Planetary Harmonics | Larry Berg

 

 

» The heavenly motions are nothing but a continuous song for several voices, to be perceived by the intellect, not by the ear; a music which, through discordant tensions, through syncopations and cadenzas as it were, progresses toward certain predesigned six-voiced cadences, and thereby sets landmarks in the immeasureable flow of time. « 

— Johannes Kepler, 1619, The Harmony of the Universe, Book V, Chapter 7. 

 

Reference:
Jeffrey H. Horovitz & Richard Tourtellott (1988) - Planetary Harmonics. An Exclusive Interview with Larry Berg. 

In: Cycles, January/February 1988, Foundation of the Study of Cycles.

 

See also:

Larry Berg (2024) - The Berg Timer™, its History and Calculation.

The Harmony of Being | Geometry in Man, Nature, and Cosmos

Proportional roots: (a) the √2 proportion, (b) the √3 proportion,
and (c) the golden mean (Phi) proportion.

Loai M. Dabbour (2012) - Geometry describes the assertions of a mathematical order of the intrinsic nature of the universe. Geometry is the very basis of our reality, and we live in a coherent world governed by underlying laws. Johannes Kepler stated that geometry is underpinning the cosmos, which was based on Plato’s ideas that God created the universe according to a geometric plan. The structure of the universe is determined by and revealed as certain mathematical and geometric constants which represent a confirmation that proportions are the underlying fabric of nature. This can be seen in man, nature, and cosmos.

Root proportions based on the square.

By contemplating geometric proportions, an understanding towards the sacred truth can be obtained since geometric proportions are one of the definitive geometric qualities of life itself. The Holy Quran tells us that man has within himself all what is reflected in the universe - the best proportions. Man is the core of God’s creatures; he possesses the most harmonious proportions, reflecting of the Divine harmony of being. "We have indeed created man in best of forms" – proportions (Surah At-Tin, 95:4). Leonardo da Vinci illustrated the mathematical proportions of the human body, showing that human being exhibits clearly golden mean proportions in his body based on ratios of 1.618.The Vitruvian Man drawn by Leonardo Da Vinci is based on Vitruvius, who believed that if human proportions could be incorporated into buildings, they would become perfect in their geometry. According to Vitruvius, the distance from fingertip to fingertip should be the same as that from head to toe. The sacred mean rules can be seen in the ratios of body parts throughout the human body. The human body contains in its proportions all the important geometric geodesic measures and functions. The proportions of ideal man are at the center of a circle of invariant cosmic relationships.

Proportions of Venus’ and Earth’s mean orbits.

The mathematical harmony of the universe can be seen from the proportions of the planets in our solar system. For example, the ratio of the sacred mean can be seen in the rotations of Venus and Earth around the Sun in that for each five years that the Earth rotates around the Sun, Venus rotates around it eight times. The connection between 5 and 8, both of which are Fibonacci numbers, is the golden mean proportion (8/5 = 1.6). The result of this motion is that Venus draws a pentagon around the Sun every eight years (Figure A). Figure B shows that a circle is drawn, which represents Venus’ mean orbit. A pentagon is constructed inside it and a small circle placed through the arm-crossing points. The radius of this small circle divides the radius of the large one into golden sections and can be used to space Venus’ orbit from Earth’s orbit. It can be seen from the agreement between eightfold and fivefold geometries that eight touching circles are drawn from Venus’ mean orbit. In turn, the circumference circle is enclosing these eight circles, defining Earth’s mean orbit. The ratio of the mean orbits of Venus’s to Earth is the √2 proportion. The geometric representation of these orbits creates the golden mean proportion.

Harmony of the Spheres | Dance of the Planets

James Ferguson’s (1710-1776) representation of the apparent motion of the Sun, Mercury, and Venus from the Earth, based on similar diagrams by Giovanni Cassini (1625-1712) and  Roger Long (1680-1770). Taken from the "Astronomy" article in the first edition of the Encyclopædia Britannica (1771; Volume 1, Fig. 2 of Plate XL facing page 449). This geocentric diagram shows, from the location of the Earth, the Sun's apparent annual orbit, the orbit of Mercury for 7 years, and the orbit of Venus for 8 years, after which Venus returns to almost the same apparent position in relation to the Earth and Sun. In Arabic, Venus is called “El Zahra” - the flower. See HERE + HERE + HERE + HERE

Earth - Mercury Cycle.
This and all following graphics by John Martineau.

Earth - Venus Cycle:
Earth = 8 years x 365.256 days/year = 2,922.05 days
Venus = 13 years x 224.701 days/year = 2,921.11 days (ie. 99.9%)

Earth - Mars Cycle.

Earth - Jupiter Cycle.

Saturn - Uranus Cycle.

Jupiter - Saturn Cycle.

Venus - Mars Cycle.

The radius of the Moon compared to the Earth's is 3:11

Radius of Moon = 1,080 miles = 3 x 360
Radius of Earth = 3,960 miles = 11 x 360 = 33 x 1 x 2 x 3 x 4 x 5
Radius of Earth plus Radius of Moon = 5,040 miles = 1 x 2 x 3 x 4 x 5 x 6 x 7 = 7 x 8 x 9 x 10
The ratio 3:11 is 27.3%, and the orbit of the Moon takes 27.3 days, which is also the average rotation period of a sunspot. The closest to farthest distance ratio that Venus and Mars each experiences in the Mars-Venus dance is also 3:11. The Earth orbits between them. The sizes of the Moon and the Earth is drawn to scale in the last illustration above, where the perimeters of the dotted square and the dotted circle are of the same length: The perimeter of the dotted red square is 4 x Earth’s diameter = 4 x 7,920 miles = 31,680 miles. The circumference of the dotted blue circle is 2 pi x radius = 2 x 3.142 x 5040 miles = 31,667 miles (ie. 99.9%).

