The Values Values of Solfeggio Counts in Lo Shu, in Central Addition’s of Contracted Integers. Paul Martyn-Smith. 2012/2013. +1234 5 6789 Central Values in +3s = 36, + 6s = 63 Base. The Solfeggio Counts of + 111 give 3 repeating numbers = + 3s and + 6s, but +1s +8s = 9s, as in +2s +7s, 72, 45, 54 but they do this in the ascending and descending values such as 12 + 87, all = 99 bases. 714 417 = 222s 147 174 = 222s 825 528 = 444s 258 285 = 444s 936 639 = 666s 369 396 = 666s 147 741 = 888s 471 417 = 888s 258 852 = 1110s Cn 582 528 = 1110s Cn 369 963 = 333s 693 639 = 333s 471 174 = 555s 714 741 = 555s 582 285 = 777s 825 852 = 777s 693 396 = 999s. 936 963 = 999s 693 + 417 = 1110, 396 + 714 = 1110111. 147 + 963 and 174 + 936 = 1110111 When these values are placed into the +5 to +4 Contracted Integer runs the value = 111, 222, 333, 444, to 999 so pairs = 10s through central 5s. +3s +6s +5 Central run. +4s +5s = 5 C run 258 852 = 11 111s 1s 159 951 = 6s = 11 111 1 714 417 = 222s 615 516 = 3s = 222 369 963 = 333s 261 162 = 9s = 333 825 528 = 444s 726 627 = 6s = 444 471 174 = 555s c 372 273 = 3s = 555 c 639 936 = 666s 837 738 = 9s = 666 582 285 = 777s 483 384 = 6s = 777 147 741 = 888s 948 849 = 3s = 888 693 396 = 999s 594 495 = 9s = 999 +1to +8s +2s + 7s 123 321 135 531 234 432 246 642 345 543 357 753 456 654 468 864 567 765 579 975 678 876 681 186 789 987 792 297 891 198 813 318 912 219 924 429 123 198 +1/+8s 234 219 345 321 456 432 567 543 = 111 678 654 789 765 891 876 912 987
+1 to +8 +8 = 5 to 4s central run. and then +1 (10s)s (10s)s central central run. 456 654 = 111 3 - 912 219 = 222 912 219 = 222 6 -123 321 = 444 567 756 = 333 9 -234 432 = 666 123 321 = 444 3 -345 543 = 888 678 876 = 555 6 -456 654 = 1110 567 756 = 666 9 -567 765 = 333 789 987 = 777 3 -678 876 = 555 345 543 = 888 6 -789 987 = 777 891 198 = 999 9 -891 198 = 999 all opposites opposit es = 10s = 111011 10111. 1. 123 321 Central +2 to 7s. 24681357 9 345 543 567 756 789 987 912 219 = 222s 234 432 456 654 678 876 891 198
All of the 8 Spoke values in Lo Shu are central 5, which as reversals = + 4s, so all the values make 9s, as +9 always produces the same value in Contracted Integers = 111s, 222s, 333s, 444s to 999s pairing = 10s. In the Lo Shu the total of the opposite pairings = 11101 1011 11 ( = +10s + central 5 = 15) but only the 8 Spoke values produce +1s to +8s, +2 to +7, 36, and 45s. The same set of values as found in ‘The Well’ and ‘Bagua’ appear in all the 3 x 3 Magic Squares found in ‘The Chinese Book of Changes’. 492 357 816 159 to 951 = + 4s to +5s. 258 to 852 = + 3s to +6s. 357 to 753 = +2s to +7s. 456 to 654 = +1s to +8s. As with 12345678 9 12345678 the placement of central value runs = 24681357 = 9 24681357, 48372615 9 48372615 = opposites = 9s in each direction = 18, 81, 27, 72, 45 and 54 (also = 99), and each can create 8 x 8 Magic Squares with a match to the binary expansion of Trigrams = 6s, 12, 18, 24, (30), 36, 42, 48, 54 = (1234 5 6789) = 60. 3s, 6s and 9s are the products as also seen in Fibonacci Pairings. +3s and +6s recur every 4th letter or number = 147, 174, 147147 and 174174 as repeating values, but as with all the values = 9s the sequence is ascending and descending = 222s, and the values 1 to 8, 2 to 7 and 4 to 5 have ascending and descending values in their contracted integer runs stating with 1,2,3,4,5,6,7,8, 9. In this the +1 = 1234[5]6789 ascending is matched to +8s descending = 8765[4]3219, so sequences = 9s. +1s central +5 has a value of 1110s, and 8 has a value of 333s with a central value of 666s. 198 765 432 etc., gives the triplets of +8s and the match of +1 = 123 + 198 = 321, so the pairings of reversals appear naturally as 123 to 321 in 1 to 8. 198 or 891 appear as the central values and in the t he binary count, this = 44 (45) 46 (C45 to 90 = the total within central value of Magic Square) or 210 (270) 330 = 540 = 810. Lee Burton and I had investigated the form of the Lo Shu to give 90 as pairs in all directions.
