Tumbling Dekany in 3D and stereo - coming soon

This is an advance warning!

Those of you lucky enough to have sight in at least two eyes, should set in
motion now, a process to find, beg, buy, steal or make yourself some
anaglyph 3D glasses (red/green or red/blue or red/cyan).

And for those of you with hearing in at least two ears, headphones wouldn't
be a bad idea either.

'Cause you're gonna have music and pictures comin' at ya from the 4th
dimension. A concert movie that runs for the age of the universe and only
takes 100 k to download.

Enough hype? What's really happened is that for the past two weeks, Andrew
F. and I (that's <AMiltonF@a...>) have been collaborating on an audiovisual
demonstration of Erv Wilson's {1,3,5,7,9} dekany, with Dave Keenan on Excel
formulae and charts, and Andrew F. on VBA macros and MIDI.

We've got a few rough edges to knock off yet. But you'll kill yourself if
you don't have 3D glasses when it finally arrives.

US residents can order them for free from this page, if you download and
install their free software.
http://www.3dexpo.com/cgi-bin/freeglasses.pl
There are some other useful links on this page.
http://mars.jpl.nasa.gov/MPF/mpf/glasses.html

If you're making your own, left eye red is the convention we've assumed,
but it's easy enough to edit the chart.

For folks who don't have a Windows machine, I'm real sorry (I love Macs
too) but you're just gonna have to find a friend who'll let you use their PC.

It's a shame it's too late to get it into this year's Microthon. :-)

To hear some other stuff from Andrew F. while you're waiting, visit
http://www.egroups.com/files/tuning/AMiltonF/

Regards,
-- Dave Keenan
http://dkeenan.com

--- In tuning@egroups.com, David C Keenan <D.KEENAN@U...> wrote:

http://www.egroups.com/message/tuning/15456

>
> US residents can order them for free from this page, if you
download
and install their free software.
> http://www.3dexpo.com/cgi-bin/freeglasses.pl

Ummm. This looks interesting, but what will I be installing on my
machine? I don't like the sound of the program "Depthcharge."

What will it do, blow up my hard drive??

Just a little curious....

_________ ___ __ __ _
Joseph Pehrson

Here's another good deal
http://www.3dglasses.com/free3d.htm

-- Dave Keenan
http://dkeenan.com

Here it is, as promised (except it is 150 kB, not 100 kB).

http://dkeenan.com/Music/StereoDekany.xls

You will have to trust us and enable Excel macros. You probably need
Excel 97 or later running on some flavour of 32-bit Windows and of
course a General MIDI capable sound card.

You may need to choose your MIDI sound source. Then put on your 3D
glasses (left eye red) and hit the Go button. On some versions of
Windows and/or Excel, you may find it takes a lot of clicks on the
Stop button before it turns off.

Sterile demonstration or ambient music? You decide.

-- Dave Keenan and Andrew F.

--- In tuning@egroups.com, "Dave Keenan" <D.KEENAN@U...> wrote:

> http://www.egroups.com/message/tuning/16010
>
> Here it is, as promised (except it is 150 kB, not 100 kB).
>
> http://dkeenan.com/Music/StereoDekany.xls
>

This is one of most amazing things I've ever seen having
to do with tuning. Congrats to Excelmeister Dave K.!
Are you sure you don't want to be involved in my software
project?

-monz
http://www.ixpres.com/interval/monzo/homepage.html
'All roads lead to n^0'

--- In tuning@egroups.com, "Dave Keenan" <D.KEENAN@U...> wrote:

http://www.egroups.com/message/tuning/16010

> Sterile demonstration or ambient music? You decide.
>
> -- Dave Keenan and Andrew F.

Hardly... and EXCELlent demonstration of the possibilities of this
program! Hmmm. And to think I know only how to do an "if"
statement...

CONGRATS!!
_________ ___ __ __
Joseph Pehrson

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:
> This is one of most amazing things I've ever seen having
> to do with tuning. Congrats to Excelmeister Dave K.!

Thanks Monz. And congrats to Andrew F. <AMortonF@...> who only joined
the list recently. He spent way more time than he could really spare,
writing and debugging the Visual Basic macros that allow us to hear
the dekany as it rotates.

Of course the real genius behind this thing is Erv Wilson. Can someone
please arrange to get him in front of a PC with some 3D glasses and
headphones to experience it?

