Review of Freemasonry

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by Bro. William Steve Burkle KT, 32°
Scioto Lodge No. 6, Chillicothe, Ohio.
Philo Lodge No. 243, South River, New Jersey

The Tetractys and the Sephiroth represent similar concepts; however the link between these two concepts would not be readily apparent were it not for their common use of the Tetragrammaton. The Tetagrammaton serves as a bridge between these concepts which span time, culture (Greek and Hebrew), and multiple Masonic rites and rituals. This paper discusses the Tetragrammaton, the Tetractys, and the Sephiroth and shows how the three are related.


One of the things I’ve learned about Freemasonry is that rarely does a single symbol stand alone in its allusion; rather it shares the same allusion or parts of the same allusion with many other symbols. This commonality of allusion in our symbolism is not always obvious, and in many cases the commonality exists as an overlap with another symbol or allusion. Overlap such as this is a useful bridging technique, helping us make a connection between related concepts. The ability to discern such overlap often becomes difficult however when the overlapping concepts span cultures, languages, time, and in some cases several different rites and degrees within those rites.

One such difficult to discern overlap exists in which a similar theme spans cultural and language differences between the ancient Greeks and the Hebrews; a time period of several centuries; the Blue Lodge, Scottish Rite, and York Rite; and multiple degrees in each of these rites. Ultimately, by connecting these symbols at the overlap (i.e. bridging), we begin to see a common concept emerge of greater breadth than can be seen by looking at any single piece. The symbols to which I refer are the Greek (Pythagorean) symbol known as the Tetractys and the Kabalistic symbol known as the Sephiroth. The bridge which connects these two important symbols is the Tetragrammaton a glyph representing the ineffable name of the Deity.

This paper will examine the Tetractys and the Sephiroth and demonstrate how they are linked by the Tetragrammaton. It will further explore the commonality in meaning to be found in the Tetractys and Sephiroth.  We will begin this exploration by examining the Tetragrammaton, which is the bridge connecting the two symbols. The reader should be aware that this exploration involves three concepts which could each warrant an entire book-length discussion. I will provide here no more than a summary of these concepts with the hope that I will be forgiven for any omissions.

The Tetragrammaton

Literally, the word Tetragrammaton[i] means “having four letters” and is the name given to the four Hebrew letters (Yod-He-Vav-He) which represent the name of God. In the English transliteration these letters are usually shown as YHVH or IHVH and are pronounced as either “Yahweh” or “Jehovah”.  In Hebrew the pronunciation is commonly[ii] Adonai or Elohim depending upon Masoretic or vowel points employed. The use of the Tetragrammaton to represent the name of God can be positively traced to a time prior to the 9th Century B.C.E. based upon archeological[iii] evidence. It is probably much older. In Hebrew tradition[iv], the actual name of God could be pronounced only by the High Priest and only once each year on the occasion of Yom Kippur, the Day of Atonement. Over time (possibly a time corresponding to the destruction of the second Temple), the correct pronunciation of the ineffable name was forever lost.

 There are many interesting correspondences between the signs and symbols of Freemasonry and the Tetragrammaton. For example, according to Bro. Manly P. Hall[v]:

“By placing the four letters of the Tetragrammaton (IHVH)in a vertical column, a figure closely resembling the human body is produced, with Yod for the head, the first He for the arms and shoulders, Vau for the trunk of the body, and the final He for the hips and legs. If the Hebrew letters be exchanged for their English equivalents, the form is not materially changed or the analogy altered.”


This concept is illustrated in Figure 1.


            tetra01.jpg - 17071 BytesThe reader will notice that all three of the penalties of the obligations for the symbolic degrees are represented in this figure as are the anatomical points upon which Master Hiram Abif was assaulted by the three ruffians.  The Perfect Points of Entry are also to be found in the nested characters of the ineffable name.

As is the case with all the symbols we will be discussing, the Tetragrammaton is visible primarily in the degrees of the York Rite and Scottish Rite; however this was not always the case. Ritual has undergone dramatic change over the centuries, and the Blue Lodge MM Degree at one time directly included the Tetragrammaton in its symbolism[vi]. According to Mackey[vii]:

"JEHOVAH is, of all the significant words of Masonry, by far the most important. Reghellini very properly calls it 'the basis of our dogma and of our mysteries.'...The history of the introduction of this word into the ritualism of Freemasonry would be highly interesting, were it not so obscure. Being in almost all respects an esoteric
symbol... That this name, in its mystical use, was not unknown to the Medieval Freemasons there can be no doubt... It is now conceded, from indisputable evidence, that the holy name was, in the earlier years, and, indeed, up to the middle of the last century, attached to the Third Degree, and then called the Master's Word...Third Degree refers to 'the mystic word, the Tetragrammaton.'"

