ARTICLE 13
by
Stephen M.
Phillips
Flat 4,
Oakwood House, 117119 West Hill Road. Bournemouth. Dorset BH2 5PH.
England.
Website: http://smphillips.mysite.com
Abstract
Not only are there seven notes of the
Pythagorean musical scale but also seven types of 36 groups of notes can be
played using a tetractys array of ten notes. These groups constitute a Tree
of Life pattern because they correspond to the 36 corners of the seven
enfolded polygons in each half of the inner form of the Tree of Life. The
same is true for the 524 ways in which the ten notes can be played to create
5–10 sounds, for they correspond to the 524 yods of the whole inner Tree of
Life. These sequences include 240 sequences of 10 notes and 240 sequences of
eight, nine and 10 sounds. Tetractys arrays of the ten octaves of each note
of the Pythagorean scale generate 1680 sequences of ten notes, that is,
16,800 notes. This musical pattern is similar to the 16800 spirillae in the
ten whorls of the heterotic superstring described over a century ago by
Annie Besant and C.W. Leadbeater. It suggests that the heterotic superstring
of ordinary matter is like a tenstringed harp whose 240 musical sequences
(actually ten sets of 24) correspond to 240 gauge charges of the superstring
symmetry group E_{8} spread out over its length, each set of 24
sequences being analogous to the 24 charges carried by each of the 10 whorls
of the superstring. The analogy predicts that the heterotic superstring of
shadow matter consists of five whorls with 12600 spirillae. The
E_{8}×E_{8} heterotic superstring is like a selfplaying,
musical instrument whose states are its score and whose unified force
described by E_{8} is the music that it makes.

1
THE 36 CORNERS OF THE 7 ENFOLDED POLYGONS DENOTE THE 36
MUSICAL ELEMENTS THAT A TETRACTYS OF 10 NOTES CAN PLAY
2
1. Musical potential of tetractys of
notes
Consider a tetractys array of 10 notes of the Pythagorean scale labelled
by letters of the alphabet:
1
2
3
4 
A
B C
D E F
G H I J

What these notes are need not
be known at this point; they will be specified later. A combination of notes played together
defines a harmonic interval or a chord and their various permutations played in succession
define melodic intervals and broken chords. The rule for playing a tetractys of notes is:
starting with note A, the 10 notes are played in four stages, each one using
all the notes in a row and not notes in other rows. There are
seven types of basic musical elements, or ‘sounds’: the starting note A (written
‘1’), a harmonic interval formed from B & C (written
‘2’), a melodic interval formed from notes B & C
(written ‘2’), a chord (written ‘3’) and a broken chord (3) formed from D, E & F and a chord
(4) and broken chord (4) formed from G, H, I & J. The numbers of
sounds playable at each stage are listed
below:
1 
^{1}C_{1}
=

1


(1)

2 
^{2}C_{2} +
^{2}P_{2} = 1 + 2 =

3


(2
&
2×2) 
3 
^{3}C_{3} +
^{3}P_{3} = 1 + 6 =

7


(3
&
6×3) 
4 
^{4}C_{4} +
^{4}P_{4} = 1 + 24 =

25


(4
&
24×4) 

TOTAL =

36



ELOHA, the Godname of Geburah with number
value 36 (1) prescribes how many basic
harmonies and melodies can be played by using the notes in each row of the tetractys.
36
is also the number of corners in the seven enfolded
polygons forming each half of the inner form of the Tree of Life. Figure 1 shows how the numbers of
the seven types of sounds correspond to the corners of these polygons. The number of ways
(‘musical sequences’) the 10 notes can be played = 1×3×7×25 = 525. Of these, the musical
sequence 1^{.}2^{.}3^{.}4 consists of
four sounds, the least number of sounds that the tetractys can play. The 524 musical
sequences comprising 510 sounds are listed below:

Musical sequence

Number of
sounds

Number of musical
sequences

Number of sounds

1. 
1^{.}2^{.}3^{.}4 
1 + 2 + 3 + 4 = 10

1×2!×3!×4! = 288

288×10 = 2880

3
Figure 2. The (7+7) enfolded polygons have 236 yods on
their boundaries and 288 yods inside them.
4
2.
3.

1^{.}2^{.}3^{.}4
1^{.}2^{.}3^{.}4

1 + 1 + 3 +
4 = 9
1 +2 + 1 + 4
= 8


1×1×3!×4! =
144
1×2!×1×4!
= 48


44×9 =
1296
48×8 =
384




SUBTOTAL
= 480

SUBTOTAL
= 4560

4.
5.
6.
7.