> Are you sure you don't want to be involved in my software
> project?

Sorry Monz. I may look into it one day. But after this burst of tuning
list activity I'm probably gonna have to go cold turkey again for a
while.

>http://dkeenan.com/Music/StereoDekany.xls

I don't hear anything. Boo-hoo!

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
> >http://dkeenan.com/Music/StereoDekany.xls
>
> I don't hear anything. Boo-hoo!

We'll have to solve that!

What version of Windows and Excel do you have? Did you enable macros?
What do you see when you click on the MIDI Out button? Do you get
motion when you click on the Go button?

Robert Walker,

You simply have to find a way to get to see and hear it, on someone
else's computer if necessary.

Regards,
-- Dave Keenan

I just fixed a couple of minor problems and uploaded the new
version.

http://dkeenan.com/Music/StereoDekany.xls

1. The bar chart now shows the volumes of all ten notes.
2. It is transposed for a more natural human vocal range.

Regards,
-- Dave Keenan

>Here it is, as promised (except it is 150 kB, not 100 kB).
>
>http://dkeenan.com/Music/StereoDekany.xls

Awesome! Is there any way to distinguish the sounding notes and/or
intervals? Say, circles around sounding notes... maybe even ones
that scale with volume... and/or thickening the lines for sounding
dyads, maybe even scaling the thickness with volume...

-Carl

--- In tuning@egroups.com, Carl Lumma <CLUMMA@N...> wrote:
> >Here it is, as promised (except it is 150 kB, not 100 kB).
> >
> >http://dkeenan.com/Music/StereoDekany.xls
>
> Awesome! Is there any way to distinguish the sounding notes and/or
> intervals?

Yes! They are the vertices that appear closest to you when you're
wearing 3D glasses with the left eye filter red. If there's interest
from folks who don't have 3D glasses, I could make a s/s with the two
images separated, and you'll have to go cross-eyed (or wall-eyed) to
experience the 3D. This is much less comfortable, and cardboard 3D
glasses are cheap and readily available, I gave some URL's earlier in
this thread.

>Say, circles around sounding notes... maybe even ones
> that scale with volume... and/or thickening the lines for sounding
> dyads, maybe even scaling the thickness with volume...

As far as I know, such things are not possible in Excel. Of course,
it's already being made to do things that it was probably never
expected to do.

Regards,

>>Awesome! Is there any way to distinguish the sounding notes and/or
>>intervals?
>
>Yes! They are the vertices that appear closest to you when you're
>wearing 3D glasses with the left eye filter red.

Which ones are closest? Only the closest three? Is their volume
determined by their distance?

>If there's interest from folks who don't have 3D glasses, I could
>make a s/s with the two images separated, and you'll have to go
>cross-eyed (or wall-eyed) to experience the 3D. This is much less
>comfortable, and cardboard 3D glasses are cheap and readily
>available, I gave some URL's earlier in this thread.

Red/blue works like a charm for me.

>>Say, circles around sounding notes... maybe even ones
>>that scale with volume... and/or thickening the lines for sounding
>>dyads, maybe even scaling the thickness with volume...
>
>As far as I know, such things are not possible in Excel. Of course,
>it's already being made to do things that it was probably never
>expected to do.

I wouldn't have suggested it, except that you've already gone far
beyond what I thought excel could do...

Now what we need is an applet that, instead of playing what's closest,
rotates what's playing. So it takes MIDI in, maps it to the dekany,
makes the sounding vertices and edges thicker, treats the thickness as
adding real mass, and then treats the viewing angle as the source of
weak gravity.

BTW, your projection is a generalized 4-D octahedron, correct? The
2-D projections in D'Allesandro have 5-fold symmetry, though. Have I
just not seen your dekany from the right angle? I tend to think Erv
uses the same 5-D object for the 6-factor row as he does for the
5-factor (dekany) row.

-Carl

--- In tuning@egroups.com, Carl Lumma <CLUMMA@N...> wrote:
> Which ones are closest? Only the closest three? Is their volume
> determined by their distance?

If they are behind the screen they don't sound at all. Otherwise
volume is proportional to distance in front of the screen, and of
course pan is left/right position. You often get tetrads and
occasionally get to hear a complete hexany.

> Now what we need is an applet that, instead of playing what's
closest,
> rotates what's playing. So it takes MIDI in, maps it to the dekany,
> makes the sounding vertices and edges thicker, treats the thickness
as
> adding real mass, and then treats the viewing angle as the source of
> weak gravity.

