Abstract
The famous results of Carey and Clampitt [N. Carey and D. Clampitt, Aspects of well-formed scales, Music Theory Spectr. 11 (1989), pp. 187–206] focus on scales generated by one interval and explain why some of these scales are preferable to others. Those preferable are called well-formed (WF). Their explanation is based on a theorem showing equivalence between ‘symmetry’ and ‘closure’. In this paper, we propose and prove a generalization of this theorem. Instead of scales with a single generator, tone systems generated by two intervals are considered. In addition, various examples are given to illustrate the developed theoretical framework. Among them, the ancient Indian 22-śruti system is interpreted as a WF two-dimensional tone system generated by the fifth and the śruti. Finally, we draft open problems pertaining to the presented theory.
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.
