Why does complexity matter?

I'd read somewhere at one point that a good rule of thumb to test the
complexity of a temperament is to look at the size of the denominator
of the comma that it tempers out. (Let's stick to codimension 1 for
now). But why is this a good rule of thumb? Many of the temperaments
that I really like have larger commas, like Negri and Hanson. Tetracot
is also pretty sweet.

And then, on a lower complexity note, diaschismatic is turning into
one of my favorite sounds ever, and magic as well, although both of
these are around 2000-3000 for the size of the denominator. So what
does complexity matter, really?

-Mike

--- Mike Battaglia <battaglia01@...> wrote:

> I'd read somewhere at one point that a good rule of thumb to test the
> complexity of a temperament is to look at the size of the denominator
> of the comma that it tempers out. (Let's stick to codimension 1 for
> now). But why is this a good rule of thumb? Many of the temperaments
> that I really like have larger commas, like Negri and Hanson. Tetracot
> is also pretty sweet.
>
> And then, on a lower complexity note, diaschismatic is turning into
> one of my favorite sounds ever, and magic as well, although both of
> these are around 2000-3000 for the size of the denominator. So what
> does complexity matter, really?

The comparison only works vs. other temperaments of the
same rank and limit/subgroup. And as you say, only gives
the complexity of the temperament, not its error and
therefore not its badness. See item #6 here
http://lumma.org/music/theory/tctmo/

-Carl

But in what sense does this "complexity" matter? Does it roughly
correlate with Graham complexity or something?

-Mike

On Wed, May 11, 2011 at 10:32 PM, Carl Lumma <carl@...> wrote:
>
> --- Mike Battaglia <battaglia01@...> wrote:
>
> > I'd read somewhere at one point that a good rule of thumb to test the
> > complexity of a temperament is to look at the size of the denominator
> > of the comma that it tempers out. (Let's stick to codimension 1 for
> > now). But why is this a good rule of thumb? Many of the temperaments
> > that I really like have larger commas, like Negri and Hanson. Tetracot
> > is also pretty sweet.
> >
> > And then, on a lower complexity note, diaschismatic is turning into
> > one of my favorite sounds ever, and magic as well, although both of
> > these are around 2000-3000 for the size of the denominator. So what
> > does complexity matter, really?
>
> The comparison only works vs. other temperaments of the
> same rank and limit/subgroup. And as you say, only gives
> the complexity of the temperament, not its error and
> therefore not its badness. See item #6 here
> http://lumma.org/music/theory/tctmo/
>
> -Carl

Mike wrote:

> > The comparison only works vs. other temperaments of the
> > same rank and limit/subgroup. And as you say, only gives
> > the complexity of the temperament, not its error and
> > therefore not its badness. See item #6 here
> > http://lumma.org/music/theory/tctmo/
>
> But in what sense does this "complexity" matter? Does it roughly
> correlate with Graham complexity or something?

Yes. -Carl