1^{.}2^{.}3^{.}4
1^{.}2^{.}3^{.}4
1^{.}2^{.}3^{.}4
1^{.}2^{.}3^{.}4

1 + 1 + 1 +
4 = 7
1 + 2 + 3 +
1 = 7
1 + 1 + 3 +
1 = 6
1 + 2 + 1 +
1 = 5


1×1×1×4!
= 24
1×2!×3!×1 =
12
1×1×3!×1
= 6
1 ×2!×1×1
= 2


24×7 =
168
12×7
= 84
6×6
= 36
2×5 =
10




SUBTOTAL = 44

SUBTOTAL = 298




TOTAL
= 524

TOTAL
= 4858

As in the case of the sounds playable
with a tetractys, the 524 musical sequences are of seven types.
(24+12=36) sequences of two types contain the
same number (7) of sounds and
(524–36=488) sequences of five types contain different
numbers of sounds. The latter comprise two sequences
(1^{.} 2^{.}3^{.}4
) of five sounds, six sequences
(1^{.}2^{.}3^{.}4) of six sounds and 480 sequences of eight,
nine & 10 sounds that terminate in broken chords of four notes. Of the
latter,
288 (=1!×2!×3!×4!) are sequences of 10
successive notes (note, melodic interval & two broken chords). The division:
524 = 288 + 236
between the number of sequences of 10 notes
and the number of sequences of 59 sounds has its counterpart in the (7+7) enfolded
polygons, which have 236 yods on their boundaries and 288 yods inside them (Fig. 2). Furthermore, 288 yods
surround the centres of the seven separate polygons, of which 48 are corners
and 240
5
6
Figure 5. 480 corners are intrinsic to the first (6+6)
polygons enfolded in 10 Trees of Life.
7
8
are hexagonal yods (Fig. 3). This division:
288 = 48 + 240
= 2×4! + 10×4! = 12×4!
characterises a Tree of Life
pattern whose counterpart for the tetractys of notes are the 12×4! sequences
(1^{.}2^{.}3^{.}4) of 10 notes, two of which contain five notes in the
rows of two and three played in either ascending or descending pitch and 10 of which contain
such notes with both ascending and descending pitch. This means that the 480 sequences split
into 10 sets of 24 sequences of 10 notes, totalling 2400 notes, and 48,
144 and 48
sequences of, respectively, eight, nine and
10 sounds, making a total of 2160 sounds in 240 more sequences. (2400+2160=4560) sounds are
played in the 480 sequences.
The number of yods in n
overlapping Trees of Life is:
Ỹ(n) =
50n + 20.
The 91 trees of CTOL have Ỹ(91) = (50×91 + 20 =
4570) yods. There are 10 yods in CTOL arranged in a tetractys down to the path connecting
Chokmah and Binah of the 91st tree. Below the highest Binah in CTOL are therefore 4560
yods, that is, the number of yods in 456 tetractyses. Supposing that these 10 highest yods
in CTOL symbolised 10 notes of the Pythagorean scale, then each yod below the Supernal
Triad of the highest tree would symbolise a sound made during the playing of the 480
sequences! This amazing property is indicative of the archetypal character of these
sequences, which are the counterpart of the (240+240=480) hexagonal yods of the (7+7)
separate polygons (Fig. 3).
Further evidence of these 480 sequences
constituting a Tree of Life pattern is as follows: the (7+7) enfolded polygons have 70
corners, that is, 68 corners outside their root edge. The number of yods that are not
external corners = 524 – 68 = 456 (Fig. 4). The (70+70) polygons
enfolded in 10 overlapping Trees of Life therefore have 4560 such yods. Each set of 70
polygons has 351 corners. 351 is the
number value of Ashim, the
Order of Angels assigned to Malkuth. This, as well as other Godnames, Archangelic names,
etc, characterise the inner form of 10
9
overlapping Trees of Life that contain
4560 yods other than corners outside their shared edges. The division
480 = 240 + 240
is present in the inner form of 10
overlapping Trees of Life as the (240+240) corners of the first (6+6) polygons enfolded in
them (Fig. 5).
We have seen that playing a tetractys of 10
notes to create 8, 9 and 10 sounds generates 480 musical sequences with 4560 sounds. Suppose
now that the same 10 notes are played in a similar way in the three possible orientations of
the tetractys. This generates (3×480=1440) sequences of 8, 9 &
10
10 sounds with (3×4560=13680) sounds. The
(7+7) enfolded, type B polygons have 1370 yods (Fig. 6), two of which are the
topmost corners of the two hexagons shared with the lowest corners of the hexagons enfolded
in the next higher tree. The number of yods in all the polygons
enfolded in the ntree = 1368n +2. There are therefore 13680 yods
intrinsic to the polygons enfolded in the 10tree, that is, yods unshared with polygons
enfolded in the 11th tree. This
shows
that the full musical potential of a
tetractys of 10 notes is encoded in the inner form of 10 Trees of Life representing the 10 Sephiroth of a single tree. Because
the tetractys and
Table 1. Table of tone ratios

