Tony Smith's Home Page


The Torah , which is described in the Talmud, is a sequence of

78,064 + 63,529 + 44,790 + 63,530 + 54,892 =

= 304,805 letters

[compare the Rig Veda]
0 Tao, Simplex Physics 1 bit 2 superposition qbit 4 spacetime 16 fermions Ilm-al-Raml 256 Cl(8) IFA 65,536 Torah Genes 2^32 ~ 4 x 10^9 Genome Base Pairs 2^64 ~ 16 x 10^18 Brain Electrons Planck 2^128 ~ 256 x 10^36 Brain GraviPhotons Uncertainty 2^256 ~ 65,536 x 10^72 Particles in Universe
Each letter is either 
one of the 22 Hebrew letters of the Sefirot 
one of the 5 Finals (which may or may not correspond 
                     to the Greek or Chinese 5 Elements), 
a total of 27 letters. 
Stan Tenen is studying relationships between 
the 22 Hebrew letters and the 5 Finals.  

Jeffrey Satinover's book, Cracking the Bible Code (Morrow 1997) discusses the structure of the Torah sequence, and much of what follows in this section of my web page is taken from that book.

A mathematical analysis of the Quran was done by Rashad Khalifa.

On one level the 304,805 letters tell a narrative 
story from Creation to the 10 Commandments, 
the story of the Five Books of Moses:  
Genesis (78,064 letters); 
Exodus (63,529 letters); 
Leviticus (44,790); 
Numbers (63,530); and 
Deuteronomy (54,892).  

There are at least 4 Hebrew-letter versions of the Torah: 
Samaritan - mixture of Babylonian-Jewish traditions, 
            preserving the narrative story but not paying 
            particular attention to the exact letter sequence; 
Ashkenazi - Northern and Eastern Jewish tradition, 
            paying attention to the exact letter sequence; 
Sephardi -  Latin and North African Jewish tradition, 
            paying attention to the exact letter sequence; and 
Yemenite -  Muslim and African Jewish tradition, 
            paying attention to the exact letter sequence. 
In the entire 304,805 letter Torah sequence, 
there are only 9 letter variations among 
the Ashkenazi, Sephardi, and Yemenite versions.  
Between those versions and the Samaritan version, 
there are about 6,000 letter variations, 
even though the narrative stories are virtually identical. 

Why is there so little variation among the Askenazi, Sephardi, and Yemenite versions?

If the original Torah of Moses were written as a continuous 
sequence of letters with no breaks or punctuation or vowels, 
involving only the 22 Hebrew letters,  
if the breaks, punctuation, and vowel placement, 
involving the 5 Finals, 
were given to Moses as a key to be passed down to successor priests, 

might there not be other keys

in addition to the key of breaks, punctuation, and vowel placement 
that produce the well-known narrative story of the Torah.  

Another example of a continuous Hebrew letter-sequence with no breaks, punctuation, or vowel placement is a set of 64 marble and granite tablets of the entire Book of Ezekiel carved in raised letters on a square grid and in continuous script, now in Jerusalem.

How might such other keys work?

(For typographical reasons, I use Latin equivalents of Hebrew letters on my web pages.)

Equal Letter Sequences are one type of key.