1234 5 6789 = 10 = 60 2345 6 7891 = 30 = 180 3456 7 8912 = 50 = 300 4567 8 9123 = 70 = 420 5678 [9] 1234 = 90 = 540 6789 1 2345 = 20 = 120 7891 2 3456 = 40 = 240 8912 3 4567 = 60 = 360 9123 4 5678 = 80 = 480 Opposites = 9 = 360 and 540 = 900. [990 = 2700] All cross-over values in 9 x 9 = 9s but pairings = 10s that in the Images of Heaven and Earth, and also the 8 Trigrams = 1 to 89 of 9 x 9 = 90 or 540 (central = 270) in 6s, and 315 to 630 in +7s (585 and 1117). The value’s of The Nine stack is each derived from the 8 x 8 squares of the Ho Tu and the pattern of the Ho Tu was + 5s = 1 to 6, 2 to 7, 3 to 8 and 4 to 9 which produces value of central 5 = 45 x 6 = 270 x 8 = 2160 in the Trigrams and Hexagrams that then = 10s - this increasing set of value’s + 111 = the average Solar Sun Spot Cycle increase = 11.1 yrs.
The values are given as 6s and 7s and so we can now look at the values of both that when joined reflect the t he Mayan System of + 13s = 585 and 1117 1117 (Venus value = 584 and 116.8). The + 7 Magic Square = 9 x 9 produces a value = 1 to 89 of 14 = 1260, so the value’s of 6s and 7s can be added together to = 1260 + 540 = 1800 or in the Hexagrams the value = 2520 + 1080 = 3600.
This ties the 3 x 3 of the Lo Shu completely to ‘The Well’ and ‘Bagua’, and in the Binary form of the Bagua it produces all the value’s of Time and Degrees of Space as given in the Direction’s or Element’s of the Ho Tu in +5s and it’s totals = +10s. The Image’s of Heaven and Earth (the 2 complete Binary Opposites of Ch’ien and K’un) produce all the 8 Trigrams, and then the 64 Hexagrams in the 8 x 8 Magic Square = all derived from the 9 x 9 = a Metric Expansion when 1 + 9 = 10s etc. The Math of ‘The Book of Changes’ is therefore complete in both contracted and expanded integers. The values in the 9 x 9 can apply to the 1 to 8 Trigrams and the Images of Heaven and Earth in the Ho Tu (C5 to 10).
The work of Lee Burton has also shown how this Lo Shu math fits into Rodin’s Torus in the opposites of the Solfeggio values, so we both can now put this math in our own way (as a unified whole) and put it forward for consideration. Drawing done by Lee Burton on Lo Shu’s = 90 opposites and contracted integer runs. Also see section Solfeggio Expansions.
The sum of the binary gained through a placement of Hexagrams into 8 x 8 = 6480 in each of the directions, this gives 12,960 light to 12,960 dark numbers in odd to even integers. The whole termed as Tones in Solfeggio are just patterns in the structure of integers and so the math is simple. The values given in the integer runs = each level as they climb up to the 9 x 9 or Nine Stack so the values above are found in i n the value from each of the central values of 5 and the pairings of 1 to 9 = 10s. This shows how the values can be related on many levels with a specific pointer toward both 5 and 9 as central values. This is because the average of all values = 5 and 9 is the produce and the directions toward this structure in integers is given in the I Ching. The I Ching appears to have many levels in the math that includes all central values and from the pairings in 3 x 3 Square upward, but to gain the value’s of Time and Measure, directions given in The River Maps must be followed. The 1 to 8s from nothing = 12345678 9 12345678 or its reversal. From 1 the + 8s = 198 765 432, and from 2 = 219876543, so again all + 1110 values found in the Lo Shu Magic Squares can be manufactured in 1 to 8, 2 to 7 and 4 to 5, and = 3s, 6s and 9s. 6s. 123 4[5]6 789 198 7[6]5 432 9s 432 9s and these can be placed into a symmetrical order. 9s. 234 5[6]7 5[6]7 891 219 8[7]6 5 543 43 3s 3s. 345 6[7]8 6[7]8 912 321 9[8]7 6 654 54 6s 6s. 456 7[8]9 7[8]9 123 432 1[9]8 7 765 65 9s 9s. 567 8[9] 8[9]1 1 234 543 2[1 2[1]9 876 3s (C9 (C9 = 45 or 270 + 60 = 330.) 3s. 678 9[1]2 9[1]2 345 654 3[2]1 9 987 87 6s 6s. 789 1[2]3 1[2]3 456 765 4[3]2 1 198 98 9s 9s. 891 2[3]4 2[3]4 567 876 5[4]3 2 219 19 3s 3s. 912 3[4]5 678 987 6[5]4 321 6s 321 6s 198 7[6]5 432 123 4[5]6 789 Contracted Integer 1 to 8s = 10s = 1111111110111111111. 678 9[1]2 345 543 2[1]9 2[1]9 876 = 1-8 Reflection 789 1[2]3 456 654 3[2]1 3[2]1 987 891 2[3]4 567 765 4[3]2 4[3]2 198 912 3[4]5 678 876 5[4]3 5[4]3 219 123 4[5]6 789 987 6[5]4 6[5]4 321 234 5[6]7 891 198 7[6]5 7[6]5 432 345 6[7]8 912 219 8[7]6 8[7]6 543 456 7[8]9 123 321 9[8]7 9[8]7 654 567 8[9]1 234 432 1[9]8 1[9]8 765 + 765 + ------------------ X ----------------543 2[1]9 876 678 9[1]2 9[1]2 345 = 345 = All Al l = 10s 1 0s = 11 1111 1111 1111 1110 1011 1111 1111 1111 111. 