Music Generation from Statistical Models of Harmony

Abstract

This article investigates the problem of sampling from statistical models of music, motivated by the fact that music generated by random walk is generally atypical in style and of vastly inferior quality compared with pieces in the corpus. Specifically, we employ a multiple viewpoint system of four-part harmony, in conjunction with a small set of general rules of harmony, to evaluate an improved iterative random walk technique which efficiently finds low cross-entropy (high probability) solutions. By first using standard iterative random walk, we show that a range of very high cross-entropy harmonizations is generated. Furthermore, we demonstrate a relationship between cross-entropy and the number of rule violations; that is, there are fewer violations at lower cross-entropy. Motivated by this result, the application of an improved sampling technique was used to produce solutions of very low cross-entropy, confirming that the correlation between cross-entropy and rule violations extends into the low cross-entropy region. Various diversity measures, such as the number of non-diatonic notes per 100 melody notes, also exhibit trends with respect to cross-entropy. These findings are likely to influence future research involving the generation of samples from statistical models, in the realm of music and beyond.

Keywords:

• machine learning
• harmonization
• random walk
• probability threshold
• multiple viewpoint system
• statistical model

Acknowledgements

Special thanks to Kerstin Neubarth for valuable comments on the manuscript.

Notes

This research is partially supported by the Lrn2Cre8 project which is funded by the Future and Emerging Technologies (FET) programme within the Seventh Framework Programme for Research of the European Commission, under FET grant number 610859.

Dr Raymond Whorley, Department of Computing and Communications, The Open University, Walton Hall, Milton Keynes, MK7 6AA, UK.