07172012, 10:01 AM  #1 
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The 81 Solfeggio Tones
There can be no fewer or no more than these 81 mathematicallyrelated, 3digit elements... However, these 81 tones can spawn countless, related frequencies through multiplying by harmonic ratios.
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07172012, 10:03 AM  #2 
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We'll start by dividing all of the tones (shown in the diagram
in post #1) by their only common denominator, which is 3: I've highlighted the consecutivelynumbered pairs (i.e. 73 & 74, 86 & 87, etc.)... These pairs occur whenever the flow of numbers changes from odd to even or even to odd... Note that in the above diagram, now 37 becomes the 'primary' number as well as the main vertical (in this diagonal diagram) incremental number... IOW, there's a difference of 37 between 37 and 74, between 74 and 111, between 82 and 119, etc, etc... The next image shows the (factorof3reduced) numbers after they have been 'Vedicallyreduced' down to their digital roots: Here the diagonal columns reveal the pattern of 1/4/7, 2/5/8 and 3/6/9; the chronologically coherent 'family seeds'... The total of all 81 digits is 450 and 450/81=5.55... The total of the 9 digits in the highlighted area is 45... And uncannily encrypted at the very Center of this set of numbers is its Source: 618 753 294
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07172012, 10:05 AM  #3 
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The 81 tones are inseparably woven (or yolked) together...
It's a geometricallycoherent, crystalline structure... An archetypal projection emanating directly from the Tetractys http://en.wikipedia.org/wiki/Just_intonation employs tones that are interrelated members of the same harmonic series and are usually represented by small number ratios such as 3:2 or 5:4 or 2:1... So some of the 81 tones exist in these type of harmonic interrelationships, and one of my goals is to develop a method that would allow for a type of harmonic modulation by moving through the tones in a manner something like Tarzan swinging from one reachable vine to the next... In this way, harmonically linking two 'unrelated' tones by way of a third tone that is harmonically related to both... Or something like that... _____________________________ The relevance of all of this harmonic theory is that by establishing some 'rules of the road' in how to navigate and combine various elements (tones) of the set, one can then achieve the desired emotional or therapeutic results depending on the manner in which they're employed... {music, kymotropes, healing, or what I'm intending to achieve, a balance of all} kymo = wave, trope = to turn
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07172012, 10:09 AM  #4 
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Each subset has a different set of 'polarity reversals' or
patterns of smallest/largest leading frequency. (The S and B marked on the diagrams indicate which of the pair is 'leading' the smallest or biggest.) The 1:8 Beat Frequency subset: The 2:7 Beat Frequency subset: The 'Classic' 3:6 Beat Frequency subset: (note this is the only subset that is NOT Unicursal... MultiCursal if you will ) This specific set of 18 tones include the frequencies that are known to most people as the "Sacred Solfeggio Tones" What makes this 'beat family' sacred I hear you ask? 3:6 is an octave and we're dealing with 9 digits let me SUM UP 3,6,9 = 18 The 4:5 Beat Frequency subset: If we look at all the 4 sequences and track the frequencies linearly we can trace the Spin directions. The position of the lowest frequency spirals in a reverse direction, inward and then outward again from 1 thru to 9. All together now: Each '100hz octave group' from 19 can now be assigned to 8 tones: (4 black/ 4 white) (shown here in grey for contrast against the background) Ordinal Sequence: 123,135,147,159,162,174,186,198 234,246,258,261,273,285,297,219 345,357,369,372,384,396,318,321 456,468,471,483,495,417,429,432 567,579,582,594,516,528,531,543 678,681,693,615,627,639,642,654 789,792,714,726,738,741,753,765 891,813,825,837,849,852,864,876 912,924,936,948,951,963,975,987 Note the 3rd column = 'standard solfeggios' deosil and the 7th column = 'standard solfeggios' widdershins Also that the 1st and last BOTH start with the lowest frequency of the group ALREADY. Easier to see in the linear arrangement: Linear Sequence: 123,135,147,159,162,174,186,198 219,234,246,258,261,273,285,297 318,321,345,357,369,372,384,396 417,429,432,456,468,471,483,495 516,528,531,543,567,579,582,594 615,627,639,642,654,678,681,693 