1. ------------------ ----------------Zero is a clear division = integer = 9s. When placed into the binary x6 counts the central = 5s = Contracted Integer run +5s in +1s and + 8s: 123 4[5]6 789 987 6[5]4 321 = 111, 111, 111. 123 456 789 678 9[1]2 345 543 2[1]9 876 = 222, 222, 222. 987 654 321 234 5[6]7 891 198 7[6]5 432 = 333, 333, 333. 1110 1110 1110 789 1[2]3 456 654 3[2]1 987 = 444, 444, 444. 345 6[7]8 912 X 219 8[7]6 543 = C555, 555, 555. 891 2[3]4 567 765 4[3]2 198 = 666, 666, 666. 456 7[8]9 123 321 9[8]7 654 = 777, 777, 777. 912 3[4]5 678 876 5[4]3 219 = 888, 888, 888. 567 8[9]1 234 432 1[9]8 765 = 999, 999, 999. 987 6[5]4 321 123 4[5]6 789 = 555 555 555s
These all opposites +5s = 9 x 9 or a 18 x 18 Magic Square of Hexagrams excluding central value as reflective opposites of integer and binary values = pairs = 10s + 5s = 3s,6s,9s. 6, 6, 6, 6, 6, 6. or 987 + 219 + 432 = 639. 654 + 876 + 198 = 639 3, 3, 3, 3, 3, 3. 321 + 543 + 765 = 639 = 15s. 9, 9, 9, 9, 9, 9. 543 + 219 + 876 = 639 etc etc by placing 1 to 9 + C5, and 2 + 7 + C5. 6, 6, 6, 6, 6, 6. 3, 3, 3, 3, 3, 3. 9, 9, 9, 9, 9, 9. 6, 6, 6, 6, 6, 6. 3, 3, 3, 3, 3, 3. 9, 9, 9, 9, 9, 9. All opposites = 5s = 30 (3). 5 and 3 is the key given in I Ching. In the addition of each set of 3 values of +111s the opposites = 6s.
The values of 1 to 8, 2 to 7, 3 to 6 and 2 to 7 in the Magic Square’s of Hexagrams can be reversed so 12345678 in the Ho Tu 1 to 6, 2 to 7 become opposites in both the Binary Images and Integer Values in the 8 x 8 Magic Squares. Only 3s and 6s don’t provide 8 values = 9s as opposites as they only give what has been termed as the Solfeggio counts. The Solfeg can be investigated to see what symmetry they give, and as an example of this the Contracted Runs of 2 to 7 can be placed either left, right or as central counts to provide a 9 x 9 Magic Square in the order of +2s = base = 24, 135, and then in 2s and 7s = 186: L 246 468 681 813 135 357 579 792 924
C R (+3) 924 (3) 792 (+3) 246 (3) 924 (+3) 468 (3) 246 (+3) 681 (3) 468 (+3) 813 (3) 681 (+3) 135 (3) 813 (+3) 357 (3) 135 (+3) 579 (3) 357 (+3) 792 (3) 579
L C R 579 35 357 13 135 135 81 813 68 681 681 468 246 246 924 792 792 579 357 357 135 813 813 681 468 468 246 924 924 79 792 57 579
L 792 579 357 135 813 681 468 246 924
C (3) 579 (3) 357 (3) 135 (3) 813 (3) 681 (3) 468 (3) 246 (3) 924 (3) 792
R (3) 357 (3) 135 (3) 813 (3) 681 (3) 468 (3) 246 (3) 924 (3) 792 (3) 579 9 x 9 = 222s and 777s
L C R = +2s = 135 and +7s = 186 in Contracted Contracte d + 5s: 531 753 975 = 111s (Reflective's (Reflecti ve's = 579357135 531753975 = 1111s etc.) 186 318 531 = 222s 642 864 186 = 333s 297 429 297 429 642 = 444s 753 975 753 975 297 = 555s 318 531 318 531 753 = 666s 864 186 318 = 777s 429 642 864 = 888s 975 297 429 = 999s = 9 x 9 = 555 555 555s.
The 9 x 9 in +2s = 135 in +2s and + 7s = 186 give = 2s and 7s symmetrical opposites plus reversals in +5s Con Integ Run = 5s. Now values +5s and +4s: L C R 516 95 951 49 495 162 516 162 516 951 627 162 516 273 627 162 738 273 627 384 738 273 849 384 738 495 849 384 951 495 951 495 849
L C R = +5s = 162 and +4s = 159 = Con Integ +5s: 594 15 159 61 615 = 111s 111s (Reflective’s (Refle ctive’s = 516951495 516951 495 594 594159615 159615 = 1111s) 159 615 159 615 261 = 222s (Values +5s cross-over = C+4s, and 4s to C5s) 615 26 261 72 726 = 333s 261 726 372 = 444s 726 372 837 = C555s 372 837 483 = 666s 837 483 948 = 777s 483 948 594 = 888s 948 594 159 = 999s (+5s (+5s 516 951 495 = +4s - +4s = +5s 594 159 615 etc.)
The values all follow the same doubling pattern as the Trigrams the values are all +6s. The totals of 2700, 3600, 5400 and 6300 appear, and the contracted integer/solfeg sequences are all symmetrical throughout their combinations. This part of the math needs further investigation by reader to complete it, but the other part’s of math have already been proven to give exact figures in the 3 x 3, 8 x 8 and 9 x 9 etc, which produces the Metric Expansion and the pairing between 5 and 10 = 15 to infinity. This math has already been published in the two books of ‘The Sum of Things’ and ‘The Book of Divine Revelations’.