Good idea. But I can't help you, except that you're welcome to modify
Andrew's and my spreadsheet.

> BTW, your projection is a generalized 4-D octahedron, correct?

Not quite.

The 4D object is indeed the 4D generalised octahedron (the
dispentachoron).

The 3D image eventually passes thru every possible 3D projection of
the 4D object (and of course each eye's image eventually passes thru
every possible 2D projection of the 4D object). This is unlike Paul
Erlich or Robert Walkers models, which choose a single 3D projection
and rotate that.

There are 6 planes of rotation in 4D. There is no point in rotating in
the viewing plane, but the other 5 rotations are "geared together" in
a chain, with a reduction ratio of phi (or rather the best IEEE
floating point approximation of it) at each stage. So it "never
repeats" and takes as long as possible to "almost repeat".

>The
> 2-D projections in D'Allesandro have 5-fold symmetry, though. Have
I
> just not seen your dekany from the right angle?

That's right. It will happen if you watch long enough. You are more
likely to spot 2D symmetries like these while only looking thru one
color filter. The 3D throws you off, you don't "see them coming".
There are at least 2-fold, 3-fold and 5-fold symmetries. Did you see
my 3-fold one at
http://dkeenan.com/Music/DekanyGraph2.gif

> I tend to think Erv
> uses the same 5-D object for the 6-factor row as he does for the
> 5-factor (dekany) row.

I don't think so. I think he uses 4D for 5-factor row.

Regards,
-- Dave Keenan

>What version of Windows and Excel do you have?

It's Excel 97, Windows NT 4.0.

>Did you enable macros?

Yup.

What do you see when you click on the MIDI Out button?

Two different Yamaha DS-XG options -- neither one works.

>Do you get
>motion when you click on the Go button?

Yup!

Hi Dave Keenan

Just recently listened to your tumbling dekany excell spreadsheet on
a computer at my brother-in-law's Gaelic college.

Really enjoyed it, thanks. I had about 20 minutes to listen and play
around a bit.

However, forgot about the matter of the red - blue glasses (actually
have a pair with me if I'd only thought to bring them to the machine
with Excell), so will try to listen again some time.

It was a very modern p.c. with a reasonable sounding soundcard, so I
got a good idea.

Robert

We've just fixed a couple of bugs and added a feature to the tumbling
dekany at
http://dkeenan.com/Music/StereoDekany.xls

We hope that one of the bugfixes will enable sound on some machines
that didn't play it before. Paul Erlich, please let us know how it
goes.

It still only runs under Excel 97 or later on 32-bit Windows machines.
You must enable macros. Don't forget to choose your MIDI out device
using the "MIDI out" button on the spreadsheet.

The new feature is a slider to choose the distance from the viewer at
which the volume goes to zero. Thus one can hear more or fewer
simultaneous notes on average and hence more or less dissonance.

Regards,
-- Dave Keenan

Hi Dave K.!

>We hope that one of the bugfixes will enable sound on some machines
>that didn't play it before. Paul Erlich, please let us know how it
>goes.

It does play on my machine now, but it's in 12-tone equal temperament! (I
selected the reed organ patch since the "choir aahs" were thick with vibrato
and the reed organ has none, but it still has a good bunch of overtones).
Also, the note 6x7 seems to keep coming back, far more often than any of the
other notes . . .

I'm sure this will be an astounding audio/visual experience once it's fixed!

--- In tuning@y..., "Paul H. Erlich" <PERLICH@A...> wrote:
> Hi Dave K.!
> It does play on my machine now, but it's in 12-tone equal
temperament!
...
> Also, the note 6x7 seems to keep coming back, far more often than
any of the
> other notes . . .

Yikes! Thanks Paul. One usually hopes to fix more bugs than one
introduces. But not this time. I see I should have let Andy do the
changes.

I managed to scramble the position of the notes on the dispentachoron.
I believe that's fixed now.

http://dkeenan.com/Music/StereoDekany.xls

Unfortunately I haven't been able to figure out why the pitch bends
aren't working for you.

Can others please tell me if you're getting it in JI or 12-tET (or
something in between)? Choose a patch that has no vibrato, chorus or
reverb on your sound card, and lots of harmonics e.g. sawtooth.
Thanks.

