Explore a harmonic relationship
Add a birth profile or explore the example, then select a harmonic and pair in the tool.
Open the harmonic explorer →Reduce the nearest fraction
Write a pair's nearest exact angular relation as k/h turns, then divide numerator and denominator by their greatest common divisor. The remaining denominator is the reduced harmonic order. Thus 2/10 becomes 1/5: the relation is fifth order even though it appears as a conjunction in H10.
Worked explanation by Astral Atlas, derived from the integer longitude transform and ordinary fraction reduction.
Read the angle, deviation and tolerance
Read natal angle (the shorter ecliptic-longitude separation); H-angle (natal angle × selected factor, wrapped); residual (nearest H-angle distance from 0°); nearest fraction; reduced order; selected transformed orb; and a clear qualifies/does-not-qualify result. A nearest fraction remains useful outside the orb as a descriptive approximation, but it must not be displayed as an accepted contact.
Different from 'lowest harmonic'
Reduced order is arithmetic attached to one rational fraction. 'Lowest harmonic' is a search-filter convention: among contacts that qualify under a chosen range and orb, software may retain the smallest matching factor to suppress related duplicates. The former does not depend on an orb; the latter does. Keep both labels visible rather than treating them as synonyms.
Worked examples
At 72°, nearest fraction is 1/5 and reduced order 5; H5 residual is 0°, H10 residual is also 0°. At 144°, nearest fraction is 2/5 and reduced order 5. At 61°, H5 is 305° after wrapping, so residual is 55° and it does not qualify under a 16° transformed orb even though a nearest rational fraction can still be calculated. These examples describe geometry, not personal meaning.
Worked explanation by Astral Atlas, derived from the integer longitude transform and ordinary fraction reduction.
Word origin · etymology
Modern descriptive compound using mathematical 'reduce' and 'order'.
Reduced means expressed in lowest terms; order names the denominator used to index the smallest repeating angular division. It is an Atlas display term, not a historical school label attributed to Cochrane.
How we know · epistemology
Number-theoretic reduction of a stated angular fraction
For a pair 72° apart, the nearest exact fraction is 1/5 and the reduced order is 5. That pair is also conjunct in H10, but H10 does not convert its primitive relation into a tenth-harmonic teaching. Nearness is separate: the inspector should display residual and declared orb, then say whether the selected factor qualifies.
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