Asarah b’Tevet (10th Tevet) commemorates the beginning of the siege of Jerusalem in the lead-up to the destruction of the First Temple, a blockade that lasted at least 18 months.  Unlike the related fasts of 17th Tammuz or Tishah B’Av, each of which memorializes a concentrated event (the breaching of the walls; the actual destruction of the Temple), 10th Tevet marks the beginning of a lengthy period of time.