C 
D 
E 
F 
G 
A 
B 
1 
1 
9/8 
81/64 
4/3 
3/2 
27/16 
243/128 
2 
2 
9/4 
81/31 
8/3 
3 
27/8 
243/64 
3 
4 
9/2 
81/16 
16/3 
6 
27/4 
243/32 
4 
8 
9 
81/8 
32/3 
12 
27/2 
243/16 
5 
16 
18 
81/4 
64/3 
24 
27 
243/8 
6 
32 
36 
81/2 
128/3 
48 
54 
243/4 
7 
64 
72 
81 
256/3 
96 
108 
243/2 
8 
128 
144 
162 
512/3 
192 
216 
243 
9 
256 
288 
324 
1024/3 
384 
432 
486 
10 
512 
576 
648 
2048/3 
768 
864 
972 
11
the Tree of Life are equivalent symbols
of the 10fold nature of Divine Unity, what is numerically embodied in the former
has
to be identical to what is geometrically represented in
the inner form of the latter.
2. Comparison with the heterotic
E_{8}×E_{8}'
superstring
Table 1 shows the 70 notes of 10
successive octaves of the Pythagorean scale. They constitute a Tree of Life pattern because,
when converted into tetractyses, the 16 triangles making up a Tree of Life contain 70 yods
(Fig. 7). The division of the 70
notes into the 35 notes of the first five octaves and the 35 notes of the next five octaves
corresponds in the Tree of Life to the distribution of 35 yods making up its trunk* (shown in
Fig. 7 as () yods) and 35
() yods
outside it. Playing these notes arranged in seven tetractys arrays of the 10 octaves of
each note of the Pythagorean scale (Fig. 8) generates (7×240=1680)
musical sequences of 10 notes, making 16800 notes.
Compare this result with the
fact that the UPA superstring described over 100 years ago by Annie Besant and C.W.
Leadbeater consists of 10 whorls, each with 1680 spirillae, totalling 16800 spirillae. A
whorl is analogous to an octave, spirillae in different whorls corresponding to different
octaves of the same note. Each note of the Pythagorean scale has 240 sequences of its 10
octaves (Fig. 9), the counterpart of which
are sets of 240 spirillae in each whorl, repeated seven times. The 240 musical sequences for
each note of the Pythagorean scale consist of 10 sets of 24 sequences of 10 notes. The 1680
sequences for all seven notes therefore comprise 10 sets of (7×24=168) sequences of 10 notes, that is 10 sets of 1680 notes
(Fig. 10). The 1680 circularly
polarised oscillations in each of the 10 string components of the superstring of ordinary
matter have as their musical counterpart these 168 cycles. Fittingly, 168
is the number value of Cholem
Yesodoth, the Mundane
Chakra of Malkuth, signifying the physical manifestation of the Tree of Life.
The superstring counterpart
of the 480 musical sequences of 8, 9 & 10 sounds is the 480 gauge charges of the gauge
symmetry group E_{8}×E_{8}' for the heterotic superstring corresponding to its 480
nonzero roots. The 240 musical sequences 1^{.}2^{.}3^{.}4 of 10 sounds match the 240 gauge charges corresponding to
the 240 nonzero roots of the
* The trunk of the Tree of Life is the geometrical sequence of point
(Kether), line (Binah–Chokmah path), triangle (Chesed, Geburah & Tiphareth at its
corners) and tetrahedron (Netzach, Hod, Yesod & Malkuth at its corners).
12
gauge symmetry group
E_{8}
for superstrings of ordinary matter. The 240
sequences:
1^{.}2^{.}3^{.}4
1^{.}2^{.}3^{.}4
1^{.}2^{.}3^{.}4