Therefore, given the aforementioned understanding that the Tetragrammaton was (and still is) used as a substitute for uttering the true name of God, then the substitute for the Masters Word in the symbolic degrees almost certainly alludes to the Tetragrammaton.

The Tetragrammaton is directly introduced during both the York and Scottish Rite Rituals[viii] as a glyph discovered encrusted upon a golden plate during the exploration of a certain vault. In the Scottish Rite version the golden plate is discovered resting upon a triangular pedestal. In the York Rite version, the glyph rests upon a triangular plate atop the Ark of the Covenant and is shown surrounded by three words encoded using a unique cipher system (commonly referred to by modern Cryptologists as the “Freemasons Cipher”). There are many variations in the details which underpin this ritual; in some versions of the Royal Arch ritual, the plate is triangular, encrusted with Jewels, and affixed to a triangular stone made of agate[ix]. Regardless of rite, version, or variation, the Tetragrammaton forms is an essential element in Freemasonry.

The Tetractys

The Tetractys is a figure consisting of ten points arranged in four rows with one, two, three,[x] and four points in each row sequentially, and which is inscribed within an equilateral triangle[xi] (see center illustration, Figure 2). The Pythagoreans believed a complex relationship existed between the structure of the Tetractys and the creation of the physical universe[xii]. Concerning the Tetractys, Manly P. Hall wrote[xiii]:

 The mysterious Pythagorean tetractys, or four rows of dots, increasing from 1 to 4, was symbolic of the stages of creation. The great Pythagorean truth that all things in Nature are regenerated through the decad, or 10, is subtly preserved in Freemasonry through these grips being effected by the uniting of 10 fingers, five on the hand of each person.”


            While the Tetractys may be used as either a multiplication or as an addition device, the more common method of use is that in which the digits of each row are summed, and the sums of each row are then summed themselves. Thus for the Tetractys shown in the center illustration of Figure 2 we have 1 X 4 (1 + 1 + 1 + 1) = 4, 2 X 3 = 6,  3 X 2 = 6, and 4 X 1 = 4. The total of these sums is 4 + 6 + 6 + 4 = 20. 

The Tetractys may also be arranged as shown by the right-hand side illustration (Figure 2) as a device which employs duple and triple progressions. When arrayed in this fashion the figure is called the “Lambdoma”. This figure is also called the “Platonic Lambda” as a result of its its inclusion in the Timaeus of Plato[xiv].  The sides of the Lambdoma have values of 1, 2, 3, 4, 9, 8, and 27.  Per the Pythagoreans, the duple progression (1, 2, 4, 8) represents the evolution of the vehicle proceeding out of unity. The triple progression inverted (27, 9, 3, 1) represents the development of consciousness. The number 1 is included in both progressions since it was considered the number from which both progressions evolved. Generally speaking, the duple progression, being even numbers represented the feminine, and the triple progression being odd numbers represented the masculine. The Tetractys was conceived to represent four Emanations and four planes[xv]. The first Emanation, the Monad, is the source of latent power and corresponds to a Geometric Point. The second Emanation occurs when the point moves thus producing a line. This Emanation is called Growth (Auxe)[xvi]. The third Emanation occurs when the line moves creating a surface or plane. This Emanation is called Skin (Khroia). The fourth and final Emanation is developed when the surface moves, generating a solid, called Body (Soma).

The first Plane is the Monad (one), and it corresponds to the virtue Wisdom. The second Plane comprises the Dyad (two) and the Triad (three), and it corresponds to the virtues Strength and Courage. The third Plane is comprised of the Tetrad (four), Pentad (five), and Hexad (six) and represents the virtue Beauty. The fourth Plane is comprised of the  Heptad (seven), the Octad (eight), Ennead (nine), and the Decad (ten).  The fourth Plane represents the virtue Justice. Beauty, Wisdom, Goodness, and the corresponding connecting properties, Love, Truth, and Trust, which are the Chaldaean Virtues all are correspondences of the Tetractys[xvii]. Through the Emanations and Planes the universe was created.

tetra02.jpg - 19756 BytesThe Tetractys also represented the four elements air, earth, fire, and water; the four rows sum to the number ten; This figure is emblematic of the Tetragrammaton[xviii], or sacred name of four letters. 