Barry Simon has a web article about Equal Letter Sequence Torah Codes. 
In it, he states that "... ELS - Equal Letter Sequences - 
are words separated by the same number of spaces. 
That is, one takes the entire Torah or a specific book, 
drops spaces between words, and 
looks for new words in the resulting stream with, for example, 
every fourth letter rather than successive letters. 
The spacings considered can be quite large ... "
"... You have to realize that the number of ELS is very, very large. 
The number of letters in the Chumash is 304,805 
which means the number of ELS with spacings of 5000 or less, 
forwards or backwards is about 3 billion! 
So when you search for an ELS of a relatively short word, 
you are far from searching a needle in a haystack - 
rather you are searching for a blade of hay. ... "  
"... To cut to the chase, 
[Barry Simon regards] the simple word pair examples 
as an uncontrolled parlor game that [he] cannot take seriously ... 
[he finds] the Nations example totally unconvincing. 
[He also finds] find many reasons to be skeptical about 
the famous Rabbis example and it is far from compelling. ... "  
"... there is no well-established tradition for the codes analysis 
as there is for the established principles of halachic analysis. 
There are a very few, isolated examples of Torah personalities 
who used ELS like devices but in specific instances  
without providing us with any guidance about their general use by us.
The gemara warns us that even traditional methods 
of extracting halachic inference from the text can go awry - 
unless we have a definite mesorah telling us how to employ them. ..."  
Barry Simon makes an important point when he states 
I agree with the facts and opinions stated 
by Barry Simon in that web article.  
Here are three examples (not discussed in Barry Simon's article) 
that appear to me to be "... examples of Torah personalities 
who used ELS like devices but in specific instances  ...": 
Rambam (Maimonides), who lived about 1200 AD, 
commented on the synodic Lunar month of the Jewish calendar 
as being 
29 days, 12 hours, and 793/1080 of the next hour, 
for a total of 29 + 12/24 + 793/(1080x24) =  29.530594 days.  
Bachya (13th century AD) used an ELS with spacing 42 
that started with the first letter of Genesis           - D 
then went to the 42nd letter following that D           - R 
then went to the 42nd letter following that R           - H 
then went to the 42nd letter following that H           - B 
to produce the sequence DRHB, 
which he showed to produce the 29.530594 day synodic Lunar month. 
Bachya did not claim to have discovered 
the Torah-coding of the Jewish Lunar month, 
but gave credit to Nechunya (1st century AD).  
The Torah-code Jewish Lunar month is distinct from 
the Metonic (5th century BC) period of 6,940/235 = 29.5319   days; 
the Callipic (4th century BC) period 
of 4 Metonic cycles, of 27,759/940 =               29.53085  days
the Torah-code Jewish Lunar month is close to 
the period of Hipparchus (2nd century BC) 
of 4 Callipic cycles, of                           29.53058  days; 
is close to the currently accepted 
astonomical observation value of                   29.530588 days; 
is close to the Chinese period of Yang Wei of      29.530598 days 
used in the Ching Chhu calendar of 237 AD  
and consistent with the Chinese 
oracle-bone (13th century BC) period               29.53     days, 
described by Needham in his book 
Science and Civilization in China, 
v.III, Cambridge 1959. 
Some of the calendric data above 
are from the Encyclopaedia Britannica. 
(Thanks to Sam Tarshish for correcting 
 some of my errors on an earlier version 
 of this page.)


There are interesting correspondences between Jewish Kabbala, Torah, and Talmud, and Chinese Buddhism and Taoism. A book that discusses some such correspondences is The Jew in the Lotus, by Rodger Kamenetz, HarperCollins 1995.


Nechunya (1st century AD) and DeMin Acco (13th century AD) 
used the 42-letter name at the start of Genesis 
to calculate that the Age of Our Universe should be 
42 x 1,000 Divine Years, 
and that a Divine Year should be 365 x 1,000 years, 
so that the Age of Our Universe should be 
42 x 1,000 x 365 x 1,000  =  15,330,000,000 years, 
a figure that is consistent 
with present-day astronomical observations and calculations.  
in Genesis there is encoded Mishne Torah, 
the title of the work of Rambam (Maimonides) that codified 
the 613 Commandments given to Moses, 
beginning with the first Commandment given in Egypt 
and ending with 
the 613th Commandment given 50 days later at Sinai.  
Between the beginning of Mishe to the beginning of Torah 
there are 613 letters, one for each commandment. 
As Stan Tenen has noted, 
the 613 Commandments are divided 
into 365 negative Commandments and 248 positive Commandments. 
The 365 correspond to the central number 
in the 27x27 Magic Square and the 9x9x9 Magic Cube.  
The 248 correspond to the 248-dimensional Lie algebra E8, 
the 8-dimensional E8 lattice, and the (3,5) Torus Knot.    

Keys of other types could be based on underlying mathematical structures of the Torah Sequence.

Here are some examples of possibly useful mathematical structures: 
Symmetry Groups; 3,10 Torus Knot; 27 Elements; GF(4) Quantum Codes. 

