Monday, May 23, 2022

Declination Quads

 

I was checking out Declination Quads which are called Magi Dek Quads in Magi Astrology.   They are midpoint-midpoint parallels, contraparallels.   Declination Midpoints aren't exclusive to Magi Astrology.  They're used in Cosmobiology.  Eleanor Kimmel goes over Declination Midpoints in her book Cosmobiology for the 21st Century.  Philip Sedgwick writes that Declination Midpoints are valid in his book Astrology of Deep Space.


I noticed some interesting things with Mercury, Venus, Ceres, and Sedna in Declination in my Astrological Nativity, and it has to do with Declination Quads which I will just refer to as DecQuads.


Mercury - 18S24

Venus - 18S10

Ceres - 21N59

Uranus - 5S26

Sedna - 1N40


Mercury parallel Venus - 14 min





The following is from Magi Astrologer Sandy L. Crowther's site.


A Magi Quad is formed whenever at least 4 planets are aligned in a symmetrical pattern that results in 2 of the sides being parallel to each other. So whenever there is a MQ, there is also a conjunction of 2 midpoints, and therefore, a conjunction of 2 midpoints occurs only when there is a Magi Quad. Visually, we can see that a MQ is the formation of two pairs of planets forming two parallel lines. Mathematically, these two pairs of planets are separated by an equal number of degrees. MQ's have a powerful influence because 2 midpoints are conjoining each other, and these midpoints are formed by two pairs of different planets (called pairings). Like MQ's, Magi Dek Quads (MDQ's - Declinational Magi Quads) are also formed when two midpoints are parallel to each other, and the two midpoints are formed by four different planets. MQ's and MDQ's are mathematically equivalent. The number of degrees separating one planet of a pairing from a planet of the other pairing will always be the same as the number of degrees separating the remaining two planets that form the Magi Quad. In the longitudes, such planetary positions create a symmetrical quadrangle where two of the sides are parallel. (See Chart below).

"When four planets are aligned together in the form of a Magi Quad, the four planets provide the native with special gifts, talents, and aptitudes that can be predicted through integrating and combining the symbolisms of the four planets." (Excerpt from The Magi Society Ephemeris).

MQ's are the single most important astrological influence for determining what type of capabilities and talents the native has. MQ's also follow the symbolism of Magi Astrology, which means that MQ's are interpreted in the same way as we interpret aspects. While Super Aspects explain and predict the probability of super success, they are somewhat limited in their ability to forecast the exact realm and nature of the success that a person can achieve - so this is where MQ's come into play. And when an Aspected MQ is formed with a conjunction that is a Super Aspect, the entire alignment of the 5 planets involved becomes a Super Aspected MQ. Most super successful people have at least one of their Super Aspects involved in the formation of a Super Aspected Magi Quad.

Pairings: Two planets comprising the MQ's are called Pairings. Composites: 3 planets of aspected MQ's are called Composites. Theory of Midpoint Equivalence: Every midpoint acts as if it were a planet, and all midpoints influence both planets and other midpoints under the same conditions as planets themselves. All midpoints are also influenced by planets and other midpoints under the same conditions as planets themselves. Midpoint Projection: The near and far midpoints exist concurrently: Midpoint project, and are simultaneously at both the far and near locations. For these reasons, we never say a midpoint is opposed (always an enhancement) or sextile to any planet or location, because the other midpoint must be either conjunct or trine.


Magi Quad Orbs 

  • Longitudes: 2 to 2.5 Degrees 
  • Declinations: 1 Degree


Magi Dek Quads are connected by diagonal lines. Magi Quads are connected by parallel lines.

http://www.jupitersweb.com/magi-quads-and-midpoint-crossings.html


I don't feel comfortable with using 1 degree orb for DecQuads, and so I decided to look for them within an orb of 10 minutes. 


Venus/Ceres - 1N55

Mercury/Ceres - 1N48

Uranus/Sedna - 1S53


Venus/Ceres contraparallel Uranus/Sedna - 2 min

Mercury/Ceres contraparallel Uranus/Sedna - 5 min


Venus/Sedna - 8S15

Mercury/Sedna - 8S22

Ceres/Uranus - 8N16


Venus/Sedna contraparallel Ceres/Uranus - 1 min

Mercury/Sedna contraparallel Ceres/Uranus - 6 min


Venus/Uranus - 11S48

Mercury/Uranus - 11S55

Ceres/Sedna - 11N50


Venus/Uranus contraparallel Ceres/Sedna - 2 min

Mercury/Uranus contraparallel Ceres/Sedna - 5 min



3 Mercury-Ceres-Uranus-Sedna DecQuads

Combined Mental Processes, Nurturing, Independence, Unconscious Depths/Otherworldly 


3 Venus-Ceres-Uranus-Sedna DecQuads

Combined Love, Nurturing, Independence, Unconscious Depths/Otherworldly 



Key Concept for Sedna is from Linda Lee Berry. 




Sedna is considered the worst in Magi Astrology. 








I also have a Mercury-Uranus-Sedna configuration in Ecliptic Longitude, and it involves Mars and Saturn to form an 11th Harmonic Irregular Pentagon.   


