Newsgroups: alt.astrology
Subject: Patterns and harmonic aspects
From: valja@tartu_ti_fs.customs.ee (Valentin Abramov)
Organization: Estonian Customs Tartu Branch
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Hi all,
Some patterns, such as the stellium, grand trine, T-square etc. are
well known; some patterns, are sometimes named, but rarely explained,
and some patterns I found neither names for nor explanations.
I have made a table of "constellations", in which I add a column for
total "power" which is the sum of the power of each aspect within it.
Comparison of the "powers" of patterns (of course, approximate) shows,
for example, that in a pattern where two squared planets are connected
to a third one, they throw two 135 deg aspects, they have nearly the
same "power" as a Yod, but I never found its description. Explanation
follows below.
Constellations of three planets:
No Name Positions of Aspects "power" explanation
planets (deg)
1 Stellium 0,0,0 3*0 3 well known
2 Grand Trine 0,120,240 3*120 1.732 well known
3 T-Square 0,90,180 180+2*90 1.707 well known
4 Wedge 0,60,180 60+120+180 1.693 ???
5 Roof 0,60,120 2*60+120 1.394 rare
6 ??? 0,90,225 90+2*135 1.000 ???
7 Yod 0,60,210 60+2*150 0.986 well known
8 ??? 0,90,210 90+120+150 0.789 ???
Constellations of four planets:
No Name Positions of Aspects "power" explanation
planets (deg)
1 Stellium 0,0,0,0 6*0 6 well known
2 Grand Cross 0,90,180,270 4*90 3.414 well known
3 Kite 0,90,180,270 3*120+180+2*60 3.707 rare
4 Mystic Rect. 0,120,180,270 2*120+2*180+2*60 3.385 rare
5 Cradle 0,60,120,180 180+2*120+3*60 3.087 ???
6 ??? 0,60,180,270 180+2*90+120+60+150 2.981 ???
7 ??? 0,90,150,240 120+2*90+60+2*150 2.563 ???
Some of these described patterns are explained rarely (marked as "rare"),
some are not explained. I think all of the described 3 planet patterns
and at least the cradle of the 4 planet patterns needs an explanation.
Not long ago in alt.astrology I saw some requests for an explanation
of the cradle, but it was never any answered...
Explanation for the "powers" of aspects:
Astrologers rarely talk about the relative "power" of aspects, but if
they talk, then the relative "powers" of aspects looks something like
this: (for example, russian astrologer Pavel Globa):
4 - conjuction,
3 - opposition and trine
2 - square and sextile
0.5 or 1 - quicunx, semisextile, semisquare, sesquiquadrate.
I read with great interest a lesson from Maggie McPherson about harmonic
aspects from ftp-site ftp.magitech.com and found a very powerful idea
about harmonic aspects, particularly if it can describe relative "powers"
and orbs of different aspects.
Here I used a fully EMPIRIC correlation for the "power" of aspects with
the assumption of the anisotropy of the universe (like in astrology the
ecliptic is divided to 12 parts). More detailed explanation follows below:
1. If harmonic matches the symmetry of space in the formation of the
aspect, (divide ring to 2,3,4,6,12), and the power decreases: 1/SQRT(k),
2. If harmonic doesn't fully match the symmetry of space (divide the ring
by 5,7,11,13...), and the power decreases: 1/k,
3. If harmonic doesn`t match the symmetry of space but has a part of the
symmetry of space (like k=10=2*5), then both parts decrease separately with
its own rule. For example, the power of decile (k=10) is 1/(SQRT(2)*5),
where k is No of harmonic.
Results for first 12 harmonics:
Harmonic Angle(s) "Power"
1 0 1.0
2 180 0.707
3 120 0.577
4 90 0.500
5 72, 144 0.200
6 60 0.408
7 51.43 0.143
8 45, 135 0.250
9 40, 80, 160 0.192
10 36, 108 0.141
11 32.72 ... 0.091
12 30 0.289
This results in a satisfactorily match with the appreciations named before
and was used for calculating the "powers" of a pattern, where "power"
of a pattern is the sum of the "powers" of all aspects in the pattern.