Regards,
-- Dave Keenan

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

/tuning/topicId_15456.html#18437

>
> http://dkeenan.com/Music/StereoDekany.xls
>
> Unfortunately I haven't been able to figure out why the pitch bends
> aren't working for you.
>
> Can others please tell me if you're getting it in JI or 12-tET (or
> something in between)? Choose a patch that has no vibrato, chorus
or
> reverb on your sound card, and lots of harmonics e.g. sawtooth.
> Thanks.
>

This is kind of funny... but I believe Paul is right. It surely
sounds like 12-tET! The sound also stops halfway through, which it
didn't used to... I don't believe the "older" version was in
12-tET... And, now, I have "overwritten" my previous version, so all
is lost....

_______ ____ ___ _
Joseph Pehrson

I just uploaded a new version.

http://dkeenan.com/Music/StereoDekany.xls

I think we're down to one major bug now.

I believe its tuned in JI now. Paul?

But every second time I hit the "Go" button (after hitting "Stop")
there are 5 notes which don't sound at all, namely 4x5, 5x6, 4x9, 5x9,
6x9. I see their volume indicator bars going up but no sound
corresponding to them.

It is possible that this problem won't occur on other machines. Please
let me know.

The workaround is of course to hit "Go", "Stop", "Go" each time. But
the important thing is to acertain whether it is working correctly the
first time.

Regards,
-- Dave Keenan

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

/tuning/topicId_15456.html#18449

> I just uploaded a new version.
>
> http://dkeenan.com/Music/StereoDekany.xls

This sounds correct now... (A LOT different!)

It also doesn't stop sounding half way through now.... It's great.

________ ____ ____ _
Joseph Pehrson

Dave wrote,

>I believe its tuned in JI now. Paul?

Yes! I didn't like the lead-sawtooth patch, since it has chorus on it, so
once again I used reed organ, and . . . perfect!

Dave Keenan wrote,

>But every second time I hit the "Go" button (after hitting "Stop")
>there are 5 notes which don't sound at all, namely 4x5, 5x6, 4x9, 5x9,
>6x9. I see their volume indicator bars going up but no sound
>corresponding to them.

>It is possible that this problem won't occur on other machines. Please
>let me know.

I don't have this problem, even after changing the factors (I like changing
4 to 8) . . . This is a fantastic acheivement, Dave and Andy! I'll have to
nominate this

********************************************
*XENHARMONIC MULTIMEDIA PROGRAM OF THE YEAR*
********************************************

(should be a Grammy category, huh?)

How about a hexany version so that one can get familiar with the workings of
CPS in 3-d before moving on to 4-d? To be honest, the visual spinning 4-d
solid loses me (maybe I really need those 3-d glasses, though most 3-d
effects don't work on my eyes), but it's probably the best way to generate a
never-repeating sequence of the various consonant chords in interleaving
fashion . . . yay!

Dave, I notice one minor problem -- when I choose the factors 1, 3, 5, 7,
and 9, it says that 1x5 is C2, and 1x3 is Eb2, even though 1x3 should be
(and in fact sounds) lower than 1x5. A very minor bug, to be sure . . .
(also I could use a subwoofer for those low notes)

--- In tuning@y..., "Paul H. Erlich" <PERLICH@A...> wrote:
> Dave, I notice one minor problem -- when I choose the factors 1, 3,
5, 7,
> and 9, it says that 1x5 is C2, and 1x3 is Eb2, even though 1x3
should be
> (and in fact sounds) lower than 1x5.

Ok. That's fixed. As you guessed, it was only a problem in calculating
the octave number for the note name. The actual pitch was correct.

http://dkeenan.com/Music/StereoDekany.xls

Keep those bug reports coming.

Regards,
-- Dave Keenan

--- In tuning@y..., "Paul H. Erlich" <PERLICH@A...> wrote:
>This is a fantastic acheivement, Dave and Andy! I'll
have to
> nominate this
>
> ********************************************
> *XENHARMONIC MULTIMEDIA PROGRAM OF THE YEAR*
> ********************************************
>
> (should be a Grammy category, huh?)

Thanks Paul. I imagine the list of nominations for this category would
be pretty short. :-)

> How about a hexany version so that one can get familiar with the
workings of
> CPS in 3-d before moving on to 4-d?

Good idea. And then one day there's the 5D eikosany to tackle. Eek!