Sun — Earth — Man | In Tune With Cosmic Rhythms

"The unanimous message of mystics of all ages that all entities in the universe are interconnected and constitute an indivisible whole is proven now by unequivocal physical experiments that have been replicated again and again. From this undeniable unity, connectedness, and inseparability follows that any action or configuration in any distant part of the universe can influence processes in the solar system inhabited by man. This is also valid for the interrelations of Sun and planets within the solar system and especially the Earth's connections with other cosmic bodies in the solar environment. 

To look at the solar system and its constituent parts as a whole that embraces a complex web of holistic interrelations, is a premise of traditional astrology, which seemed antiquated, but turns out to be trend-setting. Thus, it appears promising to subject the astrological thesis of an influence of celestial bodies on the Earth and life on its surface to a new test. The quality of the astrological body of theses matches the holistic results of modern research, as it represents the archetype of an integrating science. Astrology of this brand was a historical reality in the era of Kepler, Galileo and Newton. It is well known that Kepler was both an astrologer and one of the creative founders of modern science. Book IV of his principle work Harmonices Mundi (1619) with the heading "Book on Metaphysics, Psychology, and Astrology" is evidence of this, as well as his papers De fundamentis astrologiae certioribus (1602) and De stella nova (1604). Those who pretend that Kepler was not really engaged in astrology should read these writings." 

Theodor Landscheidt - German jurist, mathematician, astronomer, astrologist, and climatologist, in Sun - Earth - Man: A Mesh of Cosmic Oscillations (1988).

Theodor Landscheidt (1989): Mini-Crash in Tune With Cosmic Rhythms.
Solar system instability events and the stock market.
In: Cycles Magazine - Volume 40, Number 6 Nov-Dec, pp. 317-319.

The Same, The Other, And The Essence │ Theology of Arithmetic

“One, two, three [...] Let me tell you then why the creator made this world of generation. He was good [...] He took the three elements of the same, the other, and the essence, and mingled them into one form, compressing by force the reluctant and unsociable nature of the other into the same. When he had mingled them with the essence and out of three made one, he again divided this whole into as many portions as was fitting, each portion being a compound of the same, the other, and the essence. And he proceeded to divide after this manner: 

First of all, he took away one part of the whole [1], and then he separated a second part which was double the first [2], and then he took away a third part which was half as much again as the second and three times as much as the first [3], and then he took a fourth part which was twice as much as the second [4], and a fifth part which was three times the third [9], and a sixth part which was eight times the first [8], and a seventh part which was twenty-seven times the first [27]. After this he filled up the double intervals [1, 2, 4, 8] and the triple [1, 3, 9, 27] cutting off yet other portions from the mixture and placing them in the intervals, so that in each interval there were two kinds of means, the one exceeding and exceeded by equal parts of its extremes [1, 4/3, 2, in which the mean 4/3 is one-third of 1 more than 1, and 1/3 of 2 less than 2], the other being that kind of mean which exceeds and is exceeded by an equal number. Where there were intervals of 3/2 and of 4/3 and of 9/8, made by the connecting terms in the former intervals, he filled up all the intervals of 4/3 with the interval of 9/8, leaving a fraction over; and the interval which this fraction expressed was in the ratio of 256 to 243. And thus the whole mixture out of which he cut these portions was all exhausted by him.

This entire compound he divided lengthways into two parts, which he joined to one another at the center like the letter X, and bent them into a circular form, connecting them with themselves and each other at the point opposite to their original meeting-point; and, comprehending them in a uniform revolution upon the same axis, he made the one the outer and the other the inner circle. Now the motion of the outer circle he called the motion of the same, and the motion of the inner circle the motion of the other or diverse. The motion of the same he carried round by the side to the right, and the motion of the diverse diagonally to the left. And he gave dominion to the motion of the same and like, for that he left single and undivided; but the inner motion he divided in six places and made seven unequal circles having their intervals in ratios of two-and three, three of each, and bade the orbits proceed in a direction opposite to one another; and three [Sun, Mercury, Venus] he made to move with equal swiftness, and the remaining four [Moon, Saturn, Mars, Jupiter] to move with unequal swiftness to the three and to one another, but in due proportion.” Timaeus - Plato (360 BCE)

Johannes Kepler knew that "ubi materia, ibi geometria" (where there is Matter, there is Geometry), and "that the geometrical things have
provided the Creator with the model for decorating the whole world". In Harmonices Mundi (The Harmony of the World, 1619) he related musical
consonance and the angular velocities of the planets, for example, the ratio between Jupiter’s maximum and Mars minimum speed is as 5:24. That
is equivalent to the interval of two octaves plus a minor third. The two octaves are eliminated by dividing 24 with 4, which gives the ratio
of 5:6, a minor third. From his studies of planetary harmonics Kepler also arrived at the bold conclusion that between Jupiter and Mars must
exist an unknown planet: "Intra Jovem et Martem posui planetum." (Between Jupiter and Mars I put a planet.") Some 170 years later the so-called
asteroid belt was found in the corresponding place.