Poor man's harmonic entropy graphs uploaded

I've put these in the photos section.

Recall that "standard" ? HE is a Gaussian smoothing of ?(2^(x/1200))',
whereas the poor man simply contents himself with a central difference
operator on ?(2^(x/1200)). I've put up graphs of poor man for Del_s,
with s 5, 10, 25 and 50 cents. These are very fast and easy to
compute, and might be useful for that reason.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> I've put these in the photos section.
>
> Recall that "standard" ? HE is a Gaussian smoothing of ?(2^
(x/1200))',
> whereas the poor man simply contents himself with a central
difference
> operator on ?(2^(x/1200)). I've put up graphs of poor man for Del_s,
> with s 5, 10, 25 and 50 cents. These are very fast and easy to
> compute, and might be useful for that reason.

Unfortunately, their features bear little resemblance to those of
harmonic entropy curves. Yet they are interesting in their own right.
Are those global maxima at the golden ratio or something?

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:
> --- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
> > I've put these in the photos section.
> >
> > Recall that "standard" ? HE is a Gaussian smoothing of ?(2^
> (x/1200))',
> > whereas the poor man simply contents himself with a central
> difference
> > operator on ?(2^(x/1200)). I've put up graphs of poor man for Del_s,
> > with s 5, 10, 25 and 50 cents. These are very fast and easy to
> > compute, and might be useful for that reason.
>
> Unfortunately, their features bear little resemblance to those of
> harmonic entropy curves. Yet they are interesting in their own right.
> Are those global maxima at the golden ratio or something?

There ought to be a global maximum there, so I assume that's what it is.

If this isn't HE, what is it, I wonder? Of course, we haven't yet done
what I first suggested, and did Gaussian smoothing.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:

> > Are those global maxima at the golden ratio or something?
>
> There ought to be a global maximum there, so I assume that's what
>it is.

The global maximum should really be at 65-70 cents or so, but your
function is pretty low there.

--- In tuning-math@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:
> --- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
>
> > > Are those global maxima at the golden ratio or something?
> >
> > There ought to be a global maximum there, so I assume that's what
> >it is.
>
> The global maximum should really be at 65-70 cents or so, but your
> function is pretty low there.

I'll look more carefully at what you did and see if I can get ? or
Conway's box function (inverse ?) to replicate it.