Question for Igs

Do you want me to include even ratios in the 15-limit diamond as well;
e.g. things like 5/4? Or only ratios with odd factors, things like
5/1?

-Mike

It won't matter, because with the presence of Just 2/1's, the error will be the same for all octave-equivalent intervals.

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Do you want me to include even ratios in the 15-limit diamond as well;
> e.g. things like 5/4? Or only ratios with odd factors, things like
> 5/1?
>
> -Mike
>

On Mon, Jan 16, 2012 at 8:53 PM, cityoftheasleep
<igliashon@...> wrote:
>
> It won't matter, because with the presence of Just 2/1's, the error will be the same for all octave-equivalent intervals.
>
> -Igs

It will matter, because I'm taking an average. If we allow 2/1, then
I'll be averaging 5/1, 5/2, 5/4, and 10/1, which is four intervals
that are octave-equivalent to 5/1. And I'll be averaging 3/1, 3/2,
6/1, and 12/1, which is also four intervals octave-equivalent to 3/1.
But, for 11/1, I'll only be averaging 11/8, 11/4, and 11/1, which is
only three octave-equivalent intervals to 11/1. Allowing octaves
changes the number of times each interval appears.

-Mike

Oh, I see. Then no, don't include octave-duplicates.

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Mon, Jan 16, 2012 at 8:53 PM, cityoftheasleep
> <igliashon@...> wrote:
> >
> > It won't matter, because with the presence of Just 2/1's, the error will be the same for all octave-equivalent intervals.
> >
> > -Igs
>
> It will matter, because I'm taking an average. If we allow 2/1, then
> I'll be averaging 5/1, 5/2, 5/4, and 10/1, which is four intervals
> that are octave-equivalent to 5/1. And I'll be averaging 3/1, 3/2,
> 6/1, and 12/1, which is also four intervals octave-equivalent to 3/1.
> But, for 11/1, I'll only be averaging 11/8, 11/4, and 11/1, which is
> only three octave-equivalent intervals to 11/1. Allowing octaves
> changes the number of times each interval appears.
>
> -Mike
>