  1 - symmetry groups related to the 22 Hebrew letters plus 5 Finals, a total of 27.   A general cubic surface is a del Pezzo surface, and has a configration of 27 lines whose symmetry group is the Weyl group of the Lie algebra E6, and to other octonionic structures such as the E8 lattice, the Leech lattice, and related symmetry groups and codes; and  

  2 - the (3,10) Torus Knot
    studied by Stan Tenen and the Meru Foundation, 
    who produced the image above.  

[compare the geometry of a Compton Radius Vortex]

    Stan Tenen notes that the winding pattern 
    of the (3,10) Torus Knot has 
    the pattern of a pseudo-magic square, in which 
    the diagonals and the central row and column add to 15 
    and the total of all 9 numbers is 45.  

[compare the full 3x3 Magic Square]

     Stan Tenen also says: 
"The 3,5 knot appears to be (one of the) most compact possible 
ways to arrange for the letters of the first verse of Genesis 
to pair off. ... For purposes of understanding Kabbalistic texts, 
it appears that two 3,5 torus knots ... fused into a single 3,10 knot, 
better fits the descriptions.  ... The 3,5 knot makes only 3 hands, 

[compare quaternion imaginaries ijk, the 3-sphere, and Poincare Dodecahedral 3-space]

... but the 3,10 knot allows for 6 hands around a still center, 

[compare octonion imaginaries ijk and IJK mirroring each other through octonion imaginary E]

and thus it fits the Biblical description 
of 6 "days" of activity and a "day" of rest.  ...
... One more thing about the 3,10 knot.  
The 3,10 knot is defined by a braided column of 99 tetrahedra.  

[Each column of 99 tetrahedra represents 3 turns in the knot.

Each of the 3 turns in the knot is represented by a column segment of 33 tetrahedra. Each segment of 33 tetrahedra has 4x33 = 132 faces, of which 132/2 = 66 are internal and 132/2 =66 are external. The 66 external faces form 3 strings of 22 faces each, and each string corresponds to the 22 Hebrew letters.

Alternatively, each column of 99 tetrahedra can be represented by 9 column segments of 11 tetrahedra, each representing 1/3 of a turn in the knot. Each segment of 11 tetrahdedra has 4x11/2 = 22 external faces, corresponding to the 22 Hebrew letters. The 22 external faces of each cylindrical segment can then represent a torus by being a tiling element, or tile, in a hexagonal tiling of a 2-dimensional plane.

Each tile has 6 nearest neighbors. If the 6 nearest neighbors are added to the central tile, the group of 7 tiles can correspond to the 7 octonion imaginaries with ijkIJK as neighbors of the central E.

The group of 7 tiles can itself form a single tile in a hexagonal tiling of the plane, so that a set of 7 imaginary octonions is reflexively similar to a single imaginary octonion. You can then consider the group of 7 groups of 7, and so on, in a reflexive-fractal-self-similar way.]

That's 49 from the top, 1 in the center, and 49 to the bottom.  
These numbers are extremely evocative, 
because of other discussions in Genesis and in Kabbalah.  
The 49/50 cycle is the Jubilee cycle - 
- and it's also overwhelmingly the most common 
equal interval letter-skip pattern 
that's been statistically detected in the text. 
(The 50th point, sphere, or tetrahedron is located 
at the tip of the thumb, at the center of the "apple" vortex.)  
There is discussion also of the "5 that become 50", 
which I have identified as the 5 platonic solids 
that are made up of exactly 50 sphere-points at their vertices.  
So if my model hand of 49/50 tetrahedra 
is understood as the "horn" of a cornucopia, 
then the 5 platonic solids literally tumble out of it, 
because they can be reconstructed from 
the sphere-point-tetrahedra "atoms" that the hand is made from.  
In other words, the text specifies a 3,5 knot, 
but it's most productively understood 
as a kind of electron-positron pair, in the form of the 3,10 knot. 
... Also, the Jupiter-Saturn cycle appears to be a 12,40 
or perhaps a 12,39 torus knot.  This is 4 x the 3,10 knot, 
in the same sense as the 3,10 knot is twice the 3,5 
- so I think it's likely that 
the ancients considered all of these as related."    

