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The Collaborative International Dictionary
Alectryomancy

Alectryomancy \A*lec"try*o*man`cy\, n. [Gr. ? cock + -mancy.] Divination by means of a cock and grains of corn placed on the letters of the alphabet, the letters being put together in the order in which the grains were eaten.
--Amer. Cyc.

Douglas Harper's Etymology Dictionary
alectryomancy

"divination by means of a cock and grains of corn," 1680s, from Latinized form of Greek alektryon "cock" + manteia "oracle" (see -mancy). The first element is literally "warder-off, fighter," related to alexein "to ward off, drive or keep off" (see Alexander, and compare Alekto, name of one of the three Furies). Perhaps originally a personal name, applied at first to the fighting cock, then to cocks generally.

Wiktionary
alectryomancy

n. A form of divination in which the diviner observes a bird, several birds (or most preferably the white rooster or cockerel) pecking at grain that the diviner has scattered on the ground.

Wikipedia
Alectryomancy

Alectryomancy (also called alectoromancy or alectromancy; derivation comes from the Greek words ἀλεκτρυών alectryon and μαντεία manteia, which mean rooster and divination respectively) is a form of divination in which the diviner observes a bird, several birds, or most preferably a white rooster or cockerel pecking at grain (such as wheat) that the diviner has scattered on the ground. It was the responsibility of the pullularius to feed and keep the birds used. The observer may place grain in the shape of letters and thus discern a divinatory revelation by noting which letters the birds peck at, or the diviner may just interpret the pattern left by the birds' pecking in randomly scattered grain.

In another version, the observer tethers the bird in the center of a circle, around the perimeter of which is marked the alphabet, with a piece of grain at each letter. For each grain the bird pecks, the observer writes down the letter which that grain represents. The observer also replaces each grain as the bird eats it, so that letters may be repeated. The sequence of letters recorded will presumably contain a message.

This form of divination is related to Ouija, by the random selection of letters; to gyromancy, by the random selection of letters from a circle around the diviner himself; and to orniscopy, divination by the movements of birds.

Alectormancy is also sacrificing a sacred rooster. The use of the sacred rooster through alectryomancy may be further understood within that religious character and likewise defined as the cockfight or cockfighting with the intent of communication between the gods and man.