>To be honest, the visual spinning 4-d
> solid loses me (maybe I really need those 3-d glasses, though most
3-d
> effects don't work on my eyes),

Oh yes. There's no hope of following any notes without the 3D glasses
to separate near from far. I'm sure that such a simple uncluttered 3D
scene will "pop" for you in a short time with the glasses. Headphones
help too, in clarifying the stereo pan corresponding to the visible
motion of the near notes.

>but it's probably the best way to generate a
> never-repeating sequence of the various consonant chords in
interleaving
> fashion . . . yay!

Yes. A somewhat unexpected use for the golden ratio in a musical
context.

Regards,
-- Dave Keenan

You can think of this, rather than as a Dekany tumbling in 4 dimensions, as
an observer "orbiting" around a fixed Dekany in space. Which leads to the
idea: what if, instead of just a single Dekany, you had the full infinite
4-d lattice in space? Then, perhaps, in addition to the orbital motion, you
could add other motions to have the observer wander slowly through various
parts of the lattice? That could relieve the monotony of just hearing the
same 10 notes forever (though I've had quite a lot of enjoyment today from
various dekanies, including 2)5 [8,9,10,11,12] . . . particularly when
increasing the "distance at which volume goes to zero" to 200).

--- In tuning@y..., "Paul H. Erlich" <PERLICH@A...> wrote:
> You can think of this, rather than as a Dekany tumbling in 4
dimensions, as
> an observer "orbiting" around a fixed Dekany in space. Which leads
to the
> idea: what if, instead of just a single Dekany, you had the full
infinite
> 4-d lattice in space? Then, perhaps, in addition to the orbital
motion, you
> could add other motions to have the observer wander slowly through
various
> parts of the lattice?

Good idea. That would require 5 dimensions wouldn't it? I don't think
I'll be coding it any time soon. :-)

>That could relieve the monotony of just hearing the
> same 10 notes forever

One listener told me it was dope-smoking music. Don't try this at home
children. ;-)

>(though I've had quite a lot of enjoyment today from
> various dekanies, including 2)5 [8,9,10,11,12] . . . particularly
when
> increasing the "distance at which volume goes to zero" to 200).

Wild.

Paul, I've taken your (email) suggestion to make the Reed Organ the
default patch, since the sawtooth eventually fades to nothing on your
tone generator and presumably others.

Regards,
-- Dave Keenan

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

/tuning/topicId_15456.html#18457

> How about a hexany version so that one can get familiar with the
workings of CPS in 3-d before moving on to 4-d?

OK.. Dumbo again... but how does one actually see the 4th dimension??
Is this the movement in space over time that's being referred to??
:(

_________ _____ _____ _
Joseph Pehrson

>Good idea. That would require 5 dimensions wouldn't it?

It would still be the same 4 dimensions as in the dekany.

>I don't think
>I'll be coding it any time soon. :-)

:-(

>Paul, I've taken your (email) suggestion to make the Reed Organ the
>default patch, since the sawtooth eventually fades to nothing on your
>tone generator and presumably others.

Reed Organ also has a certain historical significance in JI -- think
Partch's Chromelodeon and Ellis's harmonium.

Greg Schiemer wrote:

>
>In the previous version I was able to select and change one of the generators
>without stopping. With the new version, when I do that, the following error
>message appears
>
>   Method 'Calculate' of object '_Global' failed

I've been able to recreate this message after pressing "Go" and then clicking
on a cell and changing its value manually (not with a slider or check box).

Could you elaborate on this a bit? Are you selecting and changing the
contents of a cell? Which version do you mean by "previous" (I'm thinking
you mean the version that didn't generate MIDI messages). Which version of
Excel are you using? Which OS? Does it happen every time or only some of
the time?

thanks,
Andy

Hey guys!

It's official. I'm a composer.

Well an algorithmic one anyway. :-)
And of course Andy already was.

Our "Ten voices from the fourth dimension" (or rather a 3 minute
segment of it) is to be "performed" at Dave Cope's concert of short
algorithmic compositions. The concert is on April 25 at 8pm in UCSC's
Recital Hall. I just arranged for 200 paper-framed 3D glasses to be
delivered.

How can I let Erv Wilson know about this?

Regards,
-- Dave Keenan

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
> Hey guys!
>
> It's official. I'm a composer.

