Agamemnon had three daughters together with Clytemnestra: Elektra, Ifigenia and Chrysothemis. The incident you have in mind was the time when the Godess Artemis had caused the winds to blow no more i Aulis. Artemis demanded a human sacrifice else the winds would not more again. According to some sources Agamemnon had to sacrifice his daughter, but according to others Artemis stopped him just before he killed her and offered a hind to take her place.
This incident is not about Agamemnons cruel nature. It is a tale about the Gods testing the loyalty of their chosen ones. A parallel example exists in the old testament where Gods asks Abraham to sacrifice Joseph . That Abraham accepts to undertake this bloody deed is not a tale about his cruelty or wicked nature, but a tale of God testing the loyalty of his chosen people.
One could ask why Agamemnon was at Aulis in the first place? That ha was because he was coming to his brother's aid. During the wedding of Peleus and Thetis the goddess of bickering Eris had not been invited. She then threw a golden apple into the room where the party was upon which was written "For the most beautiful" both Hera , Athena and Afrodit wanted the apple and made the innocent Paris be the judge. Yet they all tried to bribe him. Hera would give him the greatest of kingdoms, Athena would give him wisdom, while Afrodit would give him the most beautiful woman in the world. He chose the woman. This woman was Helena who already was married to Melenalos the brother of Agamemnon . Afrodit kidnapped her. Agamemnon then came to his brother's aid in helping him to bring back his lost and beloved wife.
To return to Clytemnestra now. If her motive indeed was to revenge her daughter Ifigenia (which perhaps never was killed in the first place)then it is truly odd that she afterwards would treat her other daughter Elektra with almost the same contempt as a common slave. Sofokles describes this very well. As I see this all evidence points towards the conclusion that Clytemnestra killed her husband for one reason only and that was so that she could live in luxery with her lover. She was less a mother than she was and adulteress I think.
"Priam bade her (Helen ) draw nigh. "My child," said he, "take your seat in front of me that you may see your former husband, your kinsmen and your friends. I lay no blame upon you, it is the gods, not you who are to blame. It is they that have brought about this terrible war with the Achaeans. Tell me, then, who is yonder huge hero so great and goodly? I have seen men taller by a head, but none so comely and so royal. Surely he must be a king." "Sir," answered Helen , "father of my husband, dear and reverend in my eyes, would that I had chosen death rather than to have come here with your son, far from my bridal chamber, my friends, my darling daughter, and all the companions of my girlhood. But it was not to be, and my lot is one of tears and sorrow. As for your question, the hero of whom you ask is Agamemnon , son of Atreus, a good king and a brave soldier, brother-in-law as surely as that he lives, to my abhorred and miserable self." (Illiad Book III)
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