48 sequences of 10 sounds
144 sequences of nine sounds
48 sequences of eight
sounds

correspond to the 240 gauge charges
associated with the 240 nonzero roots of the gauge symmetry group E8' for
heterotic superstrings of shadow matter. 2160 sounds are created by the 240 ways of playing
a tetractys of 10 notes to generate eight, nine & 10 sounds. 216 is not only the 55th note, where 55 is the 10th triangular number, but
also the 26th whole tone
ratio (2), showing how the Godname YAHWEH
with number value 26 prescribes
this number in the context of shadow superstrings. 216 is the number of Geburah, whose Godname number (36) is the number of different musical elements playable with a
tetractys of 10 notes. (7×2160=15120) sounds are made by the 1680 ways of playing
tetractys arrays of 10 successive octaves of the seven notes of the Pythagorean scale. As
each spirilla of the superstring of ordinary matter corresponds to a note in the 1680
sequences of 10 sounds. This suggests that the
Figure 11 The number of spirillae in one
of the whorls of the shadow superstring is encoded in the Tree of Life blueprint as the
yod population of the seven enfolded polygons with 2ndorder tetractyses as their
sectors.
shadow superstring is made up of 15120
spirillae instead of 16800 spirillae. As 15120 = 70×216, this number is generated by assigning the number value
216
of Geburah to each of the 70 yods making up the Tree of
Life. Unlike ordinary superstrings, however, where the sounds played in each sequence are
the notes of the 10 octaves, this number is, in the case of shadow superstrings, not the
same for the different types of sequences. This
13
means that the sounds cannot
correspond evenly to
their whorls for each of the 1680 sequences. There are (7×48=336) sequences of 10 sounds, 336 sequences of eight sounds and
(7×144=1008=3×336) sequences of nine sounds. Supposing that 336 sequences correspond to a
whorl, then the shadow superstring consists of five whorls instead of 10 whorls, one
comprising (10×336=3360) spirillae, one consisting of (8×336=2688) spirillae and three
consisting of (9×1008=9072) spirillae, that is, 3024 in each one. 3360 is the number of
spirillae on average in each of the five revolutions of the UPA superstring. It is encoded
in the inner form of the Tree of Life as the number of yods in the seven enfolded polygons
when their 47 sectors are turned into 2ndorder tetractyses (Fig. 11). The 1680 sequences of
eight, nine & 10 sounds produce a total of 15120 sounds corresponding to which are the
15120 spirillae of the shadow
superstring, whilst the 1680 sequences of
10 notes produce 16800 notes, corresponding to which are the 16800 spirillae of the ordinary
superstring. The analogy between the musical potential of the tetractys and the oscillatory
nature of the heterotic superstring of ordinary matter enables one to predict the form of
the heterotic superstring of shadow matter.
The conclusion that shadow superstrings
have five whorls agrees with the prediction made in Article 2 that they consist of five
stringlike components.
The picture that emerges from this
comparison of the heterotic superstring described by Besant and Leadbeater with the musical
potential of a tetractys of notes drawn from 10 octaves of the Pythagorean scale is that
superstrings are a kind of musical instrument — like a harp with 10 strings which, when
plucked according to the rules given earlier,
14
create all possible harmonic and melodic
forms composed of up to four notes of the Pythagorean scale. The oscillations corresponding
to them determine both superstring structure and dynamics.
Superstrings are the musical instrument and their forces are like the sound vibrations that
the latter emit (Fig. 12). The incessant
interaction between superstrings, mediated by the exchange of the E_{8}
gauge particles, is an unheard symphony of ‘sound’
transmitted between these instruments. The photons of light emitted and absorbed by the
electrons inside atoms would be the most common sound of this symphony, for these quanta of
the electromagnetic field are but one of the gauge fields of the superstring gauge symmetry
group E_{8}. Each whorl would represent 24
sequences of a tetractys of 10 octaves of each note of the Pythagorean scale. Those forces
of nature expressed by the 240 gauge fields associated with the nonzero roots of
E_{8} have their 240 gauge charge sources in the whorls/string components of the
E_{8}×E_{8} heterotic superstring, these charges being spread out over the
