[PD] www.pd-tutorial.com

[Matt Barber]

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 <matju at 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 !!!
>
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