That's amazing -- I hadn't read this post when I just posted to that effect. Well, I guess it's so
obvious it must be true!
>
> Our "Ten voices from the fourth dimension" (or rather a 3 minute
> segment of it) is to be "performed" at Dave Cope's concert of short
> algorithmic compositions. The concert is on April 25 at 8pm in UCSC's
> Recital Hall. I just arranged for 200 paper-framed 3D glasses to be
> delivered.
>
Awesome! Congratulations!!

> How can I let Erv Wilson know about this?

I don't know, but I sincerely hope he gets to experience it, takes an interest, and steers you in
brilliant new directions with this stuff . . .

--- In tuning@y..., jpehrson@r... wrote:

> OK.. Dumbo again... but how does one actually see the 4th dimension??
> Is this the movement in space over time that's being referred to??

Hi Joseph, this is a question which caused a flurry of posts last year, with dozens of links to sites
explaining how one can attempt to visualize figures in four _spacial_ dimensions. Remember all
the talk about the tesseract, the dispentachoron, me complaining about Java not working for me,
etc., etc.? That was all part of answering this question -- looks like you should go back and
review . . . Anyway, have you had a chance to play with this much, varying the factors and the
"distance at which volume goes to zero"? I'd be interested in hearing your impressions . . . I feel
this is a great work of art which involved the contributions of Erv Wilson, Dave Keenan, Andrew
Milton F., Oscar Lanzi III, Keenan Pepper, and maybe even I had something to do with inspiring
and facilitating its creation and debugging . . . we've brought the Wilson realm of pure harmony
to life!

--- In tuning@y..., PERLICH@A... wrote:

/tuning/topicId_15456.html#18549

> --- In tuning@y..., jpehrson@r... wrote:
>
> > OK.. Dumbo again... but how does one actually see the 4th
dimension?? Is this the movement in space over time that's being
referred to??
>
> Hi Joseph, this is a question which caused a flurry of posts last
year, with dozens of links to sites explaining how one can attempt
to visualize figures in four _spacial_ dimensions. Remember all
> the talk about the tesseract, the dispentachoron, me complaining
about Java not working for me, etc., etc.? That was all part of
answering this question -- looks like you should go back and
> review . . .

Now I remember this... but I should go back over it... I recall that
many of the Wilson graphics had such qualities.

>Anyway, have you had a chance to play with this much,
varying the factors and the "distance at which volume goes to zero"?

I'm enjoying the 1,3,5,11,13... maybe because I'd worked with
hexanies resulting from factors 1,3,5,11 before..

It seems the "distance at which volume goes to zero" has to be pretty
high to get much of an effect...

I still don't have the colored glasses...

>I feel this is a great work of art which involved the contributions
of Erv Wilson, Dave Keenan, Andrew Milton F., Oscar Lanzi III, Keenan
Pepper, and maybe even I had something to do with inspiring and
facilitating its creation and debugging . . . we've brought the
Wilson realm of pure harmony to life!

Absolutely! Especially if it can be projected or something. Having
people sitting around in a room each looking at separate computers
might not result in a "fine arts" experience... at least not a
"traditional" one...

It is, indeed, a great triumph. It's going to be hard to come up
with an "encore..."

_______ ____ _ __ _
Joseph Pehrson

--- In tuning@y..., PERLICH@A... wrote:
>I feel this is a great work of art ...

Whoa there! I think we might be getting a little carried away. It
isn't a great work of art.

> which involved the contributions of Erv
Wilson, Dave Keenan, Andrew
> Milton F., Oscar Lanzi III, Keenan Pepper, and maybe even I had
something to do with inspiring
> and facilitating its creation and debugging . . .

Absolutely. As I said earlier, the real genius behind this thing is
Erv Wilson's (someone _has_ emailed me his contact details, thanks).
Its hard to know where to stop with acknowledgements. But as well as
those listed in the spreadsheet so far, I'd like to thank everyone on
the tuning list who helped me understand Wilson's CPS's and gave Andy
and I feedback on the thing. I should also thank the Microsoft
programmers who made Excel and VBA what they are.

Regards,
-- Dave Keenan

--- In tuning@y..., jpehrson@r... wrote:

> OK.. Dumbo again... but how does one actually see the 4th
dimension??

One doesn't. You can just forget this idea.

If you watch 2D projections (e.g. shadows) of an unfamiliar rotating
3D object it will usually eventually "pop" and you will grok its 3D
form. But I don't expect this ever to happen while watching 3D
projections of a 4D object.