strings as the counterparts of the 240 musical sequences that can be played with a tetractys
of 10 octaves of each note of the Pythagorean scale. It is as if the basic forces acting on
matter were patterns of sounds — not in air, of course, but in the sense of states of
vibration of superstrings with a spin of 1. The 240 sequences associated with each note
consist of 10 sets of 24 sequences, which correlate with the 24 gauge charges and their
corresponding waves that travel around each whorl of the superstring. To every gauge charge
corresponds a musical sequence, shaped according to the pattern of the tetractys, of 10
octaves of each note of the Pythagorean scale. Matter ultimately is a perfect
harmony.
Additional evidence for the validity of
this musical interpretation of the superstring is the fact that a tetractys of 10 notes can
generate 90 harmonic and melodic intervals, chords and broken chords of up to four notes
(3), whilst the 10 stringlike,
curves of the superstring need (10×9=90) spatial
15
coordinate variables to describe their
motion in 10dimensional spacetime.* In other words, the heterotic
superstring is like a 10stringed harp or lyre (Fig. 13) whose range of musical
sounds is defined by the sum (90) of integers making up the Platonic Lambda Tetractys — the
very set of numbers whose relative proportions were discovered by the ancient Greeks to
determine the tone ratios of the notes of the Pythagorean scale! As shown in reference 2,
these 90 musical elements correlate with the 90 edges of the five Platonic solids. The Ideas
of the Divine Mind manifest in time (music), space (Platonic solids) and spacetime
(superstrings) in analogous ways quantified by the same parameters.
If the musical analogy with superstring theory is correct, then the
remaining (525–480=45) sequences of 47 sounds also require interpretation. There are two
sets of sequences of seven sounds (one of 24, one of 12), six sequences of six sounds, two
sequences of five sounds and one sequence of four sounds. Those other than the lattermost
correspond to 44 yods on the boundaries (including the root edge) of some of the (7+7)
enfolded polygons. The largest polygon — the dodecagon — has only 36 yods on its boundary, so a combination of polygons must be
considered. They must be identical because a pair of dissimilar polygons would lead to an
asymmetric distribution of the yods corresponding to the 480 sequences, which is,
intuitively, unappealing. The only possible pair is the two octagons (Fig. 14). The two corners
() of their root edge
denote the two sequences of five sounds, the 12 () corners denote the 12 sequences
of seven sounds and the 30 (o) yods denote the 30 sequences of either six or seven sounds.
The 44 sequences must include four that correspond to all four yods of the root edge
because no pair of similar polygons has 44 yods outside their root edge (4). This means that the 480
sequences correspond to the 288 yods inside the boundaries of the (7+7) polygons and to the
192 yods on the boundaries of all the polygons except the pair of octagons.
What is so special about an octagon? When
its sectors are turned into tetractyses, its yod population is 49, which is the number value of EL ChAI, the Godname of Yesod. The pair
of octagons has 90 yods outside their root edge and so they embody or
* In 11d supergravity spacetime the number 90 is the number of transverse
coordinate variables of the 10 closed curves/whorls of the heterotic superstring of
ordinary matter, the 10 coordinate variables measured along them corresponding to the 10
notes arranged as a tetractys.
16
generate the very archetypal number that we
found (5) in the context of the Lambda
Tetractys, the Platonic solids, the musical potential of a tetractys of 10 notes and the
geometry of the heterotic superstring. Furthermore, a pair of separate, type B octagons has
240 yods surrounding their centres (6), so that they also embody this
dynamical parameter of superstrings and its musical counterpart — the number of musical
sequences playable with a tetractys of 10 notes. That the very polygon not involved in the encoding of the number 480 should define two numbers
central to the musical analogy with superstrings is remarkable evidence of mathematical
‘Divine Design.’ Coincidence — the refuge of the sceptic — is implausible because it
requires two fortuitous concurrences.
3.
Conclusion
Although modern music uses the 13 notes of
the tempered, chromatic scale, it originated in the West from the eightnote Pythagorean
scale mathematically explained by Pythagoras. It is only the latter that can lay claim to
