The 81 Solfeggio Tones

[Fatal Guillotine]

There can be no fewer or no more than these
81 mathematically-related, 3-digit elements...

However, these 81 tones can spawn countless, related
frequencies through multiplying by harmonic ratios.

[Fatal Guillotine]

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 consecutively-numbered 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 (factor-of-3-reduced) numbers after
they have been 'Vedically-reduced' 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

[Fatal Guillotine]

The 81 tones are inseparably woven (or yolked) together...

It's a geometrically-coherent, crystalline structure...

An archetypal projection emanating directly from the Tetractys


http://en.wikipedia.org/wiki/Just_intonation


employs tones that are inter-related 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
inter-relationships, 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

[Fatal Guillotine]

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 1-9 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

[Fatal Guillotine]

Here are a few other graphs dealing with 27:

[Fatal Guillotine]

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 (3-digit) tones
as a 2-digit 'coordinate value' resulting in a 'shorthand' method
of referring to (or graphically depicting) the 3-digit values...

Here are the 81 tones shown as 3-digit frequencies:





Here is the same arrangement of the 81 tones,
but this time shown as 2-digit coordinate values
(disregard the different color-codings and focus on the numerical alignments):

[Fatal Guillotine]

Subset of 27 tones
{anchored by the 37 points of the Hemicube}

[Fatal Guillotine]

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 (2-digit) 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 FINE-STRUCTURE 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."

[Fatal Guillotine]

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 3-digit 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...