From David Cochrane:
Harmonic 11: Restless and on the move, seeking something new. An inclination to be a pioneer or innovator or to be involved with music, dance, travel, or other dynamic activities. Some proneness to instability or insomnia if taken to an extreme, in which case avoidance of stimulants is important.


Mercury, Saturn, Uranus, and Sedna form an Isosceles Trapezoid with the following corresponding midpoint pictures:

Mercury/Sedna oppose Saturn/Uranus - 1 min
Mercury oppose Saturn/Sedna - 16 min
Sedna oppose Mercury/Uranus - 17 min


Therefore, my Astrological Nativity has a very strong Mercury-Uranus-Sedna signature.













Trans-Neptunian Dwarf Planet/candidates and Overexcitabilities

 Transneptunian Dwarf Planets and Overexcitabilities

"Dabrowski's Theory of Positive Disintegration

"Dabrowski talked about OE's - over-excitabilities ("superstimulatabilities"), and how the gifted were extremely sensitive in a variety of areas. It's a stimulus-response difference from the norms. It means that in these 5 areas a person reacts more strongly than normal for a longer period than normal to a stimulus that may be very small. It involves not just psychological factors but central nervous system sensitivity."

http://www.hoagiesgifted.org/dabrowski.htm


Pluto is the planet of elimination of boundaries, and is compared to being the other side. This could be death, afterlife, or could be the subterranean depths of the human psyche. It is possible that Pluto's fellow transneptunian objects could be similar to Pluto. I believe that Pluto and its fellow transneptunians can be energies so metaphysical that they can be hard to handle and can manifest as problems on the physical plane.

Their very distant location, their tendency to orbit off the ecliptic as well as some of them with highly elliptical orbits make them objects that are divergent from the planets. Therefore, people with strong transneptunian energies can be divergent from the norm. They can be quite the nonconformists. I suspect that these are the same people that can relate to personality types like Indigo,Crystal,Earth Angel,Lightworker too. The same energies could be prominent in people with neurodivergences like Dyslexia,Dyspraxia,ADHD, Autistic Spectrum. The energies could be prominent in people that are schizophrenic,bipolar. The symptoms/traits of neurodivergence overlap with those of schizophrenia,bipolar. Because of the narrow-minded views about the metaphysical and sensitivities by scientific,mental health commmunity, metaphysically oriented types could get misdiagnosed as schizophrenics or bipolars. Transneptunian dwarf planet people can find it hard to live in a society with mainstream religion and psychiatry.

Astrologers tend to focus on Moon, Neptune, and Watersigns in regards to sensitivity, but I actually believe that the ultrasensitive nature of Pluto has been overlooked. Neptune is said to be the planet of ultrasensitivity. As an object that orbits beyond Neptune, it would make sense for Pluto to be associated with ultrasensitivity that is more pronounced than Neptune. Pluto is associated with intensity. Maybe the intensity is actually connected to an ultrasensitivity. For the more we react to stimuli and internalize it, the more intense we are. Now we know that Pluto isn't the only object in the transneptunian regions of our solar system. Pluto's fellow transneptunian dwarf planets could also be similar to Pluto. Sedna has the greatest average distance of all objects in our solar system, and so it make sense to be an object that is associated with the greatest ultrasensitivity and intensity.

In Wrong Planet Group which is a group for Autistic Spectrum people, an Aspie asked if Aspies feel things more intensely than NT's. Aspie is another term for Aspergers. NT stands for Neurotypical which means normal neurological processing people. There was talk about feeling but internalizing as the intensity of feeling is often overwhelming. The Aspies said that it has to do with sensory issues that include heightened senses. They say that they are more emotionally intense than most. I said that I could relate even though I don't have Aspergers. I said that I am Dyslexic, Dyspraxic, ADHD, and so I am not an NT. I pointed out that sensory processing/integation issues is common in people with neurodivergent condtions in general and not just autistic spectrum. I also said that some people even wonder if sensory processing/integration issues and Dyspraxia are one and the same. I even pointed out that Dyslexia, Dyspraxia, and ADHD overlap in symptoms/traits as well as have considerable co-morbidity. I said that I wouldn't generalize NT's. I pointed out that not all NT's are the same. I said that definitely not all non-Autistic Spectrum people are the same for there are other ND's that aren't autistic spectrum that don't fit the neurological norms. I find it interesting that Autistic Spectrum people talk about feeling more intensely than NT's. It makes sense when you look at it from the view of overexcitabilities. I believe that the transneptunian dwarf planet energy is strongly connected to overexcitabilities, sensory processing/integration issues,and neurodivergent conditions.

People that are into Metaphysical,New Age beliefs label overexcitabilities as traits as "Indigo", "Crystal", "Earth Angel", and "Lightworker." which they are linked to being gifted. Overexcitabilities are said to be a very common thing in gifted people

I believe that transneptunian dwarf planet/candidate energy is strongly connected to all these things.



What Aspies were actually referring to was Intense World Theory. 


