sentences:  Tropes in this sense were devised and named by Josef Matthias Hauer in connection with his own twelve-tone technique, developed simultaneously with but overshadowed by Arnold Schoenberg's.Hauer discovered the 44 tropes, pairs of complementary hexachords, in 1921, allowing him to classify any of the 479,001,600 twelve-tone melodies into one of 44 types .The primary purpose of the tropes is not analysis (although it can be used for it) but composition.