  3 - 3x3x3 Magic Cube with 27 elements.   Stan Tenen shows a correspondence between the 27 Hebrew letters plus Finals and the 8 vertices, 12 edge-centers, 6 face-centers, and 1 body-center of a 3-dimensional cube.
    There exists a 3x3x3 Magic Cube 
10 24 8 26 1 15 6 17 19   23 7 12 3 14 25 16 21 5   9 11 22 13 27 2 20 4 18
    with central 14 and sum 42.   
    If the 27 entries of the 3x3x3 Magic Cube are put on a line, 
    two such lines generate a 27x27 Magic Square with center 365. 
    There exists a 9x9x9 Magic Cube with center 365.  
    Both the 27x27 Magic Square 
    and the 9x9x9 Magic Cube have 3^6 = 729 entries.  

Stan Tenen interprets the 27 letters of the Magic Cube, which looks like a Rubik cube, as in the following diagram:


With respect to the letters in Stan Tenen's cube, the Archetypal level begins with Aleph and ends with its completion Tet, which means snake in Hebrew, which corresponds to Ouroboros, the primordial snake (or pair of snakes) seizing its tail (or their tails), which was according to Barbara Walker's Woman's Dictionary of Symbols and Sacred Objects a symbol of the great World Serpent that encircled the World and symbolized the entire life of nature. Walker noted that other names for Ouoroboros included the Phoenician word Taaut, Thoth, Hermes, and Zeus. The Snake symbolizes the Chinese years that are equivalent (mod 12) to 1941.

Nathaniel Hellerstein has remarked that 27 = 3^3  
can be represented as the 27 functions from Z3 to Z3.  
27 can also be represented as
3^3  =  (2 + 1)^3  =  2^3  +  3x2^2  +  3x2  +  1  =
                   =   8   +  12     +   6   +  1  =  27
That decomposition may correspond to Hebrew letters by
8                   +    12        +   6   +  1
    5 Final + 3 Elementary        12 Simple        7 Double

Notice that the decomposition of 8 into 5+3 is like the Fibonacci sequence

1 1 2 3 5 8 13 21 ...........

Hypercubes in N dimensions have 2^N vertices   
(2^3 = 8 vertices on a cube)
the total number of sub-hypercubes in
an N-dimensional hypercube is 3^N = (2+1)^N    
(3^3 = 27 in a cube,
being  8 points,
      12 lines,
       6 squares, and the
       1 cube itself.)
Here is a way to look at the 27 maps 
from domain {I,T,F} to range {i,t,f}: 
           i                t                  f
                          ITF                             3   3-to-1
          TF                I
  *       IF                T
          IT                F
          TF                                   I
          IF                                   T
  *       IT                                   F
  *        I               TF
           T               IF
           F               IT                            18   2-to-1
                           TF                  I
                           IF                  T
  *                        IT                  F
  *        I                                  TF
           T                                  IF
           F                                  IT
                            I                 TF
  *                         T                 IF
                            F                 IT
  *        I                T                  F
           T                F                  I
           F                I                  T         6  1-to-1
           I                F                  T
           F                T                  I
           T                I                  F
The starred (*) maps are maps where all the 1-to-1 submaps
take  I, T, F  onto the corresponding  i, t, f.
How do those 27 correspond to the breakdown
            8                  +      12        +   6   +  1 
    5 Final + 3 Elementary         12 Simple        7 Double 
Perhaps the 7 starred maps (*) are the 6+1= 7 Doubles,
that the  5  remaining 1-to-1 maps are the 5 Finals,
that the 12  remaining 2-to-1 maps are the 12 Simples, and 
that the  3  3-to-1 maps are the 3 Elementaries.
When you forget order,
i.e., don't distinguish among members of the domain set {I,T,F},  
the 27 maps collapse to the 10 map equivalence classes  
described by Nathaniel Hellerstein as:
Three 'pure states':          iii   ttt   fff
Six 2-to-1 states:    iit  iif   tti   ttf   ffi   fft
One triple state:                   itf
corresponding to 3 Elementaries and 7 Doubles,   
and to the 10 Sefirot points.

