Golden Cuboid...Speaker placement!!

pearsall001

If you have a rectangular room who have to try this out. I came across it on the Cardas website. I thought my system sounded fantastic already, but this mathamatical calculation for speaker placement made my system completely open up. I was dumb founded at the before & after effect. I kid you not!! My room is 13x32 & it has never sounded better. If you have the room - DO IT!! He also gives speaker placement calculations for other shaped rooms. Check it out!!

http://www.cardas.com/content.php?area=insights&content_id=26&pagestring=Room+Setup

hearingimpared

I'm reading it now . . . I wonder how this formula works with SDAs. I'll get back to you. . . PS: you've got email.

hearingimpared

Phil, I don't think I can use this. This "Golden Cuboid" assumes that the speaker are going to placed on the short wall. My room is 20' x 11.5'. I have to place the 1.2 TLs on the 20' wall because the setup instuctions call for a minimum for each speaker of 3' from the side walls and a recommended 6' to 8' between the speakers. The speakers are 2' across. This equates to the wall that the speakers are placed on be a minimum of 15.5' to 16' wall. The distance from the center of both speakers to the sweet spot should be atleast the distance of the speakers from each other which gets me about 2 to 3 feet from the back wall depending on how far from the back wall I place my speakers. I'm sure that all the walls are going to need a lot of wall treatments. Of course I am going to have to do a lot of experimenting. I just received my MYE Sound points today. I am definetely going to have to experiment BEFORE I place the points on the speakers because once they are on they are going to be a bear to move.

Lsi9

By quckly scanning over that page I am assuming they are basing that on the Golden Equation, AKA The Golden Ratio, AKA The Golden Rectangle, AKA The Fibonacci Spiral?
Something I learned in Art School. Artists for centuries as well as other areas of civilization have used this equation for aesthetic compositional reasons, the shape that is contained in it is seen in the smallest of natural things like a snail as well as the macro of nature which are the spirals of a galaxy.




What is the equation of the Fibonacci spiral?

The Golden section squares are shown in red here, the axes in blue and all the points of the squares lie on the green lines, which pass through the origin (0,0).
Also, the blue (axes) lines and the green lines are each separated from the next by 45° exactly.
The large rectangle ABDF is the exactly the same shape as CDFH, but is (exactly) phi times as large. Also it has been rotated by a quarter turn. The same applies to CDFH and HJEF and to all the golden rectangles in the diagram. So to transform OE (on the x axis) to OC (on the y axis), and indeed any point on the spiral to another point on the spiral, we expand lengths by phi times for every rotation of 90°: that is, we change (r,theta) to (r Phi,theta+Pi/2) (where, as usual, we express angles in radian measure, not degrees).
So if we say E is at (1,0), then C is at (Phi,Pi/2), A is at (Phi2, Pi), and so on.
Similarly, G is at (phi,-pi/2), and I is at (phi2, -pi) and so on because phi is 1/Phi.

The points on the spiral are therefore summarised by:

r = Phin and theta= n Pi/2
If we eliminate the n in the two equations, we get a single equation that all the points on the spiral satisfy:
r = Phi2 theta / Pi
or
r = Mtheta where M = Phi2/Pi = 1.35845627...

For ordinary (cartesian) coordinates, the x values are y values are generated from the polar coordinates as follows:
x = r cos(theta)
y = r sin(theta)
which we can then use in a Spreadsheet to generate a chart as shown here.
Such spirals, where the distance from the origin is a constant to the power of the angle, are called equiangular spirals. They also have the property that a line from the origin to any point on the curve always finds (the tangent to) the curve meeting it at the same angle.
Another name is a logarithmic spiral because the angle of any point from the "x" axis through the origin is proportional to the logarithm of the point's distance from the origin.
To see that the Fibonacci Spiral here is only an approximation to the (true) Golden Spiral above note that:
at its start there are two squares making the first rectangle but the true golden spiral above has no "start"
those two squares make a rectangle 1x2 but all rectangles in the true spiral are true Golden Rectangles 1xPhi.
All the other rectangles on the right are ratios of two neighbouring Fibonacci numbers and are therefore only approximations to Golden Rectangles

hearingimpared

Lsi9 wrote:

