Abstract
The established counterpointing and intervallic approaches to the construction of stacked canons provide limited harmonic or structural control and are computationally complex. While efficient and in complete control of harmony, Morris’ Tonnetz approach targets serial stacked canons ad minimum and does not encompass voice-leading constraints. A style-independent, constructive approach using relative chord tones, chord sequences and chord-sequence modulations is presented along with its connections to graph-theory in address of these issues. The problem of obtaining complete chords is connected to the Hamiltonian cycle problem, the problem of avoiding parallel intervals to the Eulerian cycle problem. Several efficient canon-generation algorithms are presented, along with an analysis of their computational complexity. The maximum number of distinct sub-canons of stacked canon is counted in demonstration of the connection between stacked canons and the design of larger scale imitative polyphonic structures.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
