My crucial entré to planetary harmony came when I noticed musical ratios in the synodic time periods of Jupiter and Saturn relative to the lunar year. This approach differs from the norms for “harmonies of the spheres” (a.k.a. Musica Universalis) which are geometrical and spatial, rather than temporally harmonic.
The planetary harmony I found within synodic periods became the subject of my new book The Harmonic Origins of the World (pub. 2018). These synodic ratios have been parts of my work from c. 2000, then expressed as “matrix diagrams” (Matrix of Creation, figure 2 below). In my new book, I show how ancient tuning theory seems to have presented the same information, in a different type of matrix (see figure 4).
Below I connect the outer planets using two additional (and useful) kinds of diagram, the right-angled triangle (figure 1) and the Pentad (figure 5), the latter developed in the 20th century within a discipline called Systematics.
How Planetary Harmony was Discovered
There are four main time periods relevant to the ancient discovery of musical intervals within celestial time periods as per figure 1. The ratio of the solar year (of 365.2422 days) to the lunar year (of 354.367 days of 12 months each of 29.53059 days) is not musical but was essentially how the megalithic developed their techniques of counting days using constant unite of length and building a right angled triangle when comparing two counted lengths. This ratio is shown in figure 1. geometrically it exactly fits the side and diagonal of a four-square rectangle, also shown, enabling that ratio’s creation without any counting. This multi-square rectangle fitted perfectly the use of one, two and three – square rectangle ratios, for horizon alignment and eclipse prediction, at Carnac, in present-day Brittany where the sun rises at solstice according to the diagonal of a four by three rectangle (the 3-4-5 triangle)[see my Sacred Number and the Lords of Time book, chapter two The Transmission of the Squares].
In Matrix of Creation (MOC) there was a matrix diagram of the Moon and Jupiter with tone ratio 8:9 (see MOC’s figure 9.5 below).The tone is held between ascending and descending fourths as in Plato’s World Soul, with a shared unit of one and a half lunar months and an octave of 9 to 18 lunar months. The two periods “exhaust” themselves within the frame of 108 lunar months.
Then I found a disc on Crete c.2004 in the Heraklion Museum which appeared to use the Moon’s 15:16 semitone relationship to Saturn in its calendrical counting (Article at Academia.edu: Disk of Chronos (https://www.academia.edu/27390624/A_Minoan_Calendar_of_Bronze_Age_Time).
This idea, that the megalithic were counting time to create their astronomy, completed itself in Sacred Number and the Lords of Time. Day counting has been an overlooked potential by which the Megalithic astronomers could have developed an advanced an unexpected view of time periods, then potentially connecting to the gods as planets, the “Lords of Time”. This allowed the book Lords of Time to layout a megalithic science, history. Harmonic Origins connected this to Ernest G. McClain’s ancient tuning theory (also diagrammatic) to then return to this matter of harmony as being expressed by planetary and other periods seen from the Earth, that is via the natural and equally valid geocentric perspective.
Mapping Planetary Harmony onto Ernest G McClain’s Matrices
The units of the two musical tones, of Jupiter and Saturn synods relative the lunar year, can be seen in their fractional parts, in lunar months. The Jupiter synod is 13.5 months and Saturn’s is 12.8 months. One can then look for a common denominator of one tenth of a month and use this to scale them to become integers 135 and 128. We have already seen from figure 2 above that the octave context is nine to eighteen lunar months, in the new scale 90 to 180 units, each a tenth of a lunar month long, using a “holy mountain” in the style of McClain (probably similar to those formed by specialists in the ancient near eastern world), the limiting number is high D of 180 units, embracing the lunar year = 120, the Jupiter synod = 135 and the Saturn synod = 128 as shown in figure 3.
All of the above numerical “bricks” of this holy mountain are calibrated as frequencies in units of one tenth of a lunar month. Saturn is a-flat and Jupiter is A relative to the D = limit and limit/2, whilst the lunar year is G (within the Dorian scale).
As a “proof of concept” for this approach, the brick at the top = 125 is 12.5 lunar months and 12.5 x 29.53 = 369.13 days, which is one part in 700 less than 369.66, the synod of the next outer planet, Uranus. Being directly above the lunar year, 125 divided by 120 reduces to 25/24, the chromatic semitone.
Interpreting the Pentad
These relationships can be recast into a Systematics pentad, with five terms, as per figure 4.
The solar year is the master of the lunar year and the solar day provides nourishment (perhaps through tides).
“An entity has meaning in its own right. This gives it an unique character and an inner and outer range of significance. Nothing less is sufficient for an independent structure. The inner range of significance includes the potentialities of the entity and partly stems from the nature or kind of entity and partly from its history. Any real thing is potentially more than it ever actually is. This is true of situations as well as of entities such as a man.”
The lunar month (and orbit) is the lower nature of the lunar year whilst the harmonies to the outer planets are the lunar year’s higher nature, forming a dyad of the lunar year’s inner significance.
“Inner significance is confined within limits; the lower limit is in its bare requirements as a particular nature; the higher limit is in the highest degree of self-realization possible for it.”
The solar year and solar day form the range of the lunar year’s outer significance, that is it’s belonging to the solar system but only as a satellite of the Earth.
The range of outer significance stems from the connections every entity has with its world; that is, from its range of significant action. The master is the highest end served by the entity; the nourishment is that which the entity needs in order to maintain its own identity.
The inference is that, the “highest end” served by the lunar year is to be harmonious to the outer planets. This application of Systematics to astronomical time periods reveals levels of meanings not available in calculations or geometries of other sorts. Sacred geometries function as statements of structural significance and these become iconic / symbolic but very often the meanings of a sacred image becomes lost knowledge.
Systematics was developed from the analytic structuralism and toxonomies of recent centuries, where a very limited set of terms or factors are generated to recognise (within diversity) a smaller structure of meaning based upon the early numbers which do not exceed the human grasp. Whilst Systematics is modern, it seems compatible to an ancient number science which constrained number to the smallest possible in the service of astronomy, measure, geometry and music (the traditional arts).
The outer planets were found to be harmonic with the moon after the megalithic had developed the means to compare day counts using triangular geometries. This knowledge developed the ancient idea that the planets were gods from which religious ideas developed. In time the true origins of religion were lost. Heliocentric ideas displaced the remarkably persistent Classical doctrine of a harmony of the spheres (the geocentric planets) and then, the methodology of counting time was displaced by the Enlightenment’s scientific astronomy of space, under gravitational, not harmonic, principles.