The intense world theory of autism holds that autistic people experience the world in extreme ways. They perceive the world as so intense that it can become difficult or unbearable at times.

This theory may explain...

Sensory hypersensitivity

Stimming and self-injury as coping mechanisms

Intense feelings, including severe distress at others' pain and meltdowns

Heightened fear   

https://autism-advocacy.fandom.com/wiki/Intense_World_Theory#:~:text=The%20intense%20world%20theory%20of%20autism%20holds%20that,Sensory%20hypersensitivity.%20Stimming%20and%20self-injury%20as%20coping%20mechanisms.



Friday, May 6, 2022

Fibonacci Harmonic Aspects

 

This is a post about Fibonacci Harmonic Aspects which are Aspects with Fibonacci Number as the denominator if you look at Harmonic Aspects as Fractions of a Circle.

I listed the 1st Harmonic Aspect, 2nd Harmonic Aspect, 3rd Harmonic Aspects, 5th Harmonic Aspects, 13th Harmonic Aspects, 21st Harmonic Aspects, 34th Harmonic Aspects, 55th Harmonic Aspects, 89th Harmonic Aspects, 144th Harmonic Aspects, and 233rd Harmonic Aspects. 


In mathematics, the Fibonacci numbers, commonly denoted Fn, form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors omit the initial terms and start the sequence from 1 and 1 or from 1 and 2. Starting from 0 and 1, the next few values in the sequence are:[1]

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...

The Fibonacci numbers were first described in Indian mathematics,[2][3][4] as early as 200 BC in work by Pingala on enumerating possible patterns of Sanskrit poetry formed from syllables of two lengths. They are named after the Italian mathematician Leonardo of Pisa, later known as Fibonacci, who introduced the sequence to Western European mathematics in his 1202 book Liber Abaci.[5]

Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the Fibonacci Quarterly. Applications of Fibonacci numbers include computer algorithms such as the Fibonacci search technique and the Fibonacci heap data structure, and graphs called Fibonacci cubes used for interconnecting parallel and distributed systems. They also appear in biological settings, such as branching in trees, the arrangement of leaves on a stem, the fruit sprouts of a pineapple, the flowering of an artichoke, an uncurling fern, and the arrangement of a pine cone's bracts.

Fibonacci numbers are strongly related to the golden ratioBinet's formula expresses the nth Fibonacci number in terms of n and the golden ratio, and implies that the ratio of two consecutive Fibonacci numbers tends to the golden ratio as n increases. Fibonacci numbers are also closely related to Lucas numbers, which obey the same recurrence relation and with the Fibonacci numbers form a complementary pair of Lucas sequences.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181


Fibonacci numbers are strongly connected to the Golden Mean which is 1.618 represented by by the Greek letter phi, Φ.
Fibonacci numbers are strongly related to the golden ratio: Binet's formula expresses the nth Fibonacci number in terms of n and the golden ratio, and implies that the ratio of two consecutive Fibonacci numbers tends to the golden ratio as n increases.


In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities  and  with 

where the Greek letter phi ( or ) represents the golden ratio.[a] It is an irrational number that is a solution to the quadratic equation  with a value of[2][1]

1.618033988749....(OEISA001622)

The golden ratio is also called the golden mean or golden section (Latinsectio aurea).[3][4] Other names include extreme and mean ratio,[5] medial sectiondivine proportion (Latin: proportio divina),[6] divine section (Latin: sectio divina), golden proportiongolden cut,[7] and golden number.[8][9][10]

Mathematicians since Euclid have studied the properties of the golden ratio, including its appearance in the dimensions of a regular pentagon and in a golden rectangle, which may be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has also been used to analyze the proportions of natural objects as well as man-made systems such as financial markets, in some cases based on dubious fits to data.[11] The golden ratio appears in some patterns in nature, including the spiral arrangement of leaves and other parts of vegetation.

https://en.wikipedia.org/wiki/Golden_ratio


21 divided by 13 = 1.615384615384615

34 divided by 21 = 1.619047619047619

55 divided by 34 = 1.617647058823529

89 divided by 55 = 1.618181818181818

144 divided by 89 = 1.617977528089888




The following is from David Cochrane:


Cosmic cybernetics is a highly simplified form of astrological analysis which uses an extremely narrow segment of astrological ideas. A fundamental assumption of cosmic cybernetics, as with harmonic astrology as proposed by John Addey, is that the angular distance between planetary positions, or the projected position of planets onto the ecliptic plane, produces in some as yet undiscovered way a wave form. Each planet acts as the node or crest of a wave function and there is an effect on life on our planet from these undiscovered waves. 

Based on harmonic theory we expect that waves of higher harmonics will have proportionately smaller wave sizes so that all harmonics occur approximately equal often by chance. Even if harmonics do not occur equally often by chance due to the complex motion of planetary positions, based on harmonic theory the orb would still be based on these proportional wave sizes.

 • To establish the proportional wave sizes, the orb for the first harmonic is divided by the harmonic number. 

