At the Limits of Mensural Theory: Notes
1 The Scriptum super punctis musicalibus is still available only as Latin text in Seay 1975, i. Since writing this paper, the Tractatus alterationum and Liber imperfectionum notarum musicalium have been newly edited and translated as part of the present online edition (2007). Super punctis musicalibus will become available here in a new edition and translation in early 2008.
2 This 'classic' or strict formulation of imperfection does not take account, however, of the occasional liberties taken by composers in allowing a note to be imperfected by a smaller note whose own mensural level is itself imperfect rather than perfect. (See, for instance, the brief discussion in Rastall 1983: 72), and, indirectly, the addendum to Apel 1953: 112, ibid., 440.)
3 For a brief discussion of this source within the present online edition, see here.
4 See Seay 1975, i. 194–5: Chapter 15 'De abusu punctorum divisionis et perfectionis'.
5 Ibid., i. 174–5.