The way has been found to place the contracted integer pairs together in 1 to 8, 2 to 7, 4 to 5 to create Magic Squares 8 x 8, but in the Solfeg all values can be treated as above to complete a 9 x 9 in each of the values, but the central value in each is excluded in the 1 to 8 to give a value of time in 4 - 4 x 4 squares. As yet I’ve not been through all the sequence values and totals - but there appears to be an underlying code in the +111s just as there was found to be in the 1 to 6, 2 to 7, 3 to 8 and 4 to 9, which then produced the central 5th Element of 5 to 10 in the Ho Tu and then they produce the Lo Shu. 1s to 8s. 123 198 234 219 345 321 456 432 567 543 678 654 789 765 891 876 912 987 (333 X 888)
= 222 = 444 = 666 = 888 = 111 = 333 = 555 = 777 = 999
C5s = 1 to 8s. 456 654 = 11 111 1 912 219 = 222 567 765 = 333 123 321 = 444 678 876 = 555 234 432 = 666 789 987 = 777 345 543 = 888 891 198 = 999
C5 = 2 to 7s. C5 = 3 to 6s. C5 = 4 to 5. 357 753 = 11 111 1 258 852 = 11 111 1 159 951 = 11 111. 1. 813 318 = 222 714 417 = 222 615 516 = 222. 468 864 = 333 369 963 = 333 261 162 = 333. 924 429 = 444 825 528 = 444 726 627 = 444. 579 975 = 555 471 174 = 555 372 273 = 555. 135 531 = 666 936 639 = 666 837 738 = 666. 681 186 = 777 582 285 = 777 483 384 = 777. 246 642 = 888 147 741 = 888 948 849 = 888. 792 297 = 999 693 396 = 999 594 495 = 999.
(555 X 555)
(555 X 555)
(555 X 555)
(C5s to C4s in 1s to 8s). 456 543 = 999.(297s) 912 987 = 999. 567 432 = 999. 123 876 = 999. 678 321 = 999. 234 765 = 999. 789 219 = 999. 345 654 = 999. 891 198 = 999.
(C2s to C7s in 1 to 8s). 123 876 = 999. (297s) 345 654 = 999. 567 432 = 999. 789 219 = 999. 912 987 = 999. 234 765 = 999. 456 543 = 999. 678 321 = 999. 891 198 = 999.
(555 X 444)
(222 X 777)
(555 X 555)
(C5s to C4s = 3 to 6s). 147 852 = 999. (693s) (693s) 582 417 = 999. 936 963 = 999. 471 528 = 999. 825 174 = 999. 369 639 = 999. 714 285 = 999. 258 741 = 999. 693 396 = 999.
(C2 to C7 = 3/6s). (C1-C8s =3s/6s) 825 174 = 999. 999. (693s) (693s) 714 285 = 999. (693s) 147 852 = 999. 825 174 = 999. 369 639 = 999. 936 963 = 999. 582 417 = 999 147 852 = 999. 714 285 = 999. 258 741 = 999. 936 963 = 999. 369 639 = 999. 258 741 = 999. 471 528 = 999. 471 528 = 999. 582 417 = 999. 693 396 = 999. 693 396 = 999.
(444 X 555)
(222 X 777)
(111 (111 X 888)
This defines there’s a pattern but it needs investigating in both 9 x 9 Squares of 6s and 7s , as both are added together to then = 13, 26, 52 of the Mayan system, which appears in the structure of the binary images perfectly linked to the Chinese System. The common value of +6s and +7s = 1260 (the value of 7s in the 9 x 9), and the value of 2520 was used in the Buddhist System, and it was the period of time given between Buddhas - in this count we passed the 2520 yrs until the expected return of a Buddha in the 1980s, so if the Buddha’s statement is to be fulfilled then the time has arrived and already upon us. The
value of 1260 x 2 = 2520 appears as a cycle of Returning (of wisdom) through the arising of knowledge from the universal source, or a re-understanding of the Law or Dharma in Buddhist Texts when the source returns from within rising into consciousness. The value of 2520 = 7 x 360 and 6 x 420 (2520 x 2 = Plato’s 5040). The value of 780 x 6 = 4680, and this same value value is found in the 9 x 9, and then the 9 x 9 also gives = + 4320 as its products in the Hexagram’s single value in the Lo Shu - 4320 + 4680 = 9000. The value’s of 7s in the 9 x 9 Magic Square gives a union of the Chinese txts to various system used from ancient times, especially the Mayan in the use of 13s. The 9 x 9 count in 7s gives a total of 1260 from 89 to 1 = 14 + 1246 = 90, and these values like the +6s can be placed into the values of the Trigrams Trigrams and Hexagrams. Then the 2 value’s totals can be added together and unified into a system that gives correct predictions of eclipses and many other important aspects of the movement’s of the Sun and its cycles. The use of 111 could be seen as linked to the length of the Solar Cycle of sun-spots = a 11.1 average value, but we can also see the formations of the broken and unbroken lines give us other images of the way convection works in the form of the Hexagon. The value’s of the 7s when placed into the 9 x 9, from 1 to 89 = 1260, and the same method of finding all the Hexagram values of 7s is employed for finding the value’s of 6. The values given in the first and last line of the 9 x 9 gives the totals as they would also fit the 3 x 3 of the Lo Shu through the Stack of Nines (nine lines of numbers and their central values). 