I do not believe that higher harmonics are weaker than lower harmonics, at least up to the 180th harmonic. I believe that higher harmonics are more internal and less visible externally but are not weaker. As an example of how aspects in a harmonic chart work, a trine in the 5th harmonic chart is a 15th harmonic aspect (5 x 3). In many cases the harmonic may reduce to a lower harmonic. 


A very small orb of an aspect is not just the indicator of an aspect that is very strong.  It is also an indicator that the aspect is also of higher octave harmonics.  Example: a square within 6 minute orb is not just the 1/4 aspect, but it is also the 2/8 aspect, the 4/16 aspect, the 8/32 aspect, the 16/64 aspect, the 32/128 aspect.  It is also the 9/36 aspect, the 18/72 aspect and the 36/144 aspect.


I listed all aspects of Harmonics of Fibonacci Numbers up to the 233rd. 

I stopped at 233rd because I will be going over 360th.   David Cochrane doesn't have the view that Harmonics beyond 360 work, and I am in agreement with him.



Fibonacci Harmonic Aspects


1st Harmonic Aspect  (Conjunction in 1st Harmonic Chart)

1 is a Fibonacci Prime Number

1st Harmonic Aspect is a Fibonacci Harmonic Aspect

Maximum Orb - 15°


1 - 360° aka waning Conjunction with waxing degree being 0°


The following aspects have proportionate orbs based on 15 degree orb for Conjunction



2nd Harmonic Aspect (Conjunctions in 2nd Harmonic Chart)

2 is a Fibonacci Prime Number

Divisors are 1, 2

1st Harmonic aspect and 2nd Harmonic aspect are Fibonacci Harmonic aspects

Maximum Orb - 7° 30'


1/2 - 180°

2/2 - 360° aka waning Conjunction with waxing degree being 0°



3rd Harmonic Aspect (Conjunctions in 3rd Harmonic Chart)

3 is a Fibonacci Prime Number

Divisors - 1, 3

1st Harmonic aspect and 3rd Harmonic aspect are Fibonacci Harmonic Aspects

Maximum Orb - 5°


1/3 - 120°  aka Trine

2/3 - 60°    aka Sextile

3/3 - 360° aka waning Conjunction with waxing degree being 0°



5th Harmonic Aspects (Conjunctions in 5th Harmonic Chart)

5 is a Fibonacci Prime Number

Divisors - 1, 5

1st Harmonic and 5th Harmonic are Fibonacci Harmonics


1/5 - 72°   aka Quintile

2/5 - 144° aka BiQuintile

5/5 - 360° which is waning degree of Conjunction with waxing degree being 0°



8th Harmonic Aspects (Conjunctions in 8th Harmonic Chart)

8 is a Fibonacci Number

Factorization is 2 to the 3rd Power

Divisors - 1, 2, 4, 8

1st Harmonic aspect, 2nd Harmonic aspect, 4th Harmonic aspects, and 8th Harmonic aspects are Fibonacci Harmonic aspects

Maximum Orb - 3° 45'


1/8 - 45°   aka SemiSquare

2/8 - 90°   aka Square

3/8 - 135° aka SesquiSquare

4/8 - 180° aka Opposition

8/8 - 360° aka waning Conjunction with waxing degree being 0°



13th Harmonic Aspects (Conjunctions in 13th Harmonic Chart)

13 is a  Fibonacci Prime Number

Divisors - 1, 13

1st Harmonic aspect and 13th Harmonic aspects are Fibonacci Harmonic aspects

Maximum Orb - 1° 09'


1/13 - 27° 41' 31

2/13 - 55° 23′ 02′′

3/13 - 83° 04′ 33′′

4/13 - 110° 46′ 4′′

5/13 - 138° 27′ 35′′

6/13 - 166° 09′ 06′′

13/13 - 360° aka waning Conjunction with waxing degree being 0°



21st Harmonics (Conjunctions in 21st Harmonic Chart)

21 is a Fibonacci Number

Factorization - 3 x 7

Divisors - 1, 3, 7, 21

1st Harmonic aspect, 3rd Harmonic aspects, 7th Harmonic aspects, and 21st Harmonic aspects are Fibonacci Harmonic aspects

Maximum Orb - 0° 43'


1/21 - 17° 08′ 35′′

2/21 - 34° 17′ 10′′

3/21 - 51°25' 42''   aka Septile

4/21 - 68° 34′ 20′′

5/21 - 85° 42' 55''    

6/21 - 102° 51' 25''  aka BiSeptile

7/21 - 120°  aka Trine

8/21 - 137° 08' 40"

9/21 - 154° 17' 08''  aka TriSeptile

10/21 - 171° 25' 50''

21/21 - 360° aka waning Conjunction with waxing degree being 0°



34th Harmonic Aspects (Conjunctions in 34th Harmonic Chart)

34 is a Fibonacci Number

Factorization - 2 × 17

Divisors - 1, 2, 17, 34

1st Harmonic aspect, 2nd Harmonic aspect, 17th Harmonic aspects, and 34th Harmonic aspects are Fibonacci Harmonic aspects

Maximum Orb - 0° 26'


