Richard I'm not going to answer your question directly, but draw your attention to the difference in aesthetic between Harmonic Direction and Harmonic Proportion. And rather than elaborate here now, add that I have pondered this long and hard and given the results of my ponderings with musical examples in a 14-page Appendix in the new Master Piper edition.
Matt -- To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
