At-bach is a method of alphabetic transformation that is initially divided into three groups, in accordance with either of two systems:
- 9, 9, and 4 when the five letters with a final form (mem, nun, tzadik, pei, and chaf [refered to as mantzapach, for short]) are not considered.
- 9, 9, and 9 when the five letters with a final form are considered.
The transformation pattern is “reflective” within each group. In a group of nine, the first and last letters transform one into the other, as do the second and eighth, the third and seventh, and the fourth and sixth. The fifth letter possesses no partner within the group. The “logic” behind this transformation pattern is that in each of the groups of nine letters the sum of each pair equals 10, 100, or 1000 (all identical when calculated as reduced value).
The name At-Bach is a reference to the first two of these transformations: alef-tet and beit-chet.
In Kabbalah, this is the alphabetic transformation whose elements correspond to the sefirot within the partzuf of kingdom (malchut)–Nukva Deze’ir Anpin.