1/34 - 10° 35' 17

2/34 - 21° 10′ 34′′

3/34 - 31° 45′ 51′′

4/34 - 42° 21′ 08′′

5/34 - 52° 56′ 25′′

6/34 - 63° 31′ 42′′

7/34 - 74° 06′ 59′′

8/34 -  84° 42′ 16′′

9/34 - 95° 17′ 33′′

10/34 -  105° 52′ 50′′

11/34 -  116° 28′ 07′′

12/34 - 127° 03′ 24′′

13/34 - 137° 38′ 41

14/34 - 148° 13′ 58′′

15/34 - 158° 49′ 15′′

16/34 - 169° 24′ 32′′

17/34 - 180°   aka Opposition

34/34 - 360° aka waning Conjunction with waxing degree being 0°



55th Harmonic Aspects (Conjunctions in 55th Harmonic Chart)

55 is a Fibonacci Number

Factorization - 5 × 11

Divisors - 1, 5, 11, 55

1st Harmonic aspect, 5th Harmonic aspects, 11th Harmonic aspects, and 55th Harmonic aspects are Fibonacci Harmonic aspects

Maximum Orb - 0° 16′ 


1/55 - 6° 32' 42"

2/55 - 13° 05′ 24′′

3/55 - 19° 38′ 06′′

4/55 - 26° 10′ 48′′

5/55 -  32°43'37''  aka Undecile

6/55 -  39° 16′ 12"

7/55 - 45° 48′ 54′′

8/55 -  52° 21′ 36′′

9/55 - 58° 54′ 18′′

10/55 -  65°27'16''   aka BiUndecile

11/55 - 72°   aka Quintile

12/55 - 78° 32′ 24′′

13/55 - 85° 05′ 06′′

14/55 - 91° 37′ 48′′

15/55 - 98°10'54''   aka TriUndecile

16/55 - 104° 43′ 12′′

17/55 -  111° 15′ 54′′

18/55  - 117° 48′ 36′′

19/55 - 124° 21′ 18′′

20/55 - 130°54'32''    aka QuadriUndecile

21/55 - 137° 26′ 42′′

22/55 - 144° BiQuintile

23/55 - 150° 32′ 06′′

24/55 - 157° 04′ 48′′

25/55 - 163° 38' 10''  aka QuinqueUndecile 

26/55 - 170° 10′ 12′′

27/55 - 176° 42′ 54′′

55/55 - 360° aka waning Conjunction with waxing degree being 0°



89th Harmonic Aspects (Conjunctions in 88th Harmonic Chart)

89 is a Fibonacci Prime Number

Divisors - 1, 89

1st Harmonic aspect and 8th Harmonic aspects are Fibonacci Harmonic aspects

Maximum Orb -  0° 10′ 


1/89 - 4° 02' 42"

2/89 - 8° 05′ 24′′

3/89 -  12° 08′ 06′′

4/89 - 16° 10′ 48′′

5/89 - 20° 13′ 30′′

6/89 -  24° 16′ 12′′

7/89 -  28° 18′ 54′′

8/89 - 32° 21′ 36′′

9/89 - 36° 24′ 18′′

10/89 - 40° 27′ 

11/89 -  44° 29′ 42′′

12/89 - 48° 32′ 24′′

13/89 -  52° 35′ 06′′

14/89 -  56° 37′ 48′′

15/89 -  60° 40′ 30′′

16/89 - 64° 43′ 12′′

17/89 -  68° 45′ 54′′

18/89 -  72° 48′ 36′′

19/89 - 76° 51′ 18′′

20/89 - 80° 54′ 

21/89 - 84° 56′ 42′′

22/89 - 88° 59′ 24′′

23/89 - 93° 02′ 06′′

24/89 - 97° 04′ 48′′

25/89 - 101° 07′ 30′′

26/89 - 105° 10′ 12′′

27/89 -  109° 12′ 54′′

28/89 - 113° 15′ 36′′

29/89 -  117° 18′ 18′′

30/89 -  121° 21′ 

31/89 - 125° 23′ 42′′

32/89 - 129° 26′ 24′′

33/89 -  133° 29′ 06′′

34/89 - 137° 31′ 48′′

35/89 -  141° 34′ 30′′

36/89 -  145° 37′ 12′′

37/89 - 149° 39′ 54′′

38/89 -  153° 42′ 36′′

39/89 - 157° 45′ 18′′

40/89 -  161° 48′ 

41/89 -  165° 50′ 42′′

42/89 -  169° 53′ 24′′

43/89 - 173° 56′ 06′′

44/89 - 177° 58′ 48′′

89/89 - 360° aka waning Conjunction with waxing degree being 0°



144th Harmonic Aspects (Conjunctions in 44th Harmonic Chart)