1 = 7, 2 = 14, 3 = 21, 4 = 28, (5 = 35), 6 = 42, 7 = 49, 8 = 56, 9 = 63, so 10s = 70. These Trigram Trigram values double into the t he value’s of Hexagrams so 1 to 89 = 14 + 1246 = 1260 for all opposite numbers and Light and Dark Images as the odd to even values. In the Ho Tu the value of the opposites would = 14 + 84 = 98, 2 to 7 = 28 + 98 = 126, 3 to 8 = 42 + 112 = 154 and 4 to 9 = 56 + 126 = 182 = 280 is the value of all opposites in the 4 Outer Squares. The value of 5 and 10 = 210 which in total of the 5 Elements = 490. When the 6s and 7s are added together the Outer Squares = 240 + 280 = 520 so 260 is the average value also used in the Mayan Count. In the addition of 5 to 10 in the total’s of 7s = 490 + the value of 6s = 240 = 730 x 2 = 1460 or the amount of days of 4 yrs = the Solar rectification to the Sothic + 1 day addition all carried out at the time of Standstill (Winter Solstice Ceremony), which was the time of all birthing of ‘The Children of the Light’ (9 months after the Spring Equinox and the Fertility Rites) The value of 730 is seen in the addition of the opposites in the Magic Square with the center = 365 = 729 + 1, and the value of the extra part, as given in difference between the Tun and Haab, or Decan and Sothic = the extra 73rd 5 days period found through the /72 in the t he 360 to 365 count. All these values are contained in the values gain from the 384 lines of the Hexagrams - ‘The Stars’ or of the ‘Ta Chi’. The 5 x 73 = 365 (8640 + 120 hours or 5 days) matches to 8 x 73 = 584 in the Ve Venus nus Cycle = 13 x 73 = 949, which x 10s = 9,490,000 = 5 Baktuns or 2600 yrs of the Haab 365 count. The Mayan Tun Tun and Haab being a /72 to attain the 73rd part = the same as seen in the Egyptian Decan to Sothic Count. In the narrative of the ancestors, they arose out the underworld or dreamtime to walk the earth as light and water came forth from within the Earth. The meaning of Earth is the boundary or the covering that cloaks the dark (the body) principle so the math appears to be concerned with the value’s of the Inner then becoming what is observed without in the time space’s field of action. The cycles’ of water = 33.3 yrs, so the cycles of inundation fluctuations (in the rise and fall of the flow in rivers) appears to follow 3 Solar Sunspot Cycles = 9 cycles in 100 yrs (99.9).
Appendix = All sequences of + 111s in all +1s to +8s, 2-7, 3-6, 4-5 counts all = 99 bases: +1s - +8s. +2s - +7s. All = Base = 99s. 123 198 135 186 234 219 246 297 345 321 357 318 456 432 468 429 567 543 579 531 678 654 681 642 789 765 792 753 891 876 813 864 912 987 924 975
+3s - +6s
+4s -+ 5s
147 258 369 471 582 693 714 825 936
159 261 372 483 594 615 726 837 948
174 285 396 417 528 639 741 852 963
162 = 222s 273 = 444s 384 = 666s 495 = 888s 516 = 111s 627 = 333s 738 = 555s 849 = 777s 951 = 999s
Sequence + 2s = 24681357 9: 123 345 567 789 912 234 456 678 891
321 924 543 246 765 468 987 681 219 813 432 135 654 357 876 579 198 792
429 642 864 186 318 531 753 975 297
825 147 369 582 714 936 258 471 693
528 741 963 285 417 639 852 174 396
726 948 261 483 615 837 159 372 594
627 = 4s 849 = 8s 162 = 3s 384 = 7s 516 = 2s 738 = 6s 951 = 1s = Central +5s Lo Shu. 273 = 5s 495 = 9s = +4 Con Integer sequence (doubled).
Sequence + Central 7s = 75318642 9: 678 456 234 912 789 567 345 123 891
876 654 432 219 987 765 543 321 198
579 357 135 813 681 468 246 924 792
975 753 531 318 186 864 642 429 297
471 258 936 714 582 369 147 825 693
174 852 639 417 285 963 741 528 396
372 159 837 615 483 261 948 726 594
273 = 5s 951 = 1s = Central +5s Lo Shu. 738 = 6s 516 = 2s 384 = 7s 162 = 3s 849 = 8s 627 = 4s 495 = 9s = +5 Cn Integer Sequence (14 = 5).
Sequence + Central 5s = 51627384 9. This gives an ordered pattern of 639639639: 6= 456 3= 912 9= 567 6= 123 3= 678 9= 234 6= 789 3= 345 9= 891
654 219 765 321 876 432 987 543 198
357 813 468 924 579 135 681 246 792
753 318 864 429 975 531 186 642 297
258 714 369 825 471 936 582 147 693
852 417 963 528 174 639 285 741 396
159 615 261 726 372 837 483 948 594
951 = 1s = Lo Shu 8 Spoke Wheel Central 5s. 516 = 2s 162 = 3s 627 = 4s 273 = 5s 738 = 6s 384 = 7s 849 = 8s 495 = 9s = +1 Cn Integer Sequence (10 = 1)
Sequence + C4s = 48372615 9. This gives a pattern of 369369369: 3= 345 6= 789 9= 234 3= 678 6= 123 9= 567 3= 912 6= 456 9= 891
543 987 432 876 321 765 219 654 198
246 681 135 579 924 468 813 357 792
642 186 531 975 429 864 318 753 297
147 582 936 471 825 369 714 258 693
741 285 639 174 528 963 417 852 396
948 483 837 372 726 261 615 159 594
849 = 8s 384 = 7s 738 = 6s 273 = 5s 627 = 4s 162 = 3s 516 = 2s 951 = 1s = Central +5s Lo Shu. 495 = 9s = gives +8 sequence (all doubled).
