There has been a lot written about the Quintile series of aspects, much of it vague and very generalized. Since these angles occur with great frequency, there is relatively little written about them, and a very important one is occurring at the present time, I thought I should offer you some insights about this misunderstood but very powerful series of aspects.
The entire series is based on division of the circle by 5, yielding 72 degrees as the primary aspect in the group, also known as the Quintile. This aspect represents specialization, gifts, and unique conditions. It is an aspect of creativity. No matter how similar it may be to other quintiles in other charts and times, each quintile is a unique quality or condition, a "quintessential" circumstance that has been weaved out of the "biospheric" responses of the "4" into the human "5th."
It represents a high degree of specialized force or form, something unique brought forth, transformed out of the generic materials. Thus it shows a point of high individualization, a unique stage of development, or a talent or gift recognized and/or articulated. All the other aspects in the series to some degree show this energy of specialization, just in different phases than the Quintile.
For example the Decile, or Semi-quintile, is a 36 degree aspect showing a partly developed creative uniqueness, a minor gift, or some other manifestation of specialized creativity. It either secures a unique tendency, or is the final flowering of a gift already realized. The Biquintile, as the name implies, is a 144 degree aspect showing a unique interactive situation, where one gift interacts with another gift, creatively and/or regeneratively. It is an interactive unique form of self-expression that often involves other people and their unique gifts, whether they align harmoniously with yours or not.
Last but not least, we now take a look at the least-understood aspect in the series, the Tredecile, which precipitated this article for reasons I'll make clear shortly. This is a highly specialized aspect of 108 degrees, which besides being a mythological "Sacred number" symbolizing Divine Mother Energy, is also the complementary angle to the Quintile. Thus the Tredecile indicates a very special type of unique energy that complements whatever uniqueness, gifts, or specialized quintessence are occurring at the moment in a situation.
I have seen this aspect operate in several fashions, and all seem to involve a circumstance presenting itself that perfectly fits a unique gift or need, or a gift or unique quality that fits the need of a pre-existing circumstance. The Tredecile is complementary, interactive, and specialized, the "quintessence" of a thing perfectly complementing the "quintessence" of a circumstance. When active, it seems to bring forth unique qualities in situations that involve interaction to bring forth awareness, completion, polarization, or re-polarization. The points opposite the planets in Tredecile are often associated with how the energies manifest, some need being fulfilled, some promise brought to expression, or some specialized gift or talent completed.
I have given it the keyword "SERENDIPITY." I believe this is the best descriptor for how the Tredecile works its magic. So exactly what does this word mean? We are told the definition of Serendipity involves "the faculty or phenomenon of finding valuable or agreeable things not sought for" and "an aptitude for making desirable discoveries by accident" and "good luck in making unexpected and fortunate discoveries."