mm. When I was studying music theory we used to reserve "operation" for a function that was 1 to 1 and onto; I think that usage has been pretty standard in music theory since 1987, through the work of David Lewin. Music theorists often screw up standard math terms though, so I never know what to call anything in what company, and always suspect it will be meaningless/wrong... =o)
On Thu, Mar 19, 2009 at 1:09 PM, Mathieu Bouchard <ma...@artengine.ca> wrote: > On Thu, 19 Mar 2009, Matt Barber wrote: > >> Right, in mod-12, the other multiplications are not strictly operations >> (there is no inverse). > > They are called operations anyway. I don't know your definition of > operation. > > They're usually called "non-invertible operations", but in a Group (of Group > Theory), all elements are invertible. > > Group Theory also has an operator (written as a small straight "x" in > exponent) that makes a multiplication-wise group from an addition-wise > group. For Z/12Z (the mod 12 integers), this gives you a group make of > 1,5,7,11, which behaves like (Z/2Z)^2, which is are the 2-D vectors made of > Z/2Z (mod 2 integers): > > 1 -> (0,0) > 5 -> (0,1) > 7 -> (1,0) > 11 -> (1,1) > >> Recently I've been writing music in various 19-tone equal temperaments, >> which, since it's prime, has a complete multiplicative group. > > yes... and as a bonus, this multiplicative group acts just like Z/18Z !!! > > _ _ __ ___ _____ ________ _____________ _____________________ ... > | Mathieu Bouchard - tél:+1.514.383.3801, Montréal, Québec _______________________________________________ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management -> http://lists.puredata.info/listinfo/pd-list