Sequence + C1s: 912 123 234 345 456 567 678 789 891
219 321 432 543 654 765 876 987 198
813 924 135 246 357 468 579 681 792
318 429 531 642 753 864 975 186 297
714 825 936 147 258 369 471 582 693
417 528 639 741 852 963 174 285 396
615 726 837 948 159 261 372 483 594
516 = 2s 516 = 627 = 627 = 4s 738 = 738 = 6s 849 = 849 = 8s 951 = 1s = Central +5s Lo Shu. 162 = 162 = 3s 273 = 273 = 5s 384 = 384 = 7s 495 = 495 = 9s = gives + 2 sequence (all doubled).
186 975 864 753 642 531 429 318 297
582 471 369 258 147 936 825 714 693
285 174 963 852 741 639 528 417 396
483 372 261 159 948 837 726 615 594
384 = 7s 384 = 273 = 273 = 5s 162 = 162 = 3s 951 = 1s = Central +5s = Lo Shu. 849 = 849 = 8s 738 = 738 = 6s 627 = 627 = 4s 516 = 516 = 2s 495 = 495 = 9s = gives + 7 sequence (16 = 7).
285 174 963 852 741 639 528 417 396
615 726 837 948 159 261 372 483 594
384 273 162 951 849 738 627 516 495
Sequence + C8s: 789 678 567 456 345 234 123 912 891
987 876 765 654 543 432 321 219 198
681 579 468 357 246 135 924 813 792
Sequences + C1s to +8s: 912 123 234 345 456 567 678 789 891
987 876 765 654 543 432 321 219 198
813 924 135 246 357 468 579 681 792
186 975 864 753 642 531 429 318 297
714 825 936 147 258 369 471 582 693
= 9s = 9s = 9s = 9s = 9s = 9s = 9s = 9s = 9s
Sequences 1 to 8, 2 to 7 and 4 to 5 can expand to form Magic Squares. Plus all values double from inner value = 3 x 3, and from the sequence. The doubling = 3s, 6s or 9s.
The list of Contracted Integer Squares 9 x 9, 1s, 2s, 4s, 5s, 7s and 8s (Binary Expansion):
123 456 789 234 567 891 345 678 912 456 789 123 567 89 891 234 678 912 345 789 123 456 891 234 567 912 345 678
246 813 579 468 135 792 681 357 924 813 579 246 135 792 468 357 924 681 579 246 813 792 468 135 924 681 357
483 726 159 837 261 594 372 615 948 726 159 483 261 594 837 615 948 372 159 483 726 594 837 261 948 372 615
876 543 219 765 432 198 654 321 987 543 219 876 432 198 765 321 987 654 219 876 543 198 765 432 987 654 321
753 186 429 531 864 297 318 642 975 186 429 753 864 297 531 642 975 318 429 753 186 297 531 864 975 318 642
516 273 849 162 738 495 627 384 951 273 849 516 738 495 162 384 951 627 849 516 273 495 162 738 951 627 384
1 to 8s = 123 + 876 to 678 + 321 = 999s. The same applies applies to 2 to 7 and 4 to 5s = 9s (999 999 999) in all directions, and law of doubling always applies. Values of 3s, 6s and 9s formed in all additions between 124875 (= Binary Progression to infinity) 1 2 4 8 7 5. 123 456 789 483 726 159 753 186 429 246 813 579 876 543 219 516 273 849 369 369 369 369 369 369 369 369 369
234 567 891 837 261 594 531 864 297 468 135 792 765 432 198 162 738 495 = 693 693 693 693 693 693 693 693 693
345 678 912 372 615 948 318 642 975 681 357 924 654 321 987 627 384 951 936 936 936 936 936 936 936 936 936
456 789 123 726 159 483 186 429 753 813 579 246 543 219 876 273 849 516 = 369 369 369 369 369 369 369 369 369
567 891 234 261 594 837 864 297 531 135 792 468 432 198 765 738 495 162 693 693 693 693 693 693 396 396 396
678 912 345 615 948 372 642 975 318 357 924 681 321 987 654 384 951 627 = 936 936 936 936 936 936 936 936 936
All lines and triples follow same patterns of alternating 3, 6 or 9s, and the reader can place the rest of the values to see how they fit together. together. 124 124 875 875 = 578= 421 = 999 693 396 The Binary Expansion shows the doubling of the Contracted Integer Sequences, so both can be matched with how they work in the 3 x 3 and 9 x 9 Magic Squares already given: given: 123456789 246813579 369369369
246813579 483276159 483276159 876543219 753186429 516273849 516273849 483276159 876543219 876543219 753186429 516273849 123456789 123456789 639639639 369369369 369369369 639639639 369369369 639639639 639639639 (7 =16, 5 = 14, 9 = 18, 1= 10, 3 = 12)
