The 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 norm for "harmonies of the spheres" (a.k.a. Musica Universalis) that are geometrical and spatial rather than temporal.
My aim here is to prepare supporting material for my book, published towards the end of 2017, called The Harmonic Origins of the World, this by reviewing how these synodic periods were parts of my previous work from c. 2000, using "matrix diagrams". I will show (in my new book)how ancient tuning theory seems to have presented the same information. To avoid spilling all the beans I am now connecting the outer planets in a different (and useful) kind of diagram called the Pentad, evolved in the 20th century within Systematics (more on that in previous article).
Figure 1 The harmonic ratios between the nearest two outer planets and the lunar year
The four square rectangle with side eaqual lunar year gives, geometrically, the
solar year as diagonal length. The outer planetary synods are longer since
the planets have moved ahead of their last opposition to the sun, when
they appear to travel in a loop amongst the stars
This emerged in two stages. 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.
figure 2/ 9.5 of MOC. My original form of matrix diagram here of the whole tone between Lunar Year and Jupiter Synod.
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, also see Sacred Number and the Origins of Civilization 24-27.).
Figure 2 The Disk of Chronos has an inner ring of fifteen holes which would enable counting of the 4/5 lunar month periods which divide into the Saturn synod
The idea of counting time completed itself in Sacred Number and the Lords of Time as being the missing means by which the Megalithic astronomers could have developed an advanced and unexpected view of time periods as connecting to the gods, as planets then "Lords of Time". This allowed the book Lords of Time to layout a megalithic science, history. Harmonic Origins combines that and Ernest G. McClain's ancient tuning theory (also diagrammatic) to return to this matter of harmony as expressed by planetary and other periods, seen from Earth. McClain's first book, Myth of Invariance, can be read in pdf using the link at http://www.ernestmcclain.net/.
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. 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 1 above that the octave context is nine to eighteen lunar months, in the new scale 90 to 180. using a "holy mountain" in the style of McClain (probably similar to those formed by specialists in the ancient world), the LIMIT D=180 units then embraces the lunar year = 120, the Jupiter synod = 135 and the Saturn synod = 128 as shown in figure 3.
Figure 3 The natural harmonic context of Jupiter Saturn and the Moon
(image is from http://harmonicexplorer.org app created for Ernest G. McClain)
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.
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. Being directly above the lunar year, 125 divided by 120 reduces to 25/24, the chromatic semitone. This information can then be recast into a systematics pentad as per figure 4.
figure 4 The three nearest outer planets cast into a Pentad of Lunar Year.
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."
[blockquotes from http://www.systematics.org/pmwiki/pmwiki.php?n=Main.Pentad
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 "highest end" served by the lunar year is then to be harmonious to the outer planets; is the inference. This might indicate that Systematics applied 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. Systematics appears to apply the analytic structuralism and toxonomy of recent centuries upon a very limited set of terms, so as to recognise (within diversity) a smaller structure of meaning based upon the early numbers one to twelve. In this sense, Systematics is modern whilst being similar to an ancient number science which constrained number to the smallest possible in the service of astronomy, measure, geometry and music (the traditional arts).