terrain snaps

So I was flying over Trichord County the other day, after reading some of
Paul Erlich's navigation hints, and I managed to snap a couple of pictures
from the window. Some of those canyons and wells Margo and Dan S. have
been talking about look pretty fearsome. You wouldn't want to fall into
one, however consonant it might sound... no "gentle phi trail" here.
I've just uploaded one picture to the files area, in a folder called
'terrain' - the URL should be

http://www.egroups.com/files/tuning/terrain/terrain1.bmp

Let me know if it comes out ok. Hey, can anyone get their bearings and
recognise what part of the county I took this in? I'm hoping to go back
soon for more pictures - I'll keep you posted. I hear in the setting sun
it's quite beautiful there --Jon

--- In tuning@egroups.com, jon wild <wild@f...> wrote:

> http://www.egroups.com/files/tuning/terrain/terrain1.bmp

That's awesome. Now if someone could make an applet where you could
here the chord corresponding to each point just by clicking on the
point . . .

--- In tuning@egroups.com, jon wild <wild@f...> wrote:

> http://www.egroups.com/files/tuning/terrain/terrain1.bmp

That's awesome. Now if someone could make an applet where you could
here the chord corresponding to each point just by clicking on the
point . . .

jon wild wrote,

> So I was flying over Trichord County the other day, after reading
some of Paul Erlich's navigation hints, and I managed to snap a couple
of pictures from the window.

Whew... am I upside-down or inside out? Looking from the top down, the
area after the second horizontal ridge and to the left of the last big
vertical crest seems all, ah, well weird... it kinda makes my stomach
feel the way a sudden elevator shift does, or that instant when a car
next to you at the stop light moves but you momentarily think your
moving. Looks like a great place to hike, but I think I'll need a map
and some motion sickness business, cause my equilibrium is a huffin'
and a puffin' just looking at it!

Nice.

--Dan Stearns

--- In tuning@egroups.com, "Paul Erlich" <PERLICH@A...> wrote:

http://www.egroups.com/message/tuning/14114

> --- In tuning@egroups.com, jon wild <wild@f...> wrote:
>
> > http://www.egroups.com/files/tuning/terrain/terrain1.bmp
>
> That's awesome. Now if someone could make an applet where you could
> here the chord corresponding to each point just by clicking on the
> point . . .

This is an incredible graphic... even if it belongs over on the
Harmonic Entropy site! Wow. I urge everybody to take the time to
download it... since I almost didn't myself...
________ ___ __ __
Joseph Pehrson

--- In tuning@egroups.com, jon wild <wild@f...> wrote:
>
> So I was flying over Trichord County the other day, after reading
some of
> Paul Erlich's navigation hints, and I managed to snap a couple of
pictures
> from the window. Some of those canyons and wells Margo and Dan S.
have
> been talking about look pretty fearsome. You wouldn't want to fall
into
> one, however consonant it might sound... no "gentle phi trail"
here.

How did you determine the size of the pits? I would use 1/sqrt(n*d)
or some function of that.

I wrote

>How did you determine the size of the pits? I would use 1/sqrt(n*d)
>or some function of that.

Whoops, I meant 1/cuberoot(a*b*c).

--- In tuning@egroups.com, jon wild <wild@f...> wrote:
> http://www.egroups.com/message/tuning/14112

Hey Jon,

Now *that's* what I call a lattice-diagram!

>
> Some of those canyons and wells Margo and Dan S. have been
> talking about look pretty fearsome. You wouldn't want to fall
> into one, however consonant it might sound... no "gentle phi
> trail" here.

I was trying to invert the colors so as to turn the cavities
into hills. I agree with you that those pits look rather abysmal
<groan>, and thought that it might make for more attractive hiking
if they were shown as elevations instead. The more consonant
the triad, the more beautiful the view...
Can you make one like that?

>
> ... I'm hoping to go back soon for more pictures - I'll keep
> you posted. I hear in the setting sun it's quite beautiful there

As a matter of fact, the version I ended up with *does* look
like a sunset shapshot, so I decided to post it:

http://www.egroups.com/files/tuning/monz/terrain1monz.gif

-monz
http://www.ixpres.com/interval/monzo/homepage.html

This might help y'all find your way around:

http://www.egroups.com/files/tuning/perlich/trimap.jpg

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:
> --- In tuning@egroups.com, jon wild <wild@f...> wrote:

http://www.egroups.com/message/tuning/14131

>
> As a matter of fact, the version I ended up with *does* look
> like a sunset shapshot, so I decided to post it:
>
> http://www.egroups.com/files/tuning/monz/terrain1monz.gif
>

Now it looks a little like a "graham cracker..." I'm assuming that
has nothing to do with "Graham" Breed...