144 is a Fibonacci Number

Square of 12

Factorization - 2 to the 4th Power × 3 to the 2nd Power

Divisors - 1, 2, 3, 4, 6, 8, 12, 16, 18, 24, 36, 48, 72, 144

1st Harmonic aspect, 2nd Harmonic aspect, 3rd Harmonic aspects, 4th Harmonic aspect, 4th Harmonic aspects, 6th Harmonic aspects, 8th Harmonic aspects, 12th Harmonic aspects, 16th Harmonic aspects, 18th Harmonic aspects, 24th Harmonic aspects, 36th Harmonic aspects, 48th Harmonic aspects, 72nd Harmonic aspects and 144th Harmonic aspects are Fibonacci Harmonic aspects

Maximum Orb -  0° 06′ 


1/144 - 2° 30' 

2/144 - 5° aka 1/72  

3/144 - 7° 30'  aka 1/48

4/144 - 10° aka 1/36

5/144 - 12° 30'  aka 2/48

6/144 - 15°  aka 1/24 and Viginquartile 

7/144 - 17° 30' 

8/144 - 20°  aka SemiNovile

9/144 - 22° 30'  aka 1/16

10/144  - 25°  aka 5/72

11/144 - 27° 30'

12/144 - 30°  aka SemiSextile 

13/144 - 32° 30'  

14/144 - 35°  aka 7/72

15/144 - 37° 30'  aka 5/48

16/144 - 40° aka Novile 

17/144 - 42° 30' 

18/144 - 45° aka SemiSquare 

19/144 - 47° 30'  

20/144 - 50°  aka 5/36

21/144 - 52° 30'  aka 7/48

22/144 - 55°  aka 11/72

23/144 - 57° 30'  

24/144 - 60° aka Sextile 

25/144 - 62° 30' 

26/144 - 65°  aka 13/72

27/144 - 67° 30'  aka 3/16

28/144 - 70°  aka 7/36

29/144 - 72° 30' 

30/144 - 75° aka 5/24 aka Squile 

31/144 - 77° 30' 

32/144 - 80°  aka BiNovile 

33/144 - 82° 30'  aka 11/48

34/144 - 85° aka 17/72 and Golden Mean of Golden Mean

35/144 - 87° 30' 

36/144 - 90° aka Square 

37/144 - 92° 30' 

38/144 - 95°  aka 19/72

39/144 - 97° 30'  aka 13/48

40/144 - 100°  aka 5/18

41/144 - 102° 30' 

42/144 - 105°  aka 7/24 and Squine

43/144 - 107° 30' 

44/144 - 110°  aka 11/36

45/144 - 112° 30'  aka 5/16

46/144 - 115°  aka 23/72

47/144 - 117° 30'

48/144 -  120° aka Trine

49/144 - 122° 30'  

50/144 - 125°  aka 25/72 

51/144 - 127°30'  aka 17/48

52/144 - 130°  aka 13/36

53/144 - 132° 30' 

54/144 - 135°  aka SesquiSquare

55/144 - 137° 30'  aka Golden Mean

56/144 - 140° aka 7/18

57/144 - 142° 30'  aka 19/48

58/144  - 145°  aka 29/72

59/144 - 147° 30' 

60/144 - 150°  aka Quincunx

61/144 - 152° 30' 

62/144 - 155°  aka 31/72

63/144 - 157° 30'  aka 7/16

64/144 - 160°  aka QuadriNovile

65/144 - 162° 30' 

66/144 - 165°  aka 11/24 and Johndro

67/144 - 167° 30' 

68/144 - 170°  aka 17/36

69/144 - 172° 30'  aka 23/48

70/144  - 175°  aka 35/72

71/144 - 177° 30' 

72/144 - 180°  aka Opposition

144/144 - 360° aka waning Conjunction with waxing degree being 0°



233rd Harmonic Aspects (Conjunctions in 233rd Harmonic Chart)

233 is a Fibonacci Prime Number

Divisors - 1, 233

1st Harmonic aspect and 233rd Harmonic aspects are Fibonacci Harmonic aspects

Maximum Orb - 0° 04′ 


1/233 - 1° 32' 42"

2/233 -  3° 05′ 24′′

3/233 -  4° 38′ 06′′

4/233 - 6° 10′ 48′′

5/233 - 7° 43′ 30′′

6/233 -  9° 16′ 12′′

7/233 - 10° 48′ 54′′

8/233 - 12° 21′ 36′′

9/233 - 13° 54′ 18′′

10/233 - 15° 27′ 

11/233 - 16° 59′ 42′′

12/233 - 18° 32′ 24′′

13/233 - 20° 05′ 06′′

14/233 - 21° 37′ 48′′

15/233 - 23° 10′ 30′′

16/233 - 24° 43′ 12′′

17/233 - 26° 15′ 54′′

18/233 -  27° 48′ 36′′

19/233 -  29° 21′ 18′′

20/233 -  30° 54′ 

21/233 - 32° 26′ 42"

