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Second letter of the Greek alphabet, and same as our letter B (in capitals), and β in lower case. In modern Greek and going back a long way it's pronounced like V, but in Ancient Greek it was pronounced like Latin/English B. The change to V took place a bit after the New Testament period, I think. As the second letter, it was also used for the number two, written β'

The letter name is pronounced bee-ta in UK and bay-ta in USA, and vee-ta in modern Greece.

In fan fiction, to beta a story is to read it for the author and make suggestions, corrections, etc., before it's publicly posted; presumably derived from the notion of a beta tester in computing: not the first person to proofread, but the second. The person doing the beta is called a beta reader or a beta. In some fanfic posting forums beta'ing is evidently treated as a serious requirement, so I have seen people asking for someone to "pre-beta" a story.