Some calculated Weil tunings

I've uploaded "tipweil.py" to my files folder, which is a modification
of Keenan's TIPTOP algorithm that computes Weil tunings. You'll note,
if you try to run it, that there's an additional "skew" parameter you
can add: for now, just know that 1 is the Weil tuning, 0 is TOP, and
intermediate values interpolate between them; there will be more
detail on that later. (Note that -1 is the same as 1).

Now then, here's some selected Weil tunings, calculated to 3 decimal
places. You'll note that some of these are pretty strange, like
7-limit Pajara at <1193.803 1896.996 2771.924 3368.826| and 5-limit
Blackwood at <1188.722 1901.955 2773.22|.

Other than temperaments than subdivide the octave, most of these are
decent (porcupine's pretty weird though). I suspect that the really
strange results are arising because there's some sort of valid range
of Weil tunings for these, much like with what happens with TOP, and
just doing TIPTOP on augmented interval space and then restricting
back down to normal interval space doesn't relaly do the trick. For
now, I'll just post what I have and keep working on it.

Note also that this tends to make one or more primes tuned pure.

Name - <generators| - <tuning| - notes

5-limit:
Dicot - <1200.000, 350.978| - <1200.000 1901.955 2750.978| - (2/1, 3/1
tuned pure)
Meantone - <1200.000 696.578| - <1200.0 1896.578 2786.314| - (2/1,
5/1 tuned pure)
Augmented - <398.045 92.917| - <1194.134 1897.307 2786.314| (5/1 tuned pure)
Mavila - <1200.000 681.310| - <1200.0 1881.31 2756.07| - (2/1 tuned pure)
Porcupine - <1193.828 161.900| - <1193.828 1901.955 2771.982| - (3/1
tuned pure!!)
Blackwood - <237.744, 79.712| - <1188.722 1901.955 2773.22| - (3/1 tuned pure!!)
Srutal - <599.111 104.621| - <1198.222 1901.955 2786.314| - (3/1, 5/1
tuned pure)
Hanson - <1200.000 316.993| - <1200.0 1901.955 2784.963| - (2/1, 3/1 tuned pure)
Magic - <1200.000 380.391| - <1200.0 1901.955 2780.391| - (2/1, 3/1 tuned pure)
Negri - <1200.000 125.954| - <1200.0 1896.185 2777.861| - (2/1 tuned pure)
Tetracot - <1198.064 175.973| - <1198.064 1901.955 2781.819| - (3/1 tuned pure)

7-limit:
Meantone - <1200.000 696.578| - <1200.0 1896.578 2786.314 3365.784| -
(2/1, 5/1 tuned pure)
Magic - <1200.000 380.391| - <1200.0 1901.955 2780.391 3364.692| -
(2/1, 3/1 tuned pure)
Pajara - <596.901 106.291| - <1193.803 1896.996 2771.924 3368.826| -
(7/1 tuned pure)
Augene - <398.045 90.372| - <1194.134 1899.852 2786.314 3365.102| -
(5/1 tuned pure)
Sensi - <1196.783 442.566| - <1196.783 1901.181 2786.314 3359.796| -
(3/1, 5/1 tuned pure)

-Mike

On Sun, Sep 16, 2012 at 8:14 AM, Mike Battaglia <battaglia01@gmail.com> wrote:
> I suspect that the really
> strange results are arising because there's some sort of valid range
> of Weil tunings for these, much like with what happens with TOP, and
> just doing TIPTOP on augmented interval space and then restricting
> back down to normal interval space doesn't relaly do the trick. For
> now, I'll just post what I have and keep working on it.

Turns out I was wrong, and the values I posted were correct. I think
Weil tuning just completely sucks. Apparently, it's not a useful thing
to minimize the max integer-limit weighted error over all intervals.
It'd probably be better to look at minimizing the average
integer-limit weighted error over all intervals instead.

-Mike

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Turns out I was wrong, and the values I posted were correct. I think
> Weil tuning just completely sucks. Apparently, it's not a useful thing
> to minimize the max integer-limit weighted error over all intervals.
> It'd probably be better to look at minimizing the average
> integer-limit weighted error over all intervals instead.
>
> -Mike
>

If you set the skew to 0.5, won't that bear similarities to "minimizing the average integer-limit weighted error over all intervals?" Weil looks at the max integer-limit weighted error, and TOP looks at the average tenney-weighted error, so an intermediate skew should be somewhere between those.

Ryan

--- In tuning-math@yahoogroups.com, "Ryan Avella" <domeofatonement@...> wrote:
> If you set the skew to 0.5, won't that bear similarities to "minimizing the average integer-limit weighted error over all intervals?" Weil looks at the max integer-limit weighted error, and TOP looks at the average tenney-weighted error, so an intermediate skew should be somewhere between those.

TOP minimizes the maximum Tenney-weighted error over all intervals. So it seems that TOP "looks at" the maximum Tenney-weighted error, no?

Keenan