22/233 - 33° 59′ 24′′

23/233 -  35° 32′ 06′′

24/233 - 37° 04′ 48′′

25/233 - 38° 37′ 30′′

26/233 - 40° 10′ 12′′

27/233 -  41° 42′ 54′′

28/233 - 43° 15′ 36′′

29/233 - 44° 48′ 18′′

30/233 - 46° 21′ 

31/233 - 47° 53′ 42′′

32/233 -  49° 26′ 24′′

33/233 -  50° 59′ 6′′

34/233 -  52° 31′ 48′′

35/233 - 54° 04′ 30′′

36/233 - 55° 37′ 12′′

37/233 - 57° 09′ 54′′

38/233 - 58° 42′ 36′′

39/233 -  60° 15′ 18′′

40/233 -  61° 48′ 

41/233 - 63° 20′ 42′′

42/233 - 64° 53′ 24′′

43/233 - 66° 26′ 06′′

44/233 - 67° 58′ 48′′

45/233 - 69° 31′ 30′′

46/233 -  71° 04′ 12′′

47/233 -  72° 36′ 54′′

48/233 -  74° 09′ 36′′

49/233 - 75° 42′ 18′′

50/233 - 77° 15′ 

51/233 - 78° 47′ 42′′

52/233 -  80° 20′ 24′′

53/233 - 81° 53′ 06′′

54/233 - 83° 25′ 48′′

55/233 -  84° 58′ 30′′

56/233 -  86° 31′ 12′′

57/233 -  88° 03′ 54′′

58/233 - 89° 36′ 36′′

59/233 -  91° 09′ 18′′

60/233 - 92° 42′ 

61/233 - 94° 14′ 42′′

62/233 -  95° 47′ 24′′

63/233 -  97° 20′ 06′′

64/233 -  98° 52′ 48′′

65/233 - 100° 25′ 30′′

66/233 - 101° 58′ 12′′

67/233 - 103° 30′ 54′′

68/233 - 105° 03′ 36′′

69/233 - 106° 36′ 18′′

70/233 -  108° 09′ 

71/233 -  109° 41′ 42′′

72/233 - 111° 14′ 24′′

73/233 - 112° 47′ 06′′

74/233 - 114° 19′ 48′′

75/233 -  115° 52′ 30′′

76/233 -  117° 25′ 12′′

77/233 -  118° 57′ 54′′

78/233 -  120° 30′ 36′′

79/233 -  122° 03′ 18′′

80/233 - 123° 36′ 

81/233 -  125° 08′ 42′′

82/233 - 126° 41′ 24′′

83/233 - 128° 14′ 06′′

84/233 - 129° 46′ 48′′

85/233 - 131° 19′ 30′′

86/233 - 132° 52′ 12′′

87/233 -  134° 24′ 54′′

88/233 - 135° 57′ 36′′

89/233 - 137° 30′ 18′′

90/233 - 139° 03′ 

91/233 - 140° 35′ 42′′

92/233 - 142° 08′ 24′′

93/233 - 143° 41′ 06′′

94/233 - 145° 13′ 48′′

95/233 - 146° 46′ 30′′

96/233 -  148° 19′ 12′′

97/233 -  149° 51′ 54′′

98/233 - 151° 24′ 36′′

99/233 - 152° 57′ 18′′

100/233 - 154° 30′ 

101/233 - 156° 02′ 42′′

102/233 - 157° 35′ 24′′

103/233 -  159° 08′ 06′′

104/233 -  160° 40′ 48′′

105/233 - 162° 13′ 30′′

106/233 - 163° 46′ 12′′

107/233 - 165° 18′ 54′′

108/233 -  166° 51′ 36′′

109/233 -   168° 24′ 18′′

110/233 - 169° 57′ 

111/233 -  171° 29′ 42′′

112/233 - 173° 02′ 24′′

113/233 -  174° 35′ 6′′

114/233 - 176° 07′ 48′′

115/233 - 177° 40′ 30′′

116/233 - 179° 13′ 12′′

233/233 - 360° aka waning Conjunction with waxing degree being 0°



All of the regular aspects used in Mainstream Astrology are 144th Harmonic aspects if they are within an orb of 6 minutes


12/144 - 30°  aka SemiSextile 

24/144 - 60° aka Sextile 

36/144 - 90° aka Square 

48/144 -  120° aka Trine 

60/144 - 150°  aka Quincunx

72/144 - 180°  aka Opposition

144/144 - 360° which is waning degree of Conjunction with waxing degree of 0°


additional aspects regularly used in Cosmobiology and Uranian Astrology are 144th aspects if they are within an orb of 6 minutes

9/144 - 22° 30'  aka 1/16  (used only in Uranian Astrology)

18/144 - 45° aka SemiSquare

27/144 - 67° 30'  aka 3/16 (used only in Uranian Astrology)

54/144 - 135°  aka SesquiSquare

63/144 - 157° 30'  aka 7/16 (used only in Uranian Astrology)



In his article The Golden Section: A Cosmic Principle, Dr. Landscheidt discussed Golden Aspects