              I would like to concentrate at this point upon the Tetractys shown on the left-hand side of Figure 2 in which the Hebrew Characters of the Tetragrammaton are arrayed. The Tetractys of the Tetragrammaton is frequently associated with the Biblical passage from John 1:1[xix] :

“En arched en ho logos, kais ho logos en pros ton then, kais theism en ho logos”

Translated as:

"In the beginning was the Word, and the Word was with God, and the Word was God."

Each Hebrew Character has a corresponding numerical value (See Table 1). This is similar to the dual use of Roman letters as both alphabetic and numeric characters.

tetratable01.jpg - 10073 Bytes

            Based upon the numeric values of the Hebrew Characters shown in Table 1, the Tetractys of the Tetragrammaton would calculate as follows: 10 X 4 = 40, 5 X 3 = 15, 6 X 2 = 12, and 5 X 1 = 5. The sum of the products would then be 40 + 15 + 12 + 5 = 72. The number 72 is significant because it represents the number of ineffable names of God. Naturally, such numerical significance would be of great interest to Kabalists. In fact, Christian Mystic Jakob Boehme (1575-1624 A.D.) used a variation of this arrangement as his personal symbol[xx], and the Tetractys can be found in a form similar to that shown in Figure 2 on the apron of the 17th Degree of the Scottish Rite.  The number 72 also happens to be the maximum number of Companions in addition to the Principals and Scribes in a Royal Arch Chapter[xxi].

tetra03.jpg - 20826 BytesThe Tetractys has an unusual geometric layout as can be seen in Figure 3. A proper geometric construction can best be made by dividing the Delta triangle into a series of smaller subsidiary Deltas. Each of these subsidiary Deltas may also be divided into smaller Deltas and so on ad infinitum. This unique feature, in which each smaller piece is an exact copy of the original is called holography. Interestingly, modern scientists believe the universe to be holographic, and have connected much of the philosophy of the Pythagoreans to Quantum theory[xxii].


The Tetractys displays many more interesting geometric properties, including several related to the 3, 4, 5 Pythagorean triangle which is a prominent feature of yet another well known Masonic symbol. Knutson, Tao and Woodward[xxiii] studied the correspondence between Tetractys and honeycombs and discovered that the vertices of the honeycomb form small triangles in a Tetractys. The beehive, is also a prominent Masonic symbol. I will further mention in passing that the Tetractys is used as the basis for a type of poetry in which the first line contains one word, the next two words, etc. For a closer look at this interesting poetic style used in a Masonic context, the reader is referred to the works of Bro. Ted Berry at The Masonic Poets Society[xxiv].

            It has been suggested[xxv], [xxvi] that “the Tetractys displays the Tree of Life collected into its most efficient mathematical formation”. The Tree of Life, or Sephiroth, is itself closely associated with the Tetragrammaton, which, as mentioned, provides a convenient bridge between the two symbols. Through this bridge these two symbols may be demonstrated to embody very similar concepts.

The Sephiroth

            Figure 4 depicts the “Tree of Life” or Sephiroth. Each Sphere (Sephira) in the tree represents an emanation. Each of the vertical columns of Spheres in the Sephiroth are traditionally considered to represent a pillar, and each pillar is named according to the central concept which it represents; thus in Figure 4 we have the pillars Justice, Beauty, and Mercy left to right, respectively. This figure is a modified version of the illustration of the Sephiroth which is used in the Knight Kadosh Grade[xxvii] of the AASR. The modifications consist of the addition of all twenty-two paths, and the addition of the pseudo-Sephira Daath (Knowledge) between Kether and Tipareth in the middle pillar. The illustration also includes the Hebrew Character labels for each of the twenty-two paths and each of the ten Sephira (other than Daath). Each of the ten regular Sephiroth are the ten holy attributes which are said to inhabit spheres of the first emanation of creation[xxviii]. tetra04.jpg - 24492 BytesThe ten Sephirot are divided into masculine and feminine Sephira, with those Sephirot on the left side (left column) being feminine and those on the right side (right column) being masculine. Each of the Sephira, other than Kether, is also either masculine or feminine in relation to the Sephira which precedes or follows it.

The best description of the principles which govern the Sephiroth is perhaps best conveyed by quoting the first two of the seven ideals of Kabalism[xxix] as summarized by Dr. Wynn Westcott:

“(1).    God, the Holy One, the Supreme Incomprehensible One, AIN SUPH, is not the direct Creator of the world. Everything proceeded from the primordial source by successive emanations, each reaching a lower level than the preceding one. Hence, the Universe is, in fact, God manifested, the last and farthest removed production being matter, which is therefore seen as that which is deprived of perfection.