All you need aspire to is to become familiar with all of its possible
3D projections and how they change as the 4D object rotates.

> Is this the movement in space over time that's being referred to??

No. Not in this case. There are four spatial/harmonic dimensions
_plus_ time.

Regards,
-- Dave Keenan

Glad you're enjoying the spreadsheet!
You all should have heard the first musical rendition of the sheet,
though. I mistakingly hooked up the volume values to the pitch-bends and
this screaming banshee thing came out of it. It sounded really cool to me
but I can't imagine what Dave, expecting something completely different no
doubt, thought of it. He just politely pointed out the error and we went on.
After getting that fixed it now reminds me of a wind chime. My
favorite patch is French Horns with the transposition in the meat of their
range. Kinda sounds like a breeze blowing through tubes. I love it!

I don't have too much more to say, not understanding all the math and
stuff and not wanting to think about the ones saying it isn't art (We put
work into it - that makes it art, doesn't it?), so I'd like to thank God that
it worked, Dave Keenan for masterminding the whole thing (and taking me up on
my offer), and all the tuners that listened, enjoyed and commented on it.

Cheers,
Andy

--- In tuning@y..., AMiltonF@a... wrote:
>
> After getting that fixed it now reminds me of a wind chime.

Yes, I thought of the wind chime analogy too. A wind chime could be a good way to experience
a 2-dimensional CPS, but this is a 4-dimensional object showing various adjacencies in
4-dimensional space, so it seems to be beyond the capabilities of a real, physical wind chime
to represent -- unless perhaps you were very clever in building the wind chime!

--- In tuning@y..., PERLICH@A... wrote:
> --- In tuning@y..., AMiltonF@a... wrote:
> >
> > After getting that fixed it now reminds me of a wind chime.
>
> Yes, I thought of the wind chime analogy too. A wind chime could be
a good way to experience
> a 2-dimensional CPS, but this is a 4-dimensional object showing
various adjacencies in
> 4-dimensional space, so it seems to be beyond the capabilities of a
real, physical wind chime
> to represent -- unless perhaps you were very clever in building the
wind chime!

"The windchime that fell through a wormhole from the 4th
dimension".

This is great. I only realised yesterday the relationship to wind
chimes, when my 3 year old daughter had me hold her up so she could
clang away at one of ours (with 4 tubular bells).

I was wondering if anyone can figure out a way to make at least a 3D
windchime for an octahedral hexany, to be driven by actual wind?

-- Dave Keenan

--- In tuning@y..., "Paul H. Erlich" <PERLICH@A...> wrote:
> You can think of this, rather than as a Dekany tumbling in 4
dimensions, as
> an observer "orbiting" around a fixed Dekany in space. Which leads
to the
> idea: what if, instead of just a single Dekany, you had the full
infinite
> 4-d lattice in space? Then, perhaps, in addition to the orbital
motion, you
> could add other motions to have the observer wander slowly through
various
> parts of the lattice?

One has to calculate the distance from the observer to every note in
each iteration to determine how loud each note is. Would 171 notes be
close enough to infinity? 171-tET is 9-limit JI. So 171-tET should be
representable as a 4D periodicity block looped around in a 5th
dimension to make a hyper-hyper-toroid with gentle enough curvatures
that they wouldn't be noticed. But figuring out the 5D coordinates of
the 171 notes is beyond me at the moment.

I guess one should start by working out the 3D coordinates of
say 19-tET as a 5-limit toroid. Or first, backing up even further,
consider the 2D coordinates of 12-tET as a 3-limit circle.

Other problems are:

What happens when you change the factors from 3,5,7,9 to something
else? Does 171 notes still work? I doubt it.

In the case of the dekany the observer is tethered to the centre of
the hyperspherical shell. How do we keep from flying too far away from
the hyper-hyper-toroid?

-- Dave Keenan

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

> One has to calculate the distance from the observer to every note
in
> each iteration to determine how loud each note is. Would 171 notes
be
> close enough to infinity?

Having an infinite number of notes shouldn't be a problem. For
example, you could transform the triangular lattice so that each note
is simply at an integer point in a 4-d Cartesian lattice, and then
apply the same transformation to the motion and distance
calculations. As long as there's a finite "distance at which volume
goes to zero", it should be possible to calculate which notes are
sounding, no matter where you are in the infinite lattice.