I repeat, the idea of harmonic aspects can be very powerful, if it can
describe relative "powers" and orbs of different aspects.
So I tried to use some mathematics:
If we use linear string equations, we can compare different harmonics
in simple and clear way. Differential equations of linear strings
fixed on both ends, solve as the sum of the harmonic waves, where the
frequency of the wave is proportional to the number of harmonic k , and
the wavelength is proportional to 1/k.
The amplitude of each wave has a complicated form, depending on the initial
positions of every point of the string, but in the first approximation
the maximum possible amplitude is proportional to the wavenlength, or 1/k.
The sum of 1/1 + 1/2 + 1/3 + .... is of course infinite, but the waves are
independent (non-interactive), and there is no need to sum up the amplitudes
of different the waves, because maximum-amplitude points of different
harmonics fall to a different point on the string. If we want to find
the summary amplitude of one point on the string, we must use exact
forms of amplitude and the sum will be finite ( I repeat, amplitude
depends on the initial position of string).
Instead we can sum up the energy of waves by saying they are proportional
to the square of its amplitude. So, if the amplitude decreases like 1/k,
then the energy decreases like 1/(k*k) and this sum is, of course, finite:
E(total) = 1/1 + 1/4 + 1/9 + .... = (Pi*Pi)/6 = 1.645.
So, now we can compare different waves with energy; decreases like 1/(k*k)
that lower harmonics have more energy, than the higher harmonics (more,
than all higher harmonics together), and amplitude of waves decrease like
1/k, which don't match with the approximated relative "powers" of aspects.
So, I tried to calculate the dependence of the angle between two planets
by covering integrals between the waveforms of those planets. A simple
approximation gives only the superposition of wide maximums, where
amplitude decreases like 1/(k*k).
This result doesn`t give us the possibility to compare "powers" and orbs
of different aspects and is unsatisfactory.
So, a LINEAR STRING gives us NOTHING more than a simple ILLUSTRATION.
Amplitudes of different harmonics don`t match with the relative "power"
of aspects, given by some astrologers.
Unfortunately I haven`t access to Robert Hand`s book "Essays on Astrology".
Maybe somebody knows if Hand`s wave theory is available somewhere through
the Internet?
Here is one more example why such a simple model doesn`t work. The equation
for each linear string assumes isotropy of space. But in astrology space is
assumed as anisotropic! We have symmetry axes with different symmetry orders:
i = 3 (step 120 deg.) - trigons of air, fire etc.
i = 4 (step 90 deg.) - cardinal, fixed and mutual signs,
i = 6 (step 60 deg.) - positive and negative (In and Yan) signs,
1 = 12 (step 30 deg.) - signs itself.
So, if we rotate over a symmetry axis, we have at least four different
periodic changes in the properties of directions in space.
Naturally we can assume that harmonic waves (or something else, the name
does not matter) with a period matching the symmetry of space, it can be
more "powerful". It explains simply, why multiple 30 deg aspects, are more
important, than other aspects - it is result of periodic anisotropy of
space - Zodiacal ring is divided into 12 parts with three harmonic
subperiods. Other harmonics can exist, but because they don`t match
symmetry of space, they are "weaker".
FINALLY I assumed this fully EMPIRIC correlation for "power" of harmonics.
I emphasize, it is a fully empiric assumption. I hope someone can find
some EMPIRC MODEL, NOT THEORY, which can in some way describe harmonic
aspects and its "powers" and orbs.
And anyway, patterns with 3 or more planets needs explanation...
I acnowledge Willam Gordon for help in preparing this posting.
Best regards,
Valentin Abramov valja@tartu_ti_fs.customs.ee