have the universal validity of a law of nature as the modern musical scale is a human
fabrication, a modification of the Pythagorean scale without any theoretical basis devised
simply to increase the variety of tones available to the musician. Adhering to the earliest
Greek traditions, many writers on speculative music theory have emphasized the ‘cosmic’
nature of the Pythagorean scale, pointing to its amazing, mathematical harmonies but
offering little rational and scientific substantiation for this view, merely associations or
correspondences with occult and religious ideas. Although this article, too, refers to a
mystical tradition — Kabbalah — it makes striking quantitative
connections with both a scientific theory and a body of
information established over a hundred years ago that previous books (8) by the author have shown is
profoundly consistent with established facts of nuclear and particle physics, as well as
with still hypothetical ideas of this theory. This moves the present discussion from the
tradition of metaphysical speculation and places it in the context of the worldwide search
for an allembracing ‘theory of everything.’ Popular books about superstrings often liken
these vibrating strings to that of violin strings or piano wires. However, their authors
never intend this comparison to be other than metaphorical. How could they, in view of the
fact that the frequency range most common in music is about 500–4000 Hz, whereas
superstrings may vibrate at up to 10^{43} Hz!? Nevertheless,
such a huge difference in frequency does not imply that the mathematics of music is
irrelevant to superstring theory. It indicates
17
only the obvious fact that the latter is
not a branch of acoustics. This mathematics defines only relative, not absolute, pitches of
sounds. Could it be, therefore, that an analogy relates the mathematics of music and
superstring vibrations, one that makes their disparity in frequency irrelevant? Perhaps it
is not accidental (9) that, just as musical tones
group according to their pitch into sets of eight, so, too, eight mathematical objects (the
socalled ‘zero and seven nonzero roots of the exceptional group
E_{8}’) define this mathematical group describing the symmetry of the
unified force between heterotic superstrings. The parallel would exist because, as shown
in reference 10, superstrings — like human
beings — conform to the universal pattern of the “Image of God” blueprint, and so
they must have
mathematically analogous forms of communication, whether through sound waves in the case of
humans or by exchanging virtual messenger particles when superstrings interact with one
another. The heterotic superstring, which the author has shown (11) is the constituent of up and
down quarks in atomic nuclei, is the microscopic Tree of Life and tetractys, its 10 whorls
corresponding to the 10 Sephiroth of the former and to the 10 yods of the latter. The seven
notes of the Pythagorean scale bear a formal correspondence to the seven Sephiroth of
Construction that belong to the Tree of Life. These seven objective aspects of God appear in
the subatomic world as the seven compactified dimensions of spacetime predicted by
supergravity theory and in the heterotic superstring described by Besant & Leadbeater as
the seven orders of spirillae making up each of its whorls (12), the six higher orders
representing the winding of its string components about six of these dimensions curled up
into onedimensional circles (13). As Pythagoras discovered
2,500 years ago, the numbers 1, 2, 3, & 4 symbolised by the four rows of the tetractys
express the relative pitches of the octave, perfect fourth and perfect fifth, leading to the
beautiful, mathematical proportions of the notes of the musical Pythagorean scale.
Similarly, the 10fold, heterotic superstring of ordinary matter extends in 10 dimensions of
spacetime, both being manifestations of the universal mathematical paradigm of the
tetractys governing holistic systems. Little wonder then that its forces and oscillatory
form should turn out to be analogous to the musical sequences playable with tetractyses of
ten octaves of each note of the Pythagorean scale!
References
1) Numbers in boldface are the
number values of the Sephiroth in the four Worlds. They are calculated according to
gematria, wherein the number
18
value of a word is the sum of the numbers assigned
to its letters. They are listed in Table 2 below.
Table 2. Gematria number values of the
Sephiroth in the four Worlds.

