Date of Completion


Degree Type

Honors Thesis


Mathematics (MATH)

First Advisor

Robert Rovetti


Markov models are mathematical structures that model the transition between possible states based on the probability of moving from one state to any other. Thus, given a distribution of starting points, the model produces a chain of states that are visited in sequence. Such models have been used extensively to generate music based on probabilities, as sequences of states can represent sequences of notes and rhythms. While music generation is a common application of Markov models, most existing work attempts to reconstruct the musical style of classical Western composers. In this thesis, we produce a series of Markov chains that model the composition of Balinese gamelan gong kebyar improvisations on the reyong. This music features distinct rules and limitations. Each of the reyong’s four players can play only some of the gamelan's five tones and must use specific patterns learned only by listening and playing. And yet, the music structure also provides room for ample creativity with improvisation. The model’s probability values come from a combination of top-down and bottom-up techniques, making extensive use of Leslie Tilley’s work on the grammar of \textit{reyong norot} and example patterns from her concurrent study of musician Dewa Ketut Alit’s improvisation. The model outputs MIDI files for audio playback of the constructed songs. Though the model’s music lacks some of the improvisational creative quality that humans provide, we find that our model does produce musically interesting reyong elaborations that fit within the confines of Tilley’s grammar.

Reyong Sample 4 (with Pokok and Kempli).wav (4651 kB)
A sample song produced by the model

Reyong Sample 5 (with Pokok and Kempli).wav (9303 kB)
Another sample song produced by the model

Included in

Probability Commons