123456789 246813579 483276159 369369369 876543219 753186429 516723849 639639639 999999999 999999999 999999999 999999999 146 The Well. 297 358
The Same values are found in the 8 Spoke of the Navagraha-Yantra, and they can also then be placed into the same Contracted Integer Runs. 147s + 3s 942 94 2 26 264 4 72 729 9 186 318 864 537 759 315
174 + 6s 942 94 2 26 264 4 186 318 537 759
All in the 8 Spoke. 729 72 9 864 315
153 61 153 618 8 83 831 1 15 153 3 61 618 8 83 831 1 297 753 975 297 753 975 648 294 426 648 294 426 597 37 597 375 5 48 486 6 59 597 7 37 375 5 48 486 6 642 429 531 642 429 531 183 861 972 183 861 972 UP/ Red - 147, 258, 369, 471, 582, 693, 714, 825, 936. = + 3s Down/Yell Down/Y ell 174, 285, 396, 417, 528, 639, 741, 852, 963. = + 6s. 123s +1s 942 264 729 186 318 864 537 53 7 75 759 9 31 315 5
198s + 8s 942 264 729 186 318 864 537 53 7 75 759 9 31 315 5
186s = +7s 942 264 729 186 318 864 537 759 315
135s = + 2s 942 264 729 186 318 864 537 759 315
153 618 831 153 618 831 153 618 831 153 618 831 297 753 975 297 753 975 297 753 975 297 753 975 648 64 8 29 294 4 426 426 64 648 8 294 294 42 426 6 648 297 426 648 297 42 426 597 375 486 597 375 486 597 375 486 597 375 486 642 429 531 642 429 531 642 429 531 642 429 531 183 18 3 86 861 1 972 972 18 183 3 861 861 97 972 2 183 861 972 183 861 972 Up\ - 123, 234, 345, 456, 567, 678, 789, 891, 912 = + 1s Down\ 198, 219, 321, 432, 543, 654, 765, 876, 987 = + 8s. Left to right across - 186, 297, 318, 429, 531, 642, 753, 864, 975 = + 7s. Right to left across - 135, 246, 357, 468, 579. 681, 792, 813, 924 = + 2s. Up bottom to top - 162, 273, 384, 495, 516, 627, 738, 849, 951 = + 5s. Down Top to bottom 159, 261, 372, 483, 594, 615, 726, 837, 948 = + 4s. These values in the Navagraha-Yantra Navagraha-Yantra are exactly the same as given in the workings of the Lo Shu. They correspond to the Contracted Integer Patterns and can all be placed into the same sequences as seen above in the workings = 111s, 222s, 333s, 444, 555, 666, 777, 888s to 999s. The Navagraha also gives expanded values of integers = 729.
The Map of The Nine Stack posted is full of the math from the I Ching.
The additions of all the lines across equal a binary progression seen also in the amount of Trigrams in 64 Hexagrams, as from top to bottom = 1, 2, 4, 8,16, 32, 64, 128, 256 or in the Contract Binary Sequence = 124875124(875). 124875124(875). The addition of each diagonal line from +1s = + 8 = 12345678 = 36, 1+3+6+10+15+21+28 1+3+6+10+15+21+28 = 84 (=1+2,3,4,5,6,7), (=1+2,3,4,5,6,7), 1+4+10+20+35+56 1+4+10+20+35+56 = 126, 1+5+15+35+70 = 126, 1+6+21+56 = 84, plus the central spine = 99 = 1+2+6+20+70. The bottom line in contracted integer values = 181272181, so the investigation of each sequence in this map can be looked at, as contracted integers, and its expanded numbers. The line above the bottom one gives 17388371 = 38. The downward numbers = 1+3+10+35 = 49, 1+4+15+56 1+4+15+56 = 76, 1+5+21 = 27, and 1+6+28 = 35 (1+7 = 8, 1+8 = 16), to which the central ce ntral spine spin e = +99 can be added +1 = 303. All the diagonal di agonal values valu es = 11 111111111 = 9, 12345678 = 36, 1361631 = 21, 141282 = 18, and set against 141282 to 282141 = 333333, 15687 = 27, 171 = 9, and 18 = 9 in the crossed direction. The conclusion is that the lines do give the correct values in their expanded values as found in all other systems, but the contracted runs are not consistently matched to any special sequence of additions. But for me the 1 to 256 is enough to be of interest, and the diagonal values of 36, 84, 126 and 99 are also of importance. (My thanks to Rikki Solomon for passing on this 9 Stack image.)
