The 81 Lo Shu Tones within the 729 Fabric

[MythMath]

The 81 Lo Shu Tones




The 81 Lo Shu Tones, form a complete frequency set...

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...

[Armagdn03]

Please elaborate on the inter-relatedness of the number system. Thank you.

[MythMath]

First off, I want to say that the research that has been done on this set of
numbers has been a team effort, with everyone who has participated
sharing their efforts to help clarify the possibilities inherent within...

For the full story on the development of all this, I'd recommend reading
through this thread at abrahadabra.com and follow all the various links...
_________________________________

Next I'd like to show why I've chosen to refer
to this number set as The Lo Shu Tones:

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
ch-ch-ch-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




see article: The Mystical Lo Shu

[MythMath]

Most of these initial, explanatory posts here may be recycled from the original abra.com thread...
_______________

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

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

An archetypal projection emanating directly from the Tetractys/LoShu...
_________________

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

For examples of kymotropes see: YouTube - MythMathFilms's Channel

[MythMath]

The Toneset's obvious link to Rodin's work is the fact that
the numbers can be 'generated' by the Enneagram...

One of the main contributors to the Lo Shu Tone research goes
by the nick of j00lz at abrahadabra.com and he has compiled
several graphic charts that demonstrate how the tones can be
derived by counting out different 'beats' around the Enneagon:

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

1:2:3:4:5:6:7:8:9

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

[jtstatic]

Nice work, especially liked the ennagon shapes, they gave me some new ideas

Anyway I have one question, for example counting 147 to 174 the difference is 27 which can only be divided by 9 and 3. Why then is the next number 159, which is adding 12? In other places I think advancing in groups of 12 seems logical, because for example the first sequence of 111 is as follows:

111 +36
147 +27 (>>> 111)
174 +48
258

Now 36 and 48 can be divided with 12 and gives you a natural flow, but 27 would to me seem better divided to sections if it was advancing in 9 9 9 rather than 12 3 12. This would lead to 147 156 165 174. Also I noticed that after 258 the order flips to 3 12 12, why is that?

Could you elaborate more on this? I've glanced the threads at abrahadabra and might be it's explained somewhere, but it's just too much to grasp at one look

[MythMath]

static,

The tone sequences are 'generated'
by counting 'round the enneagon...

Each different 'count' produces a
different 18-member 'beat family'...

Study those graphs a bit more intensely
and the mysteries will begin to unravel...

Do feel free to ask more questions though also...

[jtstatic]

Ok, thx for the clarification, I suspected there was a good explanation with all the work you've done this far. I will take a closer look for sure.