(2).       All that is known or perceived is formed upon the type-model of the Sephiroth.”

            The Name of each Sephira, the Hebrew Character by which it is designated, it’s name, and it’s Correspondence are given in Table 2[xxx].

tetratable02.jpg - 34617 Bytes

tetra05.jpg - 29403 BytesThe relationship of the Tetragrammaton and the Sephiroth is illustrated in Figure 3 in which each of the “Four Worlds” of the Sephiroth are shown. Note that each World also corresponds to one of the four ancient elements.

            The source of the emanations is described as being hidden by three veils[xxxi] - “Negativity” (Ain),  which being of three letters alludes to the first three Sephiroth; “The Limitless” (Ain Soph), which alludes to the first six Sephiroth; and “The Limitless Light” (Ain Soph Aur), which being composed of nine letters alludes to the first nine Sephiroth. This complex concept is meant to describe the source as having Negative Existence and that the limitless ocean of light by which the Sephiroth manifests itself has no center, but rather concentrates in Kether, the first Sephira. As can be seen, the depth of the philosophy involved here can be a bit daunting. The cloud which comprises the Ain, Ain Soph, and Ain Soph Aur, is rendered below as Figure 6. As an interesting aside I have also provided an illustration of one well-known version of the Rosicrucian Symbol beside that of the Cloud of Ain. The similarity is worth noting.

            tetra06.jpg - 23861 Bytes The Sephiroth, much like the Tetractys may be shown to have Geometric regularity in its construction. In Figure 7, I have provided a construction of the Sephiroth which is based upon five aligned circles overlapping such that the circumference of each passes through the center(s) of the circle(s) to which it is adjacent. The points at which the circles intersect coincide with the center of the individual Sephira on the left and right pillars, and the circle centers coincide with the four Sephira (and Daath) in the middle pillar. Circles which overlap in this manner also form another important Masonic Symbol known as the Vesica Pisces. The Vesica Pisces may be demonstrated to have certain dimensions which relate to the Golden Mean; Consequently it is not surprising that the Sephiroth also contains this enigmatic coding.tetra07.jpg - 24936 Bytes




            It should be emphasized that the Tetractys and the Sephiroth are not by any means identical concepts, but rather concepts which share many similarities. One of these commonalities is that both involve the Tetragrammaton as an integral part of their meaning. Perhaps the most profound similarity however is that both propose a concept for the Creation of the Universe, both material and spiritual, which utilizes a system of Emanations which proceed in stages from the Divine to the physical universe. S.L. MacGregor Mathers[xxxiii] clearly believed that the Tetractys system of the Pythagoreans was a refinement of that provided in the earlier Sephiroth which incorporated mathematical models. This would be consistent with the reported journeys of Pythagoras to Babylonia where he would have been introduced to Kabalism. Both systems incorporate references to the Classical Elements, and both are reported to have correspondence to the Planets and to Astrology. I would add that both the Tetractys and the Sephiroth include a left-hand series of Emanations which are regarded as Feminine, and a right-hand series of Emanations which are considered Masculine.

            tetra08.jpg - 18885 BytesOne of the more interesting correspondences of the Symbols used to illustrate the Tetractys and the Sephiroth however lies in the apparent overlap between their Geometric layout. Figure 8 shows this correspondence by providing a composite image of Figure 3 and Figure 7. Note that the Geometries as depicted coincide.

I believe that it is a tribute to the genius of the men who developed Masonic ritual and symbolism that the Tetractys and the Sephiroth are both at the root of our Craft, and that they provided a bridge by which the two could be joined.

[i]     Tetragrammaton. (2008). In Merriam-Webster Online Dictionary. Retrieved December 14, 2008, 


[ii]     Tetragrammaton with Vowel Points for Various Pronunciations. (2007). In Jewish Delaware. Retrieved December 14, 2008, 


[iii]    Neuhoff, Juergen. (2007). The Tetragrammaton in the Los Lunas Decalogue. Retrieved December 14, 2008 


[iv]    Turnbull, Everett R.  & Denslow, Ray V. (1956). A History of Royal Arch Masonry. Kessinger Publishing, 2004. ISBN 1417950064, 9781417950065

[v]     Hall, Manly P. (1928). The Tree of the Sephiroth. The Secret Teachings of All Ages: An Encyclopedic Outline of Masonic, Hermetic, Qabbalistic & Rosicrucian Symbolical Philosophy. Philosophical Research Society; Revised edition (June 1978). pp. 121. ISBN-10: 089314830X; ISBN-13: 978-0893148300.