>
> In the case of the dekany the observer is tethered to the centre of
> the hyperspherical shell. How do we keep from flying too far away
from
> the hyper-hyper-toroid?

That shouldn't be an issue, since you should be dealing with a 4-d
manifold, perhaps a non-euclidean one, but certainly there is no need
to have an actual 5th dimension in which the motion takes place . . .
for example, our universe may be a finite 3-d non-euclidean manifold,
which may be "thinkable" as the hypersurface of a hypersphere in a
euclidean 4-d, but we don't go around worrying about whether we're
going to fly away from our universe into a fourth dimension . . . in
other words the world will appear Euclidean to us at any moment,
while in fact a large-scale exploration of it could reveal
otherwise . . . hope that isn't a completely stupid reply to your
question.

By the way, Dave, the octave-assignment still seems a little funny --
for example, I have

5x7 5x6
B#4 A#

right now (factors are 5 6 7 8 9) . . . also it froze up after
running for a while (here on my friend's Windows 2000 Professional,
Pentium III 800MHz system).

More "bugs" in the dekany spreadsheet:

When I choose factors 7,8,9,10,11, the note names have so many flats
that in half the transpositions, every other note name disappears
entirely. Perhaps the program should somehow "center itself" between
flats and sharps, or actually lean toward sharps since the double
sharp is just one symbol.

When I click on "stop" and then manipulate the angles, it seems that
one increment of the motion is executed with every change I make. The
reason I think that's happening is that if I change one angle and
then change it back, I don't get the same shape I started with. If
I'm right, perhaps a simple workaround would be to allow the "Speed"
slider to go all the way down to zero.

--- In tuning@y..., PERLICH@A... wrote:
> More "bugs" in the dekany spreadsheet:
>
> When I choose factors 7,8,9,10,11, the note names have so many flats
> that in half the transpositions, every other note name disappears
> entirely. Perhaps the program should somehow "center itself" between
> flats and sharps, or actually lean toward sharps since the double
> sharp is just one symbol.

Good point. The note that has zero pitch bend relative to 12-tET is
the one that is the product of the first two factors. The naming
scheme is based on 1/4-comma meantone. So a workaround is to reorder
the factors so that the first two have GOFs (greatest odd factors) of
(in order of preference) 1, 3, 9, or 5. So in this case 8,9,7,10,11
will give a good result.

This note namer was a quick hack anyway and isn't really necessary for
appreciation of the dekany, and given the above workaround, I won't be
fixing it.

But notice that the source code (Excel Formulae and Visual Basic
Macros) are completely open to all. So you are welcome to make your
own changes, provided you make it clear on the spreadsheet that you
have modified it, while continuing to acknowledge the original
authors.

It's also unfortunate that I can't arrange the volume barchart to
always be sorted by increasing pitch from left to right. It is setup
to be that way for 4,6,5,7,9.

> When I click on "stop" and then manipulate the angles, it seems that
> one increment of the motion is executed with every change I make.
The
> reason I think that's happening is that if I change one angle and
> then change it back, I don't get the same shape I started with. If
> I'm right, perhaps a simple workaround would be to allow the "Speed"
> slider to go all the way down to zero.

Yes. You're right. This is due to automatic calculation (which we do
want to be on when in "Stop" mode). Unfortunately your suggested
workaround wont work.
What you _could_ do is choose, from the menubar,
Tools/Options/Calculation/Manual. But this will be set back to
automatic every time you hit the Stop button.

However, the intended way for you to do what you are trying to do is
to uncheck "Motion" and click "Go". The angle sliders should then work
as you expect. You can uncheck "Sound" too if you want.

-- Dave Keenan

--- In tuning@y..., PERLICH@A... wrote:
> By the way, Dave, the octave-assignment still seems a little funny
--
> for example, I have
>
> 5x7 5x6
> B#4 A#

You mean there's no octave number on the 5x6? Ah. No. I tried it
myself. This is a typo right? The 5x6 is correctly called "A3" but the
5x7 should be called "B#3" except it's actually a bent C so the octave
number has been bumped. I'll see what I can do. Thanks.

> . . . also it froze up after
> running for a while (here on my friend's Windows 2000 Professional,
> Pentium III 800MHz system).

Please CC me your answers to Andy's excellent (email) questions.

Thanks heaps Paul, for all this testing.

-- Dave Keenan