714,726,738,741,753,765,789,792 813,825,837,849,852,864,876,891 912,924,936,948,951,963,975,987 Notice every 4th group represents a full reversal of 'yin+yang' or 'spin order' with the full 9 cycle returning to the same starting polarity/spin order and of course 2 and 8, 3 and 7 and 4 and 6 and also polar inverse groups. __________________ And finally, 111,222,333,444,555,666,777,888,999 represent the following whole number ratios 1:2:3:4:5:6:7:8 and any combination you care to play together these are the simplest 'purest' intervals. The logic fits with the 'Enneagram Tone Set'. They would represent the energy of the nine points as opposed to 'paths'. _______________ Full 81 tone Ordinal Sequence 111,123,135,147,159,162,174,186,198 222,234,246,258,261,273,285,297,219 333,345,357,369,372,384,396,318,321 444,456,468,471,483,495,417,429,432 555,567,579,582,594,516,528,531,543 666,678,681,693,615,627,639,642,654 777,789,792,714,726,738,741,753,765 888,891,813,825,837,849,852,864,876 999,912,924,936,948, 951,963,975,987 Full 81 tone Linear Sequence 111,123,135,147,159,162,174,186,198 219,222,234,246,258,261,273,285,297 318,321,333,345,357,369,372,384,396 417,429,432,444,456,468,471,483,495 516,528,531,543,555,567,579,582,594 615,627,639,642,654,666,678,681,693 714,726,738,741,753,765,777,789,792 813,825,837,849,852,864,876,888,891 912,924,936,948,951,963,975,987,999
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07172012, 10:13 AM  #5 
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Here are a few other graphs dealing with 27:
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07172012, 10:15 AM  #6 
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I want to introduce something here that will help
clarify some other graphs that I'll be posting... It deals with a way to represent each of the 81 (3digit) tones as a 2digit 'coordinate value' resulting in a 'shorthand' method of referring to (or graphically depicting) the 3digit values... Here are the 81 tones shown as 3digit frequencies: Here is the same arrangement of the 81 tones, but this time shown as 2digit coordinate values (disregard the different colorcodings and focus on the numerical alignments):
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07172012, 10:17 AM  #7 
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Subset of 27 tones
{anchored by the 37 points of the Hemicube}
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07172012, 10:18 AM  #8 
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More on 27 and 37
The numbers 27 and 37 are 'reciprocals' of each other: 1/27 = .037037037... 1/37 = .027027027... and 27 x 37 = 999 {999 is the largest frequency in the 81 toneset} _______________ The 27 (2digit) tones shown on the Hemicube in the previous post add up to the value of 1485: 1485/37 = 40.135135... 1485/27 = 55 The central hub around which the entire 81 Lo Shu toneset revolves is 55: 55/40.135135 = 1.370370... and 40.135135/55 = .729729... also 37/27 = 1.370370... and 27/37 = .729729... _________ 729 is the number of hexagrams in the Tai Hsuan Ching: 9 x 9 x 9 = 729 __________________ This value of 1.370370... is also quite significant: According to the United States Bureau of Standards, the physical constant (or fine structure constant) of the hydrogen atom is 37/27 x 100: As we saw above 37/27 = 1.370370... So 1.370370 x 100 = 137.037037... _______________ {The following is exerpted from chapter 4 of Wilcock's Divine Cosmos} THE FINESTRUCTURE CONSTANT This constant has been continuously studied by spectroscope analysis, and the highly revered physicist Richard P. Feynman explained the mystery in his book The Strange Theory of Light and Matter. (This value) has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it. Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows, it is one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say that the "hand of God" wrote that number, and "we don't know how He pushed His pencil."
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07172012, 10:19 AM  #9 
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The number 37,
as shown below (and in greater detail in post#2), has a pervasive, yet often 'hidden', influence in the set of 81 tones: Linear Arrangement of the 81 Lo Shu Tones shown here in their 3digit frequency form {Reduced by their only common denominator, which is 3} Note that in the above diagram, now 37 becomes the 'primary' number as well as the main vertical (in this diagonal diagram) incremental number... ____________________ 1/81 = .012345679... these digits sum to, you guessed it, 37...
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