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Notes
1 A version of that document was initially a letter to Paul Isihara dated 8/15/92. Isihara, who is Professor of Mathematics at Wheaton College (IL), had inquired by mail about open math/music problems that might interest one of his undergraduate students. I am grateful to Prof. Isihara for archiving this letter in such a way that he was able to retrieve it upon my request 30 years later!
2 A Tn/TnI set class is a class of chords, scales, or unordered pitch-class sets whose elements are equivalent by virtue of being mutually related by transposition and/or inversion.
3 The PP property eventually was identified, using different terms, in CitationLewin 1996 and CitationCohn 1996. Lewin referred to Cohn flips and cycles; I referred to maximally smooth relations and cycles.
4 This research was published in a special issue of the Journal of Music Theory, Volume 42.2, which also included CitationDouthett and Steinbach 1998, and contributions by me, Clough, Lewin, Carol Krumhansl, and Steven Soderberg.