In article <email@example.com>, David Webber <firstname.lastname@example.org> wrote: > >"graham breed" <email@example.com> wrote in message ><a href="news://2tcu4eF1ulan2U1@uni-berlin.de...">news://2tcu4eF1ulan2U1@uni-berlin.de...</a> > >> You can get an inverse from undirected intervals by enforcing >> octave equivalence. So a perfect fifth is the inverse of a >> perfect fourth. I'm not sure if the result is a group ... or at >> least one that makes sense. It wouldn't be "moving by an >> interval" anyway, but building up chords. > >It is a group, but a smaller one - there are no 9ths etc. It >becomes like addition modulo 7 instead of addition. > >Dave >-- >David Webber >Author MOZART the music processor for Windows - ><a href="http://www.mozart.co.uk">http://www.mozart.co.uk</a> >For discussion/support see ><a href="http://www.mozart.co.uk/mzusers/mailinglist.htm">http://www.mozart.co.uk/mzusers/mailinglist.htm</a>
In which case the distinction between interval, directed interval, and transposition operator still all retain their salience.
-- Matthew H. Fields <a href="http://personal.www.umich.edu/~fields">http://personal.www.umich.edu/~fields</a> Music: Splendor in Sound To be great, do things better and better. Don't wait for talent: no such thing. Brights have a naturalistic world-view. <a href="http://www.the-brights.net/">http://www.the-brights.net/</a>