Jonathan Alexander Daniel asks a question about 3^3 = 27:

"Why stop at 27?"

27 = 3^3 is the set of maps from domain {I,T,F} to range {i,t,f}. 
The following ways 
to expand (from 3 to 4), reduce, modify, or expand (to 5 and 6), 
the 27 = 3^3 maps from {I,T,F} to {i,t,f}
were suggested by e-mail conversations 
with Nathaniel Hellerstein and Chris Lofting.   

If T denotes True and F denotes False and I denotes Indeterminate, then

you can EXPAND the 27

by distinguishing between 
two different states of Indeterminancy: I = TF  and I = FT. 

The expansion looks more natural if you denote T by 1 and F by 0, so that TF = 10 and FT = 01, and if you denote the set {TF,FT,T,F} by {TF,FT,TT,FF}, so that you have {00,01,10,11}.

If you expand the domain set {I,T,F} to {TF,FT,T,F}, 
then you have 
the 3^4 = 81 ternary tetragrams of the Tai Hsuang Ching.  
If you expand the range set {i,t,f} to {tf,ft,t,f}, 
then you have 
the 4^3 = 64 = 2^6 binary hexagrams of the I Ching.
If you expand both the domain set {I,T,F} to {TF,FT,T,F} 
and the range set {i,t,f} to {tf,ft,t,f},
then you have 
the 4^4 = 16x16 = 256 elements of the Cl(8) Clifford Algebra:
                       0                       Allspaces
Cl(0)                  1                    R  Tao, Simplex Physics
Cl(1)                1   1                  C  Tai Ji
Cl(2)              1   2   1                Q  Yin-Yang, I Ching, Fa
Cl(3)            1   3   3   1              O  3 Realms, Tai Hsuan Ching
Cl(4)          1   4   6   4   1            S  5 Elements
Cl(5)        1   5  10  10   5   1          M(4,C)
Cl(6)      1   6  15  20  15   6   1        M(8,R), I Ching 
Cl(7)    1   7  21  35  35  21   7   1      M(8,R)+M(8,R), S7 {x} G2
Cl(8)  1   8  28  56  70  56  28   8   1    M(16,R), 8 Trigrams, Tarot, 
                                                    Fa, D4-D5-E6-E7 Physics
                                            2^8 = 16x16 = 8x8 + 8x8 + 
  Fa 256  128   64   32   16   8   4  2 1               + 8x8 + 8x8   Fa
     256+1024+1792+1792+1120+448+112+16+1 = 3^8 Tai Hsuan Ching

where: {x} = twisted (fibration) product, (x) = tensor product, Cl = Clifford Algebra, R = Real Numbers, C = Complex Numbers, Q = Quaternions, O = Octonions, S = Sedenions (which are a NonDistributive Algebra), M(n,K) = nxn matrix algebra over the field K. Compare 0, the Chinese plane of Original God, to Teiohard de Chardin's God of Evolutionary Convergence, to Ahura Mazda, to the God of Akhenaton, to the God of Moses, and to the unitary/unifying God of Sufi Islam. The Binomial Triangle can represent Mount Meru. Basins of Attraction interact by Zhen-Shan-Ren. These structures and symmetries are useful in Information Theory.

Cl(8N) = Cl(8) (x)...(N times)...(x) Cl(8)  Many-Worlds Quantum Theory
                                            Cellular Automata   Wei Qi 

  On the other hand,

you can REDUCE the 27

by ignoring Indeterminate states.  
If you reduce the domain set {I,T,F} to {T,F}, 
then you have 
the 3^2 = 9 ternary bigrams of the Tai Hsuang Ching.  
If you reduce the range set {i,t,f} to {t,f}, 
then you have 
the 2^3 = 8 trigrams of the Ching.
If you reduce both the domain set {I,T,F} to {T,F} 
and the range set {i,t,f} to {t,f},
then you have 
the 2^2 = 4 non-central directions of the 5 Elements. 

