[sdiy] Samchillian Anyone?

Thomas Strathmann thomas at pdp7.org
Sun Oct 10 19:36:48 CEST 2010

On 10/10/10 19:14 , cheater cheater wrote:
>> thus resulting in a finite semigroup
> I think what you mean is that the subring generated is equal to the
> ring you are working in, i.e. it is not a proper subring. After all,
> any ring Z/nZ of modulo numbers is finite.

Actually, I don't want to bother with a ring. After all: What's the 
neutral element of the underlying group? If I take the set of semitones 
S = {1, 2, ..., n} and the operation take shifting a note m by k 
semitones as m + k (mod n) then there's no k in S s.t. m + k (mod n) = 
m. Even if I imagine a neutral element and a suitable operation then 
there's still a a second operation (and corresponding semigroup) 
missing. Talking about a factor semigroup should be sufficient for the 
"problem" at hand.

Anyhow, Scott already answered my question, which only amounted to 
whether I understood his terminology correctly although he left little 
room for interpretation.


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