All-interval structures
Document Type
Conference Proceeding
Publication Date
1-1-2015
Abstract
All-interval structures are subsets of musical spaces that incorporate one and only one interval from every interval class within the space. This study examines the construction and properties of all-interval structures, using mathematical tools and concepts from geometrical and transformational music theories. Further, we investigate conditions under which certain all-interval structures are Z (or GISZ) related to one another. Finally, we make connections between the orbits of all-interval structures under certain interval-groups and the sets of lines and points in finite projective planes. In particular, we conjecture a correspondence that relates to the co-existence of such structures.
Publication Source (Journal or Book title)
Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics
First Page
279
Last Page
290
Recommended Citation
Peck, R. (2015). All-interval structures. Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 9110, 279-290. https://doi.org/10.1007/978-3-319-20603-5_29