Musical Tones of the Outer Planets

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. 

Figure 1 The harmonic ratios between the nearest two outer planets and the lunar year. The four square rectangle with side length of four, when equal to the lunar year gives, geometrically, the solar year as its diagonal length. The outer planetary synods are longer than the solar year as the planets have moved ahead of their last opposition to the sun. Such oppositions are marked by an outer planet appearing to travel in a loop, amongst the stars

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.

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 Disk of Chronos (

Figure 3 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. For more on that see my Sacred Number and the Origins of Civilization. 25-26.

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.

Figure 4 The natural harmonic context of Jupiter Saturn and the Moon
from ( 

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.

figure 5 The three nearest outer planets cast into a Pentad of Lunar Year. See discussion below.

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.”

quotes  are from  (

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.

3 thoughts on “Musical Tones of the Outer Planets”

  1. In this subject matter, one is easily drawn from the particular to the general. So, please bear with me.
    Newton guessed the dimensions of the Great Pyramid at 440 RC and 280 RC (11/7 base/height ratio). However, there are infinite combinations of integer base and heights which will yield the 11/7 ratio. A very important one is 231/147. Now, one can also look at the ratio 275/175. If there were exactly 231 Meters in the GP base, then 231/275= 0.84 Meter (=33.07 inches). If we multiply by the factor 72/73 (= 360/365), we obtain 0.828493 Meter which I would offer as a candidate for the “Megalithic Yard”. Further, 25*73 = 1825 = 5* 365 Megalithic yards = 1512 Meters, exactly. ….. Now, 1512 = 4*378 = 4 Synodic returns of planet Saturn. Also note that 1825 MY/2.5 = 730 megalithic Rods =2 * 365 =2 Earth Years. Please let me know what you think.
    Best regards, Paul Jones.

    1. Hi Paul,
      Sorry, I do not have time to go through your calculations today.
      You mention synod of Saturn but you have brought metrology into it whereas my point is that days could used to count periods using any measure (and in fact counting lunar months is even better in this case, see below). In Carnac’s Le Manio Quadrilateral 4000 BC, inches were used to count days.
      I know that by the English/late Carnac megalithic 3500 BC, megalithic yards were being used to count months. Saturn is then 12.8 months, Jupiter 13.5 months exactly and lunar year 12 months; same ratios as in figure 1.

      12.8/12 = 16/15 and 13.5/12 = 9/8.

      Since a MY has 40 megalithic inches then the units are 1/10th of a month or 4 MI.
      Please see my The Harmonic Origins of the World especially chapter 1: Climbing the Harmonic Mountain.
      Best Wishes, Richard

    2. I can now get to the other part of your message, concerning 11/7.
      John Michell’s diagram of the earth is based on two circles ratio 11 to 14. It allows us to see the Earth Moon as 11 to 3 in diameter and Pyramid as 11 base and 7 height. John also opened up the Pandora’s Box of fractal numbers based upon the first 12 numbers, in a diagram simple enough for any claimed limits to early geometry and numeracy. In metrology units are routinely obtaining and losing 11/7 in their rational fractions through the microvariations (176/175 & 441/440) of different foot modules but here you are commenting on how 11/7 adjacency exists between numbers and measures. There are many strange correlations such as the PI of 820/261 when the moon’s orbit resonates with 27.321 x 3 = 82 days and the Carnac MY = 261/8 enabling 8 MY in radius lay out a circumference of 82 stones. This work is both divergence, finding correlations, but also convergent, finding the meaning of them in terms of their likely historical development and cultural significance. Because of this, workers tend to become overwhelmed with data without a historical or theoretical perspective – which is the strong convergent feature found in traditional interpretations of monuments but then to the exclusion of numerology, metrology, geometry and even astronomy. Best Regards, Richard

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