SEPHIRAH

GODNAME

ARCHANGEL

ORDER OF
ANGELS

MUNDANE
CHAKRA

1 
Kether
(Crown)
620 
EHYEH
(I am)
21 
Metatron
(Angel of the Presence)
314 
Chaioth ha Qadesh
(Holy Living Creatures)
833

Rashith ha Gilgalim
First Swirlings.
(Primum Mobile)
636 
2 
Chokmah
(Wisdom)
73 
YAHWEH, YAH
(The Lord)
26,
15

Raziel
(Herald of the Deity)
248 
Auphanim
(Wheels)
187 
Masloth
(The Sphere of the Zodiac)
140 
3 
Binah
(Understanding)
67 
ELOHIM
(God in multiplicity)
50

Tzaphkiel
(Contemplation of God)
311

Aralim
(Thrones)
282

Shabathai
Rest.
(Saturn)
317 

Daath
(Knowledge)
474 




4 
Chesed
(Mercy)
72 
EL
(God)
31 
Tzadkiel
(Benevolence of God)
62 
Chasmalim
(Shining Ones)
428

Tzadekh
Righteousness.
(Jupiter)
194 
5 
Geburah
(Severity)
216

ELOHA
(The Almighty)
36

Samael
(Severity of God)
131

Seraphim
(Fiery Serpents)
630

Madim
Vehement Strength.
(Mars)
95 
6 
Tiphareth
(Beauty)
1081

YAHWEH ELOHIM
(God the Creator)
76 
Michael
(Like unto God)
101

Malachim
(Kings)
140

Shemesh
The Solar Light.
(Sun)
640 
7 
Netzach
(Victory)
148

YAHWEH SABAOTH
(Lord of Hosts)
129

Haniel
(Grace of God)
97 
Tarshishim or Elohim
1260

Nogah
Glittering Splendour.
(Venus)
64 
8 
Hod
(Glory)
15

ELOHIM SABAOTH
(God of Hosts)
153

Raphael
(Divine Physician)
311

Beni Elohim
(Sons of God)
112

Kokab
The Stellar Light.
(Mercury)
48 
9 
Yesod
(Foundation)
80

SHADDAI EL CHAI
(Almighty Living God)
49,
363

Gabriel
(Strong Man of God)
246

Cherubim
(The Strong)
272

Levanah
The Lunar Flame.
(Moon)
87 
10 
Malkuth
(Kingdom)
496

ADONAI MELEKH
(The Lord and King)
65,
155

Sandalphon
(Manifest Messiah)
280 
Ashim
(Souls of Fire)
351

Cholem Yesodoth
The Breaker of the Foundations.
The Elements.
(Earth)
168 
2) Article 12, p. 5.
3) Ibid, Section 4.
4) Ibid, Section 7.
5) The number of yods on the boundary of an
nsided, regular polygon divided into
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tetractyses is 3n, that is, (3n–4) yods other than the
four yods on one side. Two such enfolded polygons have (2(3n–4) = 6n – 8) yods outside their
shared edge. But there is no integer solution for n in the equation: 6n – 8 = 44. Therefore,
no pair of similar polygons can have 44 yods outside their shared edge.
6) Article 11, Section 2 & 3, and Article 12, Sections 4, 5 & 7.
7) An nsided, regular polygon with
its sectors each divided into three tetractyses (‘type B polygon’) has (15n+1)
yods. A type B octagon has (15×8 + 1 = 121) yods, i.e., 120 yods surround its
centre. Therefore, 240 yods surround the centres of two separate type B octagons.
8) Extrasensory Perception of
Quarks, Stephen M. Phillips (Theosophical Publishing House, Wheaton, Ill., USA, 1980);
Anima: Remote Viewing of Subatomic Particles, Stephen M. Phillips (Theosophical
Publishing House, Adyar, Chennai, India, 1996); ESP of Quarks and Superstrings,
Stephen M. Phillips (New Age International, New Delhi, India, 1999).
9) Article 12, Section 8.
10) The Mathematical Connection
between Religion and Science, Stephen M. Phillips (Antony Rowe Publishing,
England, 2009).
11) See Ref. 8.
12) Article 2, Section 2.
13) Ibid.
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