Atbach (אִטבִּח) is not a real word, but a factitious cabalistic term denoting by its very letters the mode of changing one word into another by a peculiar eommutation of letters. The system on which it is founded is this: as all the letters have a numerical value, they are divided into three classes, in the first of which every pair makes the number ten; in the second, a hundred; and in the third, a thousand. Thus:
דו, גז, בח, אט, every pair making ten.
מס, לע, כפ, יצ, "a hundred.
תם, שן, רŠ, קוֹ, "a thousand.
Three letters only cannot enter into any of these numerical combinations, ה, נ and ך. The first two are nevertheless coupled together; and the last is suffered to stand without commutation. The commutation then takes place between the two letters of every pair; and the term Atbach thus expresses that א is taken for ט, and ב for ִח, and conversely. To illustrate its application, the obscure word מנון, in Pr 29:21, may be turned by Atbach into סהדה, testimony (Buxtorf, De Abbreviaturis, s.v.).
(אִתבִּשׁ) is a similar term for a somewhat different principle of commutation. In this, namely, the letters are also mutually interchanged by pairs; but every pair consists of a letter from each end of the alphabet, in regular succession. Thus, as the technical term Athbash shows, א and ת, and ב and שׁ, are interchangeable; and so on throughout the whole series. By writing the Hebrew alphabet twice in two parallel lines, but the second time in an inverse order, the two letters which form every pair will come to stand in a perpendicular line. This system is also remarkable on account of Jerome having so confidently applied it to the word Sheshak, in Jer 25:26. He then propounds the same system of commutation as that called Athbash (without giving it that name however, and without adducing any higher authority for assuming this mode of commutation than the fact that it was customary to learn the Greek alphabet first straight through, and then, by way of insuring accurate retention, to repeat it by taking a letter from each end alternately), and makes שׁשׁ to be the same as בבל. (See Rosenmüller's Scholia, ad loc.) Hottinger possessed an entire Pentateuch explained on the principle of Athbash (Thesaur. Philol. p. 450).
There is also another system of less note, called ALBAI (אִלבִּם), which is only a modification of the preceding; for in it the alphabet is divided into halves, and one portion placed over the other in the natural order, and the pairs are formed out of those letters which would then stand in a row together. — Kitto, s.v.
All these methods belong to that branch of the Cabala (q.v.) which is called תּמוּרָה, commutation.