________ ___ __ __ _
Joseph Pehrson

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

http://www.egroups.com/message/tuning/14134

> This might help y'all find your way around:
>
> http://www.egroups.com/files/tuning/perlich/trimap.jpg

Thanks, Paul... This is very helpful!
______ ___ __ _
Joseph Pehrson

Paul wanted to know how the size of the pits was determined on the
terrain graphic I uploaded to the files area yesterday.

The graph is modelled according to an inverse-square law of attraction,
like gravity. You've probably seen those graphics that try to explain how
it is that massive bodies warp spacetime, by showing a thin rubber sheet
with bowling balls, billiard balls and other things sitting on it all
creating bulges in the sheet. That's what this is - the sheet is warped,
at any point, in inverse proportion to the square of the Euclidian
distance between that point and each triad. To set the "mass" of each
triad, I multiplied together the three ratio-products in their lowest
terms, took the square root, and put the result in the denominator, i.e.:

1 / sqrt( i*j / gcf(i,j) * i*k / gcf(i,k) * j*k / gcf(j,k) )

This way, a triad i:j:k gets the simple weight 1/(i*j*k) if each of i,j
and k is relatively prime to each of the other two. Something like 5:6:8
is then more "massive" than it would have been with a simple i*j*k rule,
to compensate for the fact that the 6:8 is "really" a 3:4. I can try some
other models later, like Paul's suggestion of the geometric average of the
three terms - I think this wouldn't produce enough variance in the size of
the pits though.

Unfortunately the inverse-square thing makes it difficult to comply with
Monz's request for hills instead of wells - there's a singularity at the
bottom of each pit (I offset the points being plotted so they just missed
the places where the depth is 1/0, and the "photo" is taken from such an
angle that you can't see how deep the wells really are - although it still
made Dan feel a little queasy...). I'll experiment some more with various
settings to see how I can make the countryside look a little more
welcoming. Maybe green would help, to begin with, so it doesn't look
Pluto, or like Monz's scarred desert version. And I'll trace some marker
lines across the surface, so you can see where you are.

The part of the landscape you saw is around the closed positions of the
major and minor triads, showing all the triads that are expressible as
proportions in numbers no bigger than 40. They're plotted in a
Chalmers-style triangular plane, and I calculated the coordinates using
the formula Paul posted yesterday or the day before. The idea was to have
complex ratios, like, say, 21:26:31, appear as dimples in the slopes of
the deep well around 4:5:6 - I'll try some adjustments when I get a
chance.

I just made a jpeg version to upload, but I see someone beat me to it...
Producing an encapsulated PostScript format would be the best solution
(it's rescalable without loss of resolution), but lots of people might not
have a viewer.

sorry for the long post --Jon

--- In tuning@egroups.com, jon wild <wild@f...> wrote:
>
> 1 / sqrt( i*j / gcf(i,j) * i*k / gcf(i,k) * j*k / gcf(j,k) )
>
> This way, a triad i:j:k gets the simple weight 1/(i*j*k) if each of
i,j
> and k is relatively prime to each of the other two. Something like
5:6:8
> is then more "massive" than it would have been with a simple i*j*k
rule,
> to compensate for the fact that the 6:8 is "really" a 3:4. I can
try some
> other models later, like Paul's suggestion of the geometric average
of the
> three terms - I think this wouldn't produce enough variance in the
size of
> the pits though.

Well, just using 1/(i*j*k) would still get across the "otonal" point
of triadic harmonic entropy. Am I correct that your algorithm above
gives a 4:5:6 triad and a 10:12:15 triad the same size pit? Then it's
akin to total dyadic harmonic entropy.

> The part of the landscape you saw is around the closed positions of
the
> major and minor triads,

Which are the same size?

> showing all the triads that are expressible as
> proportions in numbers no bigger than 40. They're plotted in a
> Chalmers-style triangular plane, and I calculated the coordinates
using
> the formula Paul posted yesterday or the day before. The idea was
to have
> complex ratios, like, say, 21:26:31, appear as dimples in the
slopes of
> the deep well around 4:5:6

If you used gaussian wells based on some function of 1/(i*j*k), you
would get a surface awfully similar to the triadic harmonic entropy
surface that I've been talking about (and will produce next week)
over on the harmonic entropy list (that was of course the reason for
creating these plots in the first place). Nice to know that either
accidentally or intentionally, you're thinking along the same lines.

Pits/dips certainly seem more appropriate than hills in this context!