The Conclusion on the Lo Shu. The Lo Shu is produced from the binary expansion of Trigrams and Hexagrams, from the same sequences given in the Ho Tu, but the values of the Lo Shu all makes ONEs. So there is only ever ONE, and all is +1. This has put all the values from the Ho Tu together and has ordered all +6s and +7s into 13s, and this gives 384 lines of values of simple integers their ordering. To gain sequences of change or order, all are contained in the sequences 1 to 9 = 10 = 1s with a central 5. To get the sequences it must always be the addition of +1, and therefore its reversal = + 8s. The 18 or 81 is the base of the count in
the Trigrams and Hexagrams, as this is a base of +1. I Explain all the math of the adding the last to the first value in Book 2. The Book of Creation. So let us get back to the Lo Shu as a 3 x 3 Magic Square and all the esquires of Trigrams and Hexagrams that have been given a values with a simple addition, so we count 1+1 are 2 and 2 + 2 is 4, so we have the binary count as 2 is the addition +1 +1. When the count to +9s = 99 or 999 (as found in The Well) all the binary to integer links also appear, so when this is completed we get the count of 9+1s or 10s. In the 9 x 9 Magic Square it can be taken back to its original contracted integer form and the first line is 1234 5 6789 as the central number 5 is always of the mean value of the pairs, and this changes every 9 lines to recur until infinity infinity,, as the Magic Square contains the infinity of numbers in all the additions = 10 + 5 = 15 as 5 is worth 30 and 10 = 60. It is based on all the central values derived in the 5 Squares as a +5 addition that reverse to +4s, for when the Solfeggio Sequences fit into 5 to 4s then all sequences of 9s = 1s in +1. The 9 x 9 sets out all integer counts as a Magic of all the values (I have given the math on the Solfeggio paper). The central line of the 9 x 9 = 5678 9 1234, as central 9 = 45 (45 x 6 = 270, or 315 = 7s). It's when these values are placed into their correct ordering they can all make +1s or 10s, as they are all linked to central 5 in the Lo Shu, and how it's flipped and reversed as attribute of Forces, Planets or Gods. All values double into Magic Square’s of values in the 3 x 3 but only 3s and 6s give a 3 number repeat only, the other values give a plus 8 x 8 = 1 to 9 = 10s, as are given in the math of the Ho Tu. All numbers expand and contract within the sequences given of 1 to 8s, 2s to 7, etc = 9s + 1s, as when adding 9 the same value is always attained as in 111 to 999 = 1110111 of The Lo Shu as reflective pairs or crossing-over pairs. The 8 Spoke is therefore able to be given both value and image, relating the contracted and expanded values to the binary sequence = 124875 to infinity, infinity, and this gives the same expansion as Precession from the base 6s = 25,920. The Solfeggio Count Expansions of Lo Shu. The Lo Shu doesn’t give 9s but all outer values = 10s, and the values of: 492 357 816 In each direction gives a count of 456 to 654 = +1s to +8s = 567891234[5]678912345. 258 to 852 = +3s to +6s = 528528528[5]285285285. 357 to 753 = +2s to +7s = 579246813[5]792468135. 159 to 951 = +4s to +5s = 594837261[5]948372615. The total of each count 5 to 5 = 91 + C5 = 96 x 4 = 384.
It’s the values of ‘The Well’ which give all 9s, as in this image drawn up by Lee Burton.
This image of ‘The Well’ gives 99 as the bases of all Contracted Integers = 1 to 8s, 2 to 7s, 3 to 6s and 4 to 5s, and their reversals from Light to Dark (from Ch’ien to K’un, or from Male to Female to K’un to Ch’ien 8 to 1). This fits the values of the 8 Trigrams as Chien and K’un = 1 to 8, and their combinations produce the binary pairings of ‘The Children’ in the other values. 2 = Sun and 7 = Chen, 3 = Li and 6 = K’an, 4 = Tui and 5 = Ken, but Tui and Ken give a reversal of their values as in marriage they are equal in value, so a central pivot as all is put together in the 4 to 5 or 5 to 4 run. The totals of the values = 90 plus the central 9 = 99 = 45 adding to 54, 108, then to 540 and 1080 to a 2160 total as an average in the 9 x 9 Magic Square. The value of 99 is the base of the Solfeggio Sequences in the Lo Shu, but 9 and 99 is the base to which is added 1 = 10s or 100 etc. The 1 to 9, 2 to 8, 3 to 7, and 4 to 6 transforms ‘The Well to the Lo Shu, as from 9s to 10s. The Well gives the simple Contracted Integer Sequences that can also be placed in the Trigrams Trigra ms to produce Magic Squares. The runs in each direction can be given as: 12345678[9]12345678. 24681357[9]24681357. 48372615[9]48372615. 63963963[9]69369363.
The Values in the Four 8 x 8 Magic Squares of the Ho Tu. The Contracted Integer Values in the 8 x 8 of the Ho Tu all produces 3s, 6s or 9s, but also Solfeggio Values of + 111 also appear to give the 111 + 999 = 1110111 of the Lo Shu from a base value of 99. 1 to 6 = 62733849 16277384 51622738 95166273 95166273 49511627 84955162 38499516
2 to 7 = 95166273 49511627 84955162 38499516 38499516 73844951 27388495 62733849
3 to 8 = 38499516 73844951 27388495 62733849 62733849 16277384 51622738 95166273
4 to 9 = 62733849 16277384 51622738 95166273 95166273 49511627 84955162 38499516
From the combinations of 3 x 3 and 4 x 4 all make Magic Squares, and the same doubling of values are expressed. The 3 x 3 = :162 273 384 495 516 627 738 849 951 516 627 738 849 951 162 273 384 495 951 162 273 384 495 516 627 738 849 The 4 x 4 express 3s, 6s and 9s:6273 1627 5162 9516
3849 7384 2738 6273
9516 4951 8495 3849
The Solfeggio Runs = 48 to 51 (+4s - +5s) = 99 - as given in an above section:159 162 = 222 261 273 = 444 372 384 = 666 483 495 = 888 594 516 = 111 615 627 = 333 726 738 = 555 837 849 = 777 948 951 = 999 999 + ----------162 159 = ----------111 111 All the workings given in both this paper and on the Navagraha-Yantra, as all can be combined along with the math given in both books “The Sum of Things’, and Book 2. The Book of Creation, which is the middle book of ‘The Book of Divine Revelations - The Judgements and Laws of the Sacred Mountain’ dedicated to the math of the I Ching.
