
Re: Math and music
Posted:
Oct 16, 2004 12:35 PM


In article <ckrifm$oj5$1$8302bc10@news.demon.co.uk>, David Webber <dave@musical.demon.co.uk> wrote: > >"graham breed" <usenet@microtonal.co.uk> wrote in message ><a href="news://2tcu4eF1ulan2U1@uniberlin.de...">news://2tcu4eF1ulan2U1@uniberlin.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 worldview. <a href="http://www.thebrights.net/">http://www.thebrights.net/</a>

