Circle for Carl

To refresh the memory, here's the plot of 7-limit "linear
temperaments" in blue, with the moat (in red) that Dave and I favored:

/tuning-math/files/Erlich/7lin23.gif

That used linear scaling on the axes; this version of the same plot
used log scaling on both axes:

/tuning-math/files/Erlich/7lin23loglog.g
if

The numbers labeling the points refer to this list:

/tuning-math/message/9317

Carl expressed interest in using circular moats centered around the
origin. This same moat becomes a circle around the origin if cube-
root scaling is used on both of the axes:

/tuning-math/files/Paul/carl.gif

I didn't label the points but it should be clear which point is which
from comparison with the plots above.

Ennealimmal is the point on the far lower right.

This last plot has a lot more points, since it drew from Gene's fresh
de-culling of his list of 32201, which had been culled to 126 when
the earlier plots were made. In fact, this post is partially an
excuse to immediately present something resulting from the de-
cullation. Thanks again, Gene.

I don't want this to contribute to or resume the argument about which
scaling of the axes is appropriate, I just thought it might interest
Carl, depending on what his predilection for circles was based on.
I'd like to hear Carl's thoughts.

>I don't want this to contribute to or resume the argument about which
>scaling of the axes is appropriate, I just thought it might interest
>Carl, depending on what his predilection for circles was based on.
>I'd like to hear Carl's thoughts.

Thanks Paul.

My thoughts are hoping recorded in that thread. In any case I
don't consider the "perfect list" so important.

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >I don't want this to contribute to or resume the argument about
which
> >scaling of the axes is appropriate, I just thought it might
interest
> >Carl, depending on what his predilection for circles was based on.
> >I'd like to hear Carl's thoughts.
>
> Thanks Paul.
>
> My thoughts are hoping recorded in that thread.

Hoping recorded? You mean hopefully recorded? I've just re-read the
entire contents of this list from the first 2+ months of this year,
so I'm familiar with what you said. I was left with a big question
mark as to your fundamentals, and was hoping that bouncing this off
you would help clarify.

> In any case I
> don't consider the "perfect list" so important.

Of course. Once you write music in all of them, then what? ;)

>> My thoughts are hoping recorded in that thread.
>
>Hoping recorded? You mean hopefully recorded?

Yes.

>I've just re-read the
>entire contents of this list from the first 2+ months of this year,
>so I'm familiar with what you said. I was left with a big question
>mark as to your fundamentals, and was hoping that bouncing this off
>you would help clarify.

I thought I stated my fundamentals pretty clearly. I can't give
msg. numbers, but I can copy and paste if you like.

-Carl