Still further,

you can MODIFY the 27

by ignoring Indeterminate states of the range or domain 
and expanding the Indeterminate states of the domain or range.   
If you expand the domain set {I,T,F} to {TF,FT,T,F} 
and reduce the range set {i,t,f} to {t,f},
then you have 
the 2^4 = 16  Tetragrams of IFA, 
              which contains the Trigrams of the I Ching, 
              and which seems to be equivalent to 
              the 16 sets of 4 lines, either broken or unbroken, 
and also to the Ilm al-Raml, 
              or the Science of the Sands. 
              that  was supposed to have been introduced by Idris, 
              the third prophet of Islam (after Adam and Shith) 
              who lived in Egypt 
              before the time of Noah and the flood. 
If you reduce the domain set {I,T,F} to {T,F} 
and expand the range set {i,t,f} to {tf,ft,t,f},
then you have 
the 4^2 = 16  and also get the Tetragrams of IFA, 
              the Ilm al-Raml.  

You can EXPAND the 27 beyond 3^4, to 3^5 and 3^6:

As to 3^6, we have seen that 
the 27x27 Magic Square has 3^6 = 729 entries. 
What about 3^5 = 243? 
3^5 = 243 was used by Plato when he used both 
the 2^N sequence and the 3^N sequence 
to construct a musical scale covering almost 5 octaves: 
1  4/3  3/2  2  8/3  3  4  9/2  16/3  6  8  9  27/2  18  27 
Plato recognized that the N=3 numbers were incomplete, 
so he extended the system to N=8 for 2^N and N=5 for 3^N, 
to get
0                      1
1                    2   3   =  2 + 1
2                  4       9   =  4 + 4+1
3                8           27   =  8 + 12+6+1
4             16               81   = 16 + 32+24+8+1
5           32                   243   = 32 + 80+80+40+10+1
6         64
7      128
8    256
Plato used the numbers 256 and 243 to
form the ratio 256/243, which, along with 9/8,
lets him construct the the first octave as:
1    9/8    81/64    4/3    3/2    27/16    243/128     2
by using the multiplicative intervals:
 9/8    9/8   256/243   9/8    9/8      9/8    256/243
Plato recognized that this was still approximate,
but said that the Demiurge had to stop at this point
in constructing the World Soul.

Note that he stopped at N=8 for 2^N and N=5 for 3^N, also like the Fibonacci sequence

1 1 2 3 5 8 13 21 ...........

If you take that seriously and extend to 4^N and 5^N, you would stop at 3 for 4 (4^3 = 64) and stop at 2 for 5 (5^2 = 25).Of course, you could also stop at 3 because 4 is a composite number, and not prime.



4 - GF(4) Quantum Codes. 
Quantum Information Theory 
is based on the Galois field  GF(4) = {0,1,w,w^2} 
where w    =  (1/2)( - 1 + sqrt(3) i ) 
and   w^2  =  (1/2)( - 1 - sqrt(3) i ). 
{0,1,w,w^2} generates the hexagonal lattice of Eisenstein Integers 
in the Complex Plane; corresponds to the quaternions {1,i,j,k}; 
corresponds to the Tai Hsuan Ching; and 
corresponds to symmetries of the Torah such as 
the (3,10) Torus Knot and the 3x3x3 Magic Cube.  



Torah Music

(compare Vedic Music and IFA Music)


According to a Cantor's Corner web page:

"... Biblical Cantillation ...

... Like other ancient cultures, the Jewish people sought to transmit their sacred texts orally and with the aid of melody. In fact the art of chanting the Torah is over two thousand years old and evolved from a solely oral tradition, to a formalized system of musical notation that we now call trope, taíamim, or musical cantillation.

This Biblical cantillation system is made up of 28 signs [compare the 28 generators of Spin(8) and the 24 toque of IFA Oru] and each sign stands for a specific musical pattern or melodic motif. These signs appear above and below the Hebrew text. The purpose of the cantillation signs is to punctuate, accentuate, and phrase the text and thus to enhance our understanding of the text. For example, in terms of accentuation, how do you know whether to say the English words PRO-ject or pro-JECT ñ the accent elucidates which word would make sense in a given context. The cantillation system also adds melody to text, which helps us remember the text.