[vi]    Preuss, Arthur. (1908). Study in American Freemasonry. Kessinger Publishing. 2003.  pp. 172. ISBN 0766156931, 9780766156937.

[vii]   Mackey, Albert G. (1871). Encyclopaedia of Freemasonry, Vol. I.  Kessinger Publishing Company (2003). ISBN-13: 9780766147195.

[viii]  De Hoyos, Arturo. The Mystery of the Royal Arch Word. Heredom. Volume 2, 1993. Retrieved December 27, 2008 

from Pietre-Stones Review of Freemasonry.

[ix]    De Clifford, Norman Frederick. (1902). Egypt, The Cradle of Ancient Masonry. Kessinger Publishing, 1995. ISBN 1564595242, 9781564595249

[x]     DaFoe, Stephen. (2008), Masonic Dictionary. Retrieved December 26, 2008 


[xi]    Weisstein, Eric W. "Tetracyts." From Mathworld-A Wolfram Web Resource.

[xii]  From Absolute Astronomy  Retreived December 26, 2008.

[xiii]   Hall, Manly P. (1928). The Secret Teachings of All Ages: An Encyclopedic Outline of Masonic, Hermetic, Qabbalistic & Rosicrucian Symbolical Philosophy. Philosophical Research Society; Revised edition (June 1978). ISBN-10: 089314830X; ISBN-13: 978-0893148300.

[xiv]  Plato. Timaeus. Project Gutenberg. Trans. Benjamin Jowett. Retrieved December 30, 2008 from

[xv]    Cornford, F. M. (1937). Plato's Cosmology: The Timaeus of Plato Translated with a Running Commentary, London: Routledge & Kegan Paul.

[xvi]   MacLennan, Bruce. More About the Tetractys. Retrieved December 30, 2008 


[xvii] Opsopaus, John. (2004). A Summary of Pythagorean Theology, Part V: Theurgy. Retrieved December 30, 2008 


[xviii]       Pike, Albert. Morals and Dogma of the Ancient and Accepted Scottish Rite of Freemasonry. Kessinger Publishing; Facsimile edition (March 1992). Ch 29.pp. 602. ISBN-10: 1564592758; ISBN-13: 978-1564592750

[xix]   Ibid. The Wonder of the Tetragrammaton Tetractys. Retrieved December 26, 2008 from

[xx]   Stephany, Paul. Defining Freemasonry. In Helium. Retrieved December 23, 2008 


[xxi]   Nullen, Giles C.H. Official History of Freemasonry. Retrieved December 27, 2008 from

[xxii] Arkhipov, A.A.  Harmony of the Froissart Theorem in Fundamental Dynamics of Particles and Nuclei. State Research Center “Institute for High Energy Physics”. Moscow, Russia. In arXiv:hep-ph/0208263v3 28 Jan 2003. 

Retrieved December 27, 2008 from

[xxiii]       Woodward, Chris, Knutson A., & Tao T. (2004). The Honeycomb model of $GL_n$ Tensor Products II: Facets of the Littlewood-Richardson Cone. In Journal of  American Mathematics Society. 17  no. 1, 19--48. 

Retrieved December 26, 2008 from

[xxiv]  Berry, Ted. The Masonic Poets Society. Retrieved December 26, 2008 from

[xxv] The Tetracyts of the Decad. Abrahadabra Institute Retrieved December 26, 2008 from

[xxvi] Tetracyts. All Experts Encyclopedia. Retrieved December 26, 2008 from

[xxvii] Knight Kadosh. The Thirtieth Grade of the Ancient and Accepted Scottish Rite, and the First Degree of the Chivalric Series. Hirams Web. University of Bradford.  Retrieved  on September 29, 2008.

[xxviii] Freemasonry in Israel. Retrieved December 27, 2008 from

[xxix] Cleland, J.N. The Kabbalah and Freemasonry. Bonisteel Masonic Library.  Retrieved December 27, 2008 from

[xxx] Scholem Gershom. (1990). The Formative Meanings of the Ten Sphiroth/Sephiroth Belimah.  In Origins of the Kabbalah. Princeton. Retrieved December 27, 2008 from

[xxxi] Mathers, S.L. MacGregor. (1887). Qabalah Unveiled. Reprinted (2006) as The Kabbalah: Essential Texts From The Zohar. Watkins. London. pp. 26. ISBN-10: 1-84293-128-9;  ISBN-13: 9-781842-931288.

[xxxii]  Ibid.

[xxxiii] Ibid.

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