[sdiy] Samchillian Anyone?

[cheater cheater]

On Sun, Oct 10, 2010 at 19:36, Thomas Strathmann <thomas at pdp7.org> wrote:
> 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?

The root of the scale. Alternatively, an octave up.

> 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.

n == 0 mod n.

> 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.

Yeah, I just said "ring" because Z/nZ is a ring. There's no reason to
say "the group Z/nZ" since every child knows it's also a ring. It
would be like talking about a Mercedes and saying "the red combustion
vehicle over there". It's a car :)

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

One interesting question is how to make this kind of interface polyphonic.

D.