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Jewish Kabbalah · Arrangement study

The Gra arrangement

The Gra tree begins with a practical problem: how can the three Mothers, seven Doubles and twelve Simples of Sefer Yetzirah be placed on twenty-two lines without losing their threefold pattern? Its answer is geometric—Mothers across, Doubles down and Simples on the diagonals.

The Vilna Gaon and the printed diagram

“Gra” is a Hebrew acronym for Gaon Rabbi Eliyahu: Eliyahu ben Shlomo Zalman, the Gaon of Vilna (1720–1797). He was an exceptionally influential Lithuanian rabbinic scholar, a kabbalist, and the best-known opponent of early Hasidism. The arrangement shown here is preserved in a figure printed with his commentary on Sefer Yetzirah. This reconstruction uses the Warsaw 1884 plate and Aryeh Kaplan’s discussion of its letter placements. [1] [3]

The commentary first appeared posthumously at Horodna in 1806. The plate available here comes from a later printing, so “Gra arrangement” names a received diagram rather than an autograph drawing. Editors, printers and later commentators stand between the Gaon’s teaching and the image now on the screen. [4]

Turning 3–7–12 into a diagram

Sefer Yetzirah opens with thirty-two paths of wisdom: ten sefirot and twenty-two letters. It then divides the alphabet into three Mothers, seven Doubles and twelve Simples. [2] The diagram makes that division visible by giving each class its own direction: three horizontal lines, seven verticals and twelve diagonals.

3Mothers3 horizontals
7Doubles7 verticals
12Simples12 diagonals

Every letter on this arrangement follows the rule. The rule explains the drawing, but the drawing remains an interpretation. Sefer Yetzirah supplies numbers, classes, directions and relations; it does not print this exact Tree in its early textual recensions. [2] [3]

A different middle

Beside a Kircher or Golden Dawn tree, the change is immediately visible. Tiferet stands above Chesed and Gevurah, while Yesod stands above Netzach and Hod. These shifted rows create three horizontal crossbars and leave room for the seven vertical paths. [1]

Upper centre
Keter descends directly to Tiferet through Beth.
Middle centre
Tiferet descends directly to Yesod through Resh.
Lower centre
Yesod descends directly to Malchut through Tav.
Numbering
Tiferet is 4, Chesed 5 and Gevurah 6 on this arrangement.

There are ten visible, counted sefirot here, from Keter through Malchut. This rendering does not insert Da‘at or remove Malchut. Online summaries often blend this plate with a different diagram that Kaplan called the “Natural Array,” which is one reason the application treats the source plate, the reconstruction and later claims separately. [3]

The twenty-two letters

Read down within each class. These lists are generated from the same records that draw the interactive Tree, so the path pages and the diagram always use the same letters and endpoints.

What the plate actually prints

Two letters in the 1884 figure are duplicated where the geometry requires members of another class. The reconstruction follows Kaplan’s corrected reading, while the detail pages retain the printed discrepancy in their notes. [1] [3]

ד

Daleth · path 18

Left-hand of the upper pair, and the exact mirror of Chochmah: four lines in the same four directions, with the Double Daleth dropping to Gevurah as Gimel drops to Chesed. On the 1884 plate this is where Lamed is printed for a second time, in the place where Dalet belongs; Dalet appears nowhere on it.

ת

Tav · path 32

Left, in the sixth row, and the mirror of Netzach. The Double Peh comes down from Gevurah, a diagonal comes across from Yesod, Mem crosses to Netzach, and Qoph falls to Malchut. Mem is printed twice on the 1884 plate — correctly here on the horizontal, and again at the foot of the tree where Tav belongs.

The plate also carries a small unlabelled double circle above the apex and another below the foot. Since the printing does not identify them, this reconstruction leaves them uninterpreted instead of assigning them to Ein Sof, Da‘at, a passive Malchut or another doctrine. [1]

Two diagrams, two purposes

Question Gra arrangement Kircher / Hermetic arrangement
Primary purpose here Make the 3–7–12 letter classes visible as line orientations. Serve the received Western esoteric map and its later correspondence system.
Middle rows Tiferet above Chesed/Gevurah; Yesod above Netzach/Hod. Chesed/Gevurah above Tiferet; Netzach/Hod above Yesod.
Mothers Aleph, Mem and Shin are the three horizontals. None of the three Mothers lies horizontally.
Added systems No tarot, Golden Dawn colours or planetary path scheme. Tarot, astrology, colours, elements and ritual grades are integral to its modern reception.
What its path numbers mean Local order on this arrangement. Local Hermetic order; the same number must not be used to join the two trees.

The comparison describes the two arrangements used in this application. The Gra column follows the printed plate and Kaplan’s reconstruction; the Hermetic column follows the separate history outlined on the evolution page. [1] [3] [5]

Boundaries of this reconstruction

  • It is one Jewish arrangement. Ari, Cordoveran, Gra and modern “Natural Array” diagrams answer different questions and do not share one settled path table. [3]
  • It carries no Golden Dawn correspondences. The neutral sphere tones are interface colours. They are not a hidden King or Queen scale, and no tarot card belongs on these paths.
  • The plate is not ancient. Sefer Yetzirah is far older than the plate, but the geometrical arrangement belongs to its later history of interpretation. [4]
  • Its geometry answers a particular question. Formal fidelity to the 3–7–12 rule explains this arrangement’s value. Other diagrams may preserve other lineages and do other work.

Study the live diagram with its provenance open →

Sources

  1. context National Library of Israel, “The Vilna Gaon” His dates, scholarship, Kabbalah and leadership of the opposition to Hasidism. Sefer Yetsirah, Warsaw edition (1884) The printed volume and figure from which this arrangement’s provenance begins.
  2. primary text Sefer Yetzirah, Gra version at Sefaria Ten sefirot and the twenty-two letters; continue to chapters 2–5 for the three classes.
  3. modern edition Aryeh Kaplan, Sefer Yetzirah: The Book of Creation, revised edition (1990), pp. 22–32, 132–133, 166 and 205. Copyrighted; cited by locator only. Kaplan’s figures and commentary supply the corrected reading used here.
  4. edition history First edition of the Gra’s Sefer Yetzirah commentary, Horodna 1806 Bibliographical record for the commentary’s first posthumous printing; the app’s geometry follows the later Warsaw plate.
  5. context Kabbalah, Cabala, Qabalah The wider history of the Jewish tradition and its Christian and Hermetic receptions.