by Robert Wilkinson
Yesterday we explored a few things about the aspects generated by the 5th and 10th harmonic aspect series. Today we’ll take a look at the 15th and 20th harmonic aspect series which are both derived from and based in the 5th harmonic.
Besides the decile, quintile, tredecile, and biquintile, there are two minor aspects in this group also associated with specialization and unique qualities and experiences. They are the 20th Harmonic series defined by the Vigintile (18 degrees) and the 15th Harmonic series defined by the Quindecile (24 degrees). Said to be first coined by Kepler (yes, THAT Kepler), they are fractions of a quintile.
I first learned about them via Llewellyn George’s A To Z Horoscope Maker and Delineator when I first started studying astrology in 1971. His source was James Wilson’s 1819 Dictionary of Astrology, where it originally stated these were aspects named by Kepler. The eminent astrologer John Addey also specifically wrote about these sub-harmonics of the 5th harmonic.
(NOTE: To clear up some contemporary confusion, that’s why I and other astrologers have rejected the name “quindecile” erroneously used by Noel Tyl, Thomas Ring and Ricki Reeves for the 165 degree aspect. The name “quindecile” has already been in use for centuries to mean a 24 degree aspect. My esteemed colleagues Michelle Young and Philip Graves have offered “undecaquartisextile“ as an alternative name for the 165 degree aspect, as well as more appropriate descriptors for that harmonic series. Google that term to learn more about that important aspect series, or go to any number of articles written by Michelle.)
I believe the Vigintile and Quindecile are minor but important points in the closing or opening of a cycle between planets. I believe the waxing Vigintile shows us the birth of the possibility of a gift or specialization which then hits the Quindecile point which is one-third of the way to the full gift or specialization reached by the quintile.
The next point in this pulse is reached at the decile, showing the unique qualities have come to a point where they are “halfway” to the perfected specialization of the waxing quintile, which is followed by the entry into the synthesizing “third phase” of the 54 degree angle before both the 15th and 20th harmonic series resolve at 72. Obviously when these aspects are waning, they unfold in reverse order as a “whole cycle” closes in preparation for a new birth at the conjunction.
While I don’t want to get into extensive speculation about either of these harmonic series beyond points of relative specialization, I believe that each of these angles between planets have their own special relevance. Perhaps what begins at the conjunction and shows promise of specialization at 24 degrees will hit the next level of development at a 48 degree angle, since it is the two-thirds point between the conjunction and the quintile.
For convenience, I use familiar prefixes to define each of these. While the Quindecile is 24, I would call a 48 degree angle a Biquindecile, and a 72 degree angle a Triquindecile, also known as the Quintile. I have named the fourth angle of 96 degrees in the series the Quadquindecile (or Quartaquindecile, with a nod to Philip Graves), the fifth in the series (120) the Pentaquindecile (a.k.a the trine), the sixth in the series (144) the Hexaquindecile (a.k.a. the Biquintile), and the last in the series (168) the Heptaquindecile. Equally acceptable would be the Septaquindecile.
I would use the same prefixes for the Vigintile series, and add the Octovigintile (a.k.a the biquintile) for the 144 angle, and the Nonavigintile for the 162 angle. Each of the 9 aspects in the 20th harmonic series would show a “four step” pulse to the quintile and then again to the biquintile, resolving at the 9th step in the process.
Given the Vigintile and Quindecile have been known for centuries, there is an extraordinary lack of discussion and research regarding the relevance of other aspects in either of these series. The Vigintile series includes degree values of 18, 36, 54, 72, 90, 108, 126, 144, and 162. The Quindecile series includes degree values of 24, 48. 72, 96, 120, 144, and 168.
As you can see, both series have 72 and 144 in common. It’s interesting that besides their correlation to the 5th harmonic series, one of the angular values in each of these harmonic series correlates with other aspects that are better known under other names from other aspect series. The two most obvious correlated aspects involve 90 and 120 degrees.
90 degrees is a square, and part of the 4th, 8th, and 12th harmonic series, with the 4th and 8th being found in the dischordant “Octile” series. From the values listed above, it’s also a Pentavigintile (5th aspect in the 20th harmonic series). Perhaps this is a “quintessence” that comes forth during friction or another type of square manifestation?
Then we have 120 degrees, which is the angle of three different aspects! It’s a trine, trinovile, and a Pentaquindecile (5th aspect in the 15th harmonic series). This aspect is present in the 3rd, 6th, 9th, 12th, and 15th harmonic series! Clearly 120 degrees between planets is a feast of many courses!
Though I find great meaning in the various aspects in any harmonic series, I am wary of harmonics taken to a minute scale, since if we slice harmonics thinly enough then we have hundreds of aspects. I believe that since nothing has relevance unless it has meaning, then the challenge for astrologers is to find meaning in how various aspects manifest in a consistent manner.
While this is a realm of astrology that is subject to great speculation and needs more thorough research, if we try to find “meaning” in a 3, 6, 9, or 12 degree aspect apart from its properties as a variance of an exact conjunction, then we’re stuck trying to parse meaning out of an almost infinite set of possibilities. Who can possibly state with authority the definitive differences between angles of 154+, 157, 160, 162, 163, 163+, 164, 165, 168, etc.?
The problem arises regarding orbs, since the third aspect in the 20th harmonic is very close to the septile, and the ninth aspect in the series is very close to the Pentelftile. The second aspect in the 15th harmonic is close to the semisquare, while the fourth aspect is close to the Trielftile. It could be argued that these close aspects each contributes to our experience at that part of the whole cycle, but any definitive conclusion about the blended effects will take extensive research and a fair degree of synthesis and imagination.
© Copyright 2016 Robert Wilkinson
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