{"id":19,"date":"2018-09-20T10:37:53","date_gmt":"2018-09-20T14:37:53","guid":{"rendered":"https:\/\/sites.bu.edu\/jyust\/?page_id=19"},"modified":"2026-03-26T22:39:06","modified_gmt":"2026-03-27T02:39:06","slug":"research","status":"publish","type":"page","link":"https:\/\/sites.bu.edu\/jyust\/research\/","title":{"rendered":"Research"},"content":{"rendered":"

\"\"The unifying theme of my research is applications of mathematics to music theory and analysis. I have pursued this interest in many different areas of music theory, such as theories of rhythm, harmony, scale theory, musical form, musical structure, and text setting. I am also interested in many different kinds of music, from lesser known composers of 18th century Europe to the 20th-century avant-garde to jazz, Indonesian gamelan, Persian dastgah<\/em>, and music of the African diaspora.<\/p>\n

My book,\u00a0Organized Time: Rhythm, Tonality, and Form<\/a>,\u00a0<\/em>published by Oxford University Press in 2018, proposes a general framework for temporal structure, which can be applied to rhythmic, tonal, and formal structure. It includes a lot of analysis of classical music from the 18th and 19th centuries, by well-known and lesser known composers. It also shows how we can formulate abstract claims about musical structure and apply mathematical graph theory to them. It won the Society for Music Theory<\/a>‘s prestigious\u00a0<\/span>Wallace Berry Award<\/a> in 2019. The award committee described it as<\/p>\n

. . . a book that is astonishing in both its ambition and its achievement. It offers a theory of tonal music that treats harmony, rhythm, and form as separate dimensions that might either reinforce or contradict each other, providing an appealing notation system that permits direct comparison of these dimensions. It profoundly rethinks aspects of tonal theory that we had thought pretty well settled. The theoretical framework is powerful and the analyses\u2014of both familiar and unfamiliar tonal works\u2014are deeply revealing.<\/p><\/blockquote>\n

Most of my recent research deals with the two cyclic spaces that govern much of how music works, the temporal cycles of metrical rhythms and grooves, and the pitch cycles of the octave, and an important tool for analyzing objects in these kinds of cyclic spaces, the discrete Fourier transform. A complete list of publications is here<\/a>. Below are some selected, thematically organized lists.<\/p>\n

Discrete Fourier transform of cyclic rhythms<\/h4>
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