Readers of my article Lunar Counting from Crucuno Dolmen to its Rectangle will be familiar with the finding that in 32 lunar months there are almost exactly 945 days, leading to the incredibly accurate approximation (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 leads to some 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 tone 9/8, the same tone that on "holy mountains" of Ernest G. McClain's ancient tuning theory, are only found between two tonal numbers separated horizontally 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.

If the matrix unit is one tenth of the lunar month, then three lunar years become 360 units which, taken to be do^{2} = D'' = the harmonic limiting number, which presents the matrix in figure 1.

*Figure 1 The Harmonic Matrix for 360 = 36 months, showing that the 32 lunar month period of 945 days starts the second row as harmonic number 320. Screen grabbed from my online app Harmonic Explorer for Ernest McClain's tuning mountains*

This matrix, being two dimensional, has to be read in one dimensional ways:

- The number 320 in the matrix is the 32 lunar month period whilst in between lies two lunar years as G=240.
- To the right of D = 360 lies 270 which is two Jupiter synods taking 27 lunar months.
- Saturn is the bottom left "cornerstone" of a-flat = 256: again lasting for two of it's synods of 12.8 lunar months.
- On top of the matrix is a periodicity of 25 lunar months during which exactly two synods of Uranus equal to 12.5 lunar months, complete.

The 32 month period is therefore a crucial part of the planetary matrix relating to two lunar years (240) and in each case, two synods of all the visible outer planets (250, 256, 270).

*Figure 2 Clarity of Musical Intervals when viewed counting tenths of a lunar month rather than 1/80ths, shows that all the white bricks are harmonically locked in a single system.*

The 36-month period, normally seen as 18 lunar months relative to the lunar year, figures in the day-counted lengths at Le Manio's Quadrilateral along its southern kerb, in which the 32nd stone from the start of counting is 945 day-inches from the start.

This could well be the esoteric significance of the 360 "schematic year" used as the primary exemplar of Plato's approach to tuning as in "360 days and nights", then equalling 720 as highest bounding note of the octave.

And this counting of months instead of days generates a parallel and simplified matrix approach, as it also did when day-inch counting was replaced by counting months using megalithic yards in the counted lengths. One can directly read the periodicities and work out the intervals, avoiding any significant arithmetic. This can only happen because, on the one hand, the relationships between the solar and lunar year are dominated by the numbers 7, 12 and 19; because the Metonic period completes in 19 solar years having completed 7 extra lunar months over 19 lunar years of 12 months. On the other hand, in the remarkably harmonic world as it has emerged, the lunar years are the lynch-pin and the outer planetary synods are sources of pure musical ratios relative to the lunar year; these embodying very small integer fractions such as 9/8 (Jupiter), 16/15 (Saturn) and 25/24 (Uranus). In this respect, the lunar month in decimal fraction has become the natural matrix unit.

Harmonically, 32 lunar months must occupy the location shown, relative to 36 lunar months, since these numbers forever 36/32 = 9/8 apart. What is not such a requirement is that the solar day (a.k.a. the rotation of the Earth between sunrises) should be of such a duration as to complete exactly 945 days in 32 lunar months. Removing the factor 7 from 945 one arrives at 135 days, the same number as tenths of lunar orbit in the Jupiter synod since (a) there is a minor third between E and A in figure 2 and 135 days equals 32/7 lunar months.

This shows that the rotation of the Earth, in its solar day, is adapted to the resonant environment of the lunar year and its month. The same thing is found between G=240 and the "just appeared", bottom right brick of 3^{5} = 243. These two numbers reduce to 80/81, the synodic comma, which the ratio between the lunar month and 30 sidereal days, which I have called the sidereal month.

In the Bible's harmonic code, ABRAM = 243 whilst Adam (ADM) = 45 which doubled three times equals 360. The reader will need to reference *Harmonic Origins of the World* to appreciate the fuller picture from which this work derives. Ernest McClain's tuning mountains were evidently close, if not identical, to those used in the ancient world to preserve knowledge of this system in the life of the people through stories, and the celestial components first gleaned by megalithic astronomers, as seen at Carnac, must have established the notion of separating the powers of three and five into two separate dimensions in order to resolve the synodic world of time in mountains of harmonic "brick" numbers.