"The golden section divisions within cycles formed by the rotating earth may be considered a set of astrological aspects. The complete set emerges when we superimpose the two schematic diagrams in Figures 19 and 23, related to minor and major of the golden section, and compare all of those angles we find on the right and on the left of the origin 0°. Imagine that you are standing at the rising point R, or 0°, of the diurnal circle and are looking over to the setting point at 180°. Then the superimposed golden section divisions on your right form the set 21.25°, 42.49°, 47.51°, 68.75°, 111.25°, 132.49°, 137.51° and 158.75°. The angles 338.75°, 317.51°, 312.49° and so forth, on your left repeat the set on your right when subtracted from 360°. If we extend the fractal beyond the semicircle and include the quarter circle, the golden section operation generates the additional angles 34.38°, 55.62°, 124.38° and 145.62°. It is not an arbitrary procedure to divide cycles in halves and quarters. Observation shows that spectral peaks can appear at twice and four times the driving frequency, or at half or a quarter of it (Burroughs, 1992). Statistical tests indicate that the twelve golden aspects in the complete set are reliable."

http://plasmaresources.com/ozwx/landscheidt/pdf/TheGoldenSection_ACosmicPrinciple.pdf


Some of the aspects that Dr. Theodor Landscheidt listed are near 144th Harmonic aspects

He was using a 1 degree orb for them. 


34.38° - 14/144 - 35°  aka 7/72

42.49° - 17/144 - 42°30' 

47.51° - 19/144 - 47°30'  

55.62° - 22/144 - 55°  aka 11/72

124.38° - 50/144 - 125°  aka 25/72

132.49° - 53/144 - 132°30' 

137.51° - 55/144 - 137°30'  aka Golden Mean

145.62° - 58/144  - 145°  aka 29/72


360° divided by 1.618 = 222.4969097651422° which rounds off to 222.5°

360° - 222.5° = 137.5° which is close to Dr. Landscheidt's Golden Aspect 137.51°

137.5° is The Golden Angle 


137.5° divided by 1.618 = 84.9814585908529° which rounds off to 85°

137.5° × .618 = 84.975 which rounds off to 85°

137.5° × .382 = 52.525 which rounds off to 52.53


137.5° divided by 2 = 68.75 which is one of Dr. Landscheidt's Golden Aspects
137.5° divided by 4 = 34.374 which is close to Dr. Landscheidt's Golden Aspect 34.38°


360° - 137.5° = 222.5°

222.5° divided by 2 = 111.25° which is one of Dr. Landscheidt's Golden Aspects

222.5° divided by 4 = 55.625° which is close to one of Dr. Landscheidt's Golden Aspect 55.62°


85° is one of the aspects that Dr. Landscheidt mentioned in his article on Geocentric Planetary Nodes and is The Golden Mean of Golden Mean Aspect. He included Golden Aspects as aspects that he used with Geocentric Planetary Nodes. He used a maximum of 1 degree with them.


2 objects in Golden Mean of Golden Mean aspect in Golden Mean to a 3rd object form a 144th Harmonic Isosceles Triangle.


2


85° divided by 2 = 42.5° which is close to Dr. Landscheidt's Golden Aspect 42.49°

85° divided by 4 = 21.25° which is one of the Dr. Landscheidt's Golden Aspects 21.25°


One of Dr. Landscheidt's Golden Aspects 132.49° is very close to the angle of the Euler's number. 

 The number e, also known as Euler's number, is a mathematical constant approximately equal to 2.71828

360° divided by 2.71828 = 132.4366879055874°

132°26'12'' is the Euler's angle. 

https://divergentastrology.blogspot.com/2022/03/the-eulers-aspect.html


One of Theodor Landscheidt's Golden Aspects 47.51° is very close to the Silver Mean-Pi Product 47° 29' 24''

Silver Mean is 2.4142135623

Pi is 3.14159

2.4142135623 × 3.14159 = 7.584469185186057 rounded off to 7.58

360° divided by 7.58 =  47.49 aka 47° 29' 24"


In mathematics, two quantities are in the silver ratio (or silver mean)[1][2] if the ratio of the smaller of those two quantities to the larger quantity is the same as the ratio of the larger quantity to the sum of the smaller quantity and twice the larger quantity (see below). This defines the silver ratio as an irrational mathematical constant, whose value of one plus the square root of 2 is approximately 2.4142135623. Its name is an allusion to the golden ratio; analogously to the way the golden ratio is the limiting ratio of consecutive Fibonacci numbers, the silver ratio is the limiting ratio of consecutive Pell numbers. The silver ratio is denoted by δS.

Mathematicians have studied the silver ratio since the time of the Greeks (although perhaps without giving a special name until recently) because of its connections to the square root of 2, its convergents, square triangular numbers, Pell numbers, octagons and the like.

https://en.wikipedia.org/wiki/Silver_ratio


The number π (/p/; spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. The number π appears in many formulas across mathematics and physics. It is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as 22/7 are commonly used to approximate it. Consequently, its decimal representation never ends, nor enters a permanently repeating pattern. It is a transcendental number, meaning that it cannot be a solution of an equation involving only sums, products, powers, and integers. The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge. The decimal digits of π appear to be randomly distributed,[a] but no proof of this conjecture has been found.



Blog Posts about Golden Aspects
























Divergent Astrology (21st Century Multidimensional Astrology) - The Way I Do Astrology

 The Way I do Astrology I have been studying Astrology since end of June of 1998.  My interest in Astrology as a psychological tool was insp...