel. Check the original natal separation before giving it an aspect name. H4 can bring a 90° square or a 180° opposition to conjunction, and an original conjunction also remains together in every harmonic. H6 includes 60° sextiles, 120° trines, and 180° oppositions among its sixfold steps. H10 can show a 36° decile and a 72° quintile, among other multiples of 36°. The label at the top of a card identifies its angle family, not a unique aspect diagnosis for every pair inside it.
The same pair can therefore appear in more than one wheel. A 180° natal opposition folds in every even harmonic, while a 72° separation folds in H5 and H10. Repetition follows the arithmetic of shared factors. It should not be counted as several independent observations.
Mind the orb before comparing cards
This sheet lists planetary pairs at or inside 3° in the derived wheel. Since a natal difference is multiplied by the harmonic number, a derived 3° allowance means roughly 3° divided by that number around the nearest exact natal step. At H2 that is 1.5° natal; at H10 it is 0.3° natal. The table rounds displayed positions to two decimals, while pair detection uses the unrounded longitudes.
Read the position matrix
On a phone, scroll the matrix horizontally and keep the point name in the left column. A degree such as 17.25° Sco means 17.25° within Scorpio, not a total longitude of 17.25° from Aries. To check a cell manually, convert the natal sign and degree to absolute zodiac longitude, multiply by the column number, reduce modulo 360°, and convert back to sign and degree. The browser creates the CSV from the displayed positions.
Time, location, and uncertainty
The calculation first converts the entered local civil time to UTC using the supplied historical offset. The natal engine uses a locally bundled Astronomy Engine ephemeris for apparent geocentric tropical positions. An incorrect offset or birth hour will especially affect the Moon and angles. If the time is unknown, the sheet makes a local-noon sample, leaves out the Moon and angles, and labels the limitation. A time-aware reading should wait for a reliable birth record; derived precision cannot repair an uncertain source moment.
What this sheet does not establish
The wheels do not calculate harmonic houses, transits, fate, or traits. Aspect-family names come from astrological interpretation, while the equation and distance checks are mathematical. Other programs may use different ephemerides, zodiac settings, points, orbs, and drawing conventions. Compare settings before expecting their tables to match exactly.
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