12 and 19

Hi, Gene!

What are the TOPs of 7-limit 12-equal and 5-limit 19-equal? Thanks!

Kalle

>Hi, Gene!
>
>What are the TOPs of 7-limit 12-equal and 5-limit 19-equal? Thanks!
>
>Kalle

These are very easy to calculate. Here is the formula given by
Paul...

"""
For an ET, just stretch so that the weighted errors of the most upward-
biased prime and most downward-biased prime are equal in magnitude and
opposite in sign. For 12-equal I take the mapping

[12 19 28]

divide (elementwise) by

[1 log2(3) log2(5)]

and get

[12.00000000000000 11.98766531785769 12.05894362605501]

Now we want to make the largest and smallest of these equidistant from
12, so we divide [12 19 28] by their average

[12.05894362605501+11.98766531785769 ]/2

giving

0.99806172487683 1.58026439772164 2.32881069137926

So Graham had the all the digits right, I just needed more precision.

Multiply by 12, and we get

1197.67406985219 1896.31727726597 2794.57282965511

Here it's clear we're hitting the maximum, 3.557, with both 3 and 5.
"""

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >Hi, Gene!
> >
> >What are the TOPs of 7-limit 12-equal and 5-limit 19-equal? Thanks!
> >
> >Kalle
>
> These are very easy to calculate. Here is the formula given by
> Paul...

Ok, thanks! Now I can do it myself.

> 0.99806172487683 1.58026439772164 2.32881069137926
>
> So Graham had the all the digits right, I just needed more
precision.
>
> Multiply by 12, and we get

This should be "multiply by 1200", right?

Kalle

>> Multiply by 12, and we get
>
>This should be "multiply by 1200", right?

Yup. -C.