These same trope or cantillation symbols are used to chant various Biblical books, but these symbols represent different melodic patterns in these various books. Therefore the cantillation you hear is unique for the Torah chanted on Shabbat and Festivals, for the Torah during the morning High Holy Days, for the Prophets, for The Scroll of Esther, for The Scroll of Lamentations, for The Songs of Songs, for The Scroll of Ruth, and for Job. The word "ta-am" connected to the plural ta-amim means taste or flavor and there is no doubt that these different Biblical books are chanted differently to give different meanings to their texts.

In their wanderings and exile, the Jewish people took their cantillation system wherever they went, but it absorbed some different musical styles based on their geographic location. Various musical interpretations of the which included the Ashkenazic, Sephardic, Moroccan, Syrian, Baghdadian, and Yemenite. ...".


According to an Eliezer Segal web page:

"... The Jewish Cantillation of the Bible ...

This page presents the traditional cantillation melodies used in the synagogue for the chanting of the scriptural readings from the Pentateuch (Torah, "Five Books of Moses") and the Prophets, a section from which is chanted as a "conclusion" ... "Haftarah" .... of the Torah reading on Sabbaths and festivals.

These signs, which (like the vowels) are not written down in the "official" scrolls used in the synagogue, indicate both the syntactic structure and the musicial rendering of the Biblical verses, and often the accenting of the words as well.

They are divided into three main types:

  • Connecting accents, which lead on to the next word;
  • Separating accents, which create a pause; and
  • "Stand-alone" accents, which do just that.

Some of the accents perform more than one function, and hence have been placed between columns.

The musical rendering used in this stack follows the Eastern European customs, found in most North American synagogues. Other communities, such as the German, Spanish or Yemenite Jews, have different versions (though the signs themselves and their syntactic functions) are universal. In addition, there are special renderings in use for other books of the Bible (e.g., Esther and Lamentations), or for special occasions (e.g., festivals).

Though the same cantillation signs are used (for the most part) for different books of the Bible, and they have the same accent and syntactical roles wherever they appear, they are actually chanted in different ways. This page presents samples of the main tunes used for the reading of the Torah and Prophets. Different tunes exist for other books or for certain festivals. ...

Notes that connect   Notes that separate        Notes that
 to the next word     from the next word:       stand alone
  (Conjunctive)	       pauses
Mahpakh                    Pashta               Zaqef Gadol
Munah                    Zaqef Qaton             Geresh
"Zaqef Gadol")	
Munah                      Munah                 Pazer
(Preceding               (Preceding 
a Revia')                another Munah)
Munah                    Merkha Kefullah        Telisha Gedolah
Darga                       Atnahta             Telishah Qetanah
Merkha                       Silluq              Revia'
                          (Sof Pasuq)
Tifha                        Silluq              Shalshelet
                         (Sof Parashah)
Yetiv                        Segol               Gershayim
Zarqa                     Qarnei Parah
Yerah Ben Yomo
              Qadma ve'Azla               Tevir   ...". 

Note that the above list has 29 entries, because Silluq, whose symbol is |, is counted twice.



In recent times, using somewhat different techniques, Stan Tenen's Meru Foundation has produced The Music of Genesis.

According to the CD case notes, the CD contains:






There may be, and probably are, many other symmetries that would be useful in studying the Torah, and I hope that people who have insight about such symmetries will work on them and write about them.


What about Torah study by non-Jews?  

"... a non-Jew who studies the details of the seven Noahide laws, which are incumbent on him, deserves the honors due a Kohen Gadol (Sanhedrin 59a). The study of the seven Noahide laws may lead him to study most of the precepts of the Torah (Meiri to Sanhedrin 59a; see Responsa, Rama section 10). ...

... Noahide Laws - the seven commandments given to Noah and his sons, which are binding upon all gentiles. These laws include the obligation to have a body of civil law, and the prohibitions against idolatry, immorality, bloodshed, blasphemy, stealing and robbing, and eating limbs from a live animal. ...". (From Talmud Bavli / Tractate Chagigah, The Gemara, The ArtScroll Series / Schottenstein Edition, Mesorah Publications Ltd. (1999) 13a 3)



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