Alban Berg was heavily into numerology, as were a great number of Viennese at the time (including Sigmund Freud and Arnold Schoenberg). Berg had an obsession with his "fateful number" 23 which influenced his compositions and work habits. For instance he would begin and end projects on the 23rd of the month. As well, the time signatures of his music are all in multiples of 23, so it is not uncommon to find Berg pieces in 46/23 or 69/23 time.
Berg noted other occurences of the number 23 in his life. For example, his first asthma attack occured on July 23rd and he was drafted into the army under regulation 23.
Normal people would chalk this up to coincidence but you have to be a little crazy to write something as perverse as an atonal opera. Oddly enough, it seems that this 23-madness was shared by William S. Burroughs (see the node '23')