Author: Richard Heath

Planetary Resonances with the Moon

Readers of my article [post2post id=”327″] will be familiar with the finding that in 32 lunar months there are almost exactly 945 days, leading to the incredibly accurate proximation (one part in 45000!) for the lunar month of 945/32 = 29.53125 days.

In the previous article on Seascale I noticed that 36 lunar months (three solar years) divided by 32 lunar months is the Pythagorean tone of 9/8. This led me to important thoughts regarding the tuning matrix of the Moon within the periods of the three outer planets, since the synod of Jupiter divided by the lunar year of 12 lunar months is the same tone, the tone that on “holy mountains” of Ernest G. McClain’s ancient tuning theory. Such tones are only found between two tonal numbers separated by two perfect fifths of 3/2, since 3/2 x 3/2 = 2.25 which, normalised to the octave of 1 to 2, is 1.125 or 9/8.


Figure 1 If the matrix unit is one tenth of the lunar month, then three lunar years becomes 360 units which, taken to be high do or D” = the harmonic limiting number, presents the matrix above, in the style proposed as indicative of Ancient Tuning Theory by Ernest McClain (see his The Myth of Invariance).  This Harmonic Matrix for 360 = 36 months shows that the 32 lunar month period starts row 2 as 320.
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Equal Temperament through Geometry and Metrology

The form of musical scale we use today is the (apparently modern) equal tempered scale. Its capabilities express well the new mind’s freedom of movement in that it allows us to change key to play compositions that move between alternative frameworks. This possibility was known to ancient tuning theory, could be approximated within Just intonation’s chromatic notes and was discussed by Plato as forming the constitution of one of his harmonic city states called Magnesia.

Relationship of the Equal Temperament Keyboard to the (logarithmic base-2) tone circle of an octave. We choose D (the Dorian scale) because it is symmetrical on both keyboard and tone circle. Equal Temperament supplies tones which enable any scale to be played starting from any note, though it is the Ionian (C-major) which defines modern key signatures.
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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
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