An experiment in musical composition

The high-order probabilities of element sequences can be determined from a sample of linear structures and can be used for synthesis of new structures. From theoretical considerations one can identify the qualitative conditions for satisfactory output. The theoretical concepts can be tested and quantitative parameters determined by experiment. Such an experiment has been performed by analyzing written music and by testing the analysis through the synthesis of new musical compositions, using a digital computer. A sample of 37 melodies was analyzed for the probabilities of the elements, element pairs (digrams), trigrams, and so on to the eighth order. The tables derived were used for the synthesis of original melodies by a random process. The theory and the experimental verification are considered in detail. The experimental results presented include comparative statistics of the successful syntheses using each of the eight orders of analysis, examples of melodies generated by low, medium, and high-order synthesis, and confirmation of degeneracy and other effects predicted by the theory.