By quckly scanning over that page I am assuming they are basing that on the Golden Equation, AKA The Golden Ratio, AKA The Golden Rectangle, AKA The Fibonacci Spiral?
Something I learned in Art School. Artists for centuries as well as other areas of civilization have used this equation for aesthetic compositional reasons, the shape that is contained in it is seen in the smallest of natural things like a snail as well as the macro of nature which are the spirals of a galaxy.




What is the equation of the Fibonacci spiral?

The Golden section squares are shown in red here, the axes in blue and all the points of the squares lie on the green lines, which pass through the origin (0,0).
Also, the blue (axes) lines and the green lines are each separated from the next by 45° exactly.
The large rectangle ABDF is the exactly the same shape as CDFH, but is (exactly) phi times as large. Also it has been rotated by a quarter turn. The same applies to CDFH and HJEF and to all the golden rectangles in the diagram. So to transform OE (on the x axis) to OC (on the y axis), and indeed any point on the spiral to another point on the spiral, we expand lengths by phi times for every rotation of 90°: that is, we change (r,theta) to (r Phi,theta+Pi/2) (where, as usual, we express angles in radian measure, not degrees).
So if we say E is at (1,0), then C is at (Phi,Pi/2), A is at (Phi2, Pi), and so on.
Similarly, G is at (phi,-pi/2), and I is at (phi2, -pi) and so on because phi is 1/Phi.

The points on the spiral are therefore summarised by:

r = Phin and theta= n Pi/2
If we eliminate the n in the two equations, we get a single equation that all the points on the spiral satisfy:
r = Phi2 theta / Pi
or
r = Mtheta where M = Phi2/Pi = 1.35845627...

For ordinary (cartesian) coordinates, the x values are y values are generated from the polar coordinates as follows:
x = r cos(theta)
y = r sin(theta)
which we can then use in a Spreadsheet to generate a chart as shown here.
Such spirals, where the distance from the origin is a constant to the power of the angle, are called equiangular spirals. They also have the property that a line from the origin to any point on the curve always finds (the tangent to) the curve meeting it at the same angle.
Another name is a logarithmic spiral because the angle of any point from the "x" axis through the origin is proportional to the logarithm of the point's distance from the origin.
To see that the Fibonacci Spiral here is only an approximation to the (true) Golden Spiral above note that:
at its start there are two squares making the first rectangle but the true golden spiral above has no "start"
those two squares make a rectangle 1x2 but all rectangles in the true spiral are true Golden Rectangles 1xPhi.
All the other rectangles on the right are ratios of two neighbouring Fibonacci numbers and are therefore only approximations to Golden Rectangles

Okay . . . can you put that in dummy language for me about 8th grade level should do?:D

schwarcw

I plotted that out once using a slide rule. It's one of those fun things to do with math. Some math heads will get all philosophical about these "magic" equations. Lots of fun for sure.

schwarcw

Extra points if you can post the 3D equation for the spiral in revolution.:D

hearingimpared

schwarcw wrote:

I plotted that out once using a slide rule. It's one of those fun things to do with math. Some math heads will get all philosophical about these "magic" equations. Lots of fun for sure.

My older son is a "math head." I'm going to show him this when he comes for Thanksgiving tomorrow.:)

pearsall001

hearingimpared wrote:

Okay . . . can you put that in dummy language for me about 8th grade level should do?:D

I'm with you. What the hell did he just say?? I never was that good at math. Dumb it down a bit so maybe I can understand a wee bit of all that mumbo jumbo! Bottom line, the Golden Cuboid speaker placement formula is magic in my book.

Lsi9

hearingimpared wrote:

Okay . . . can you put that in dummy language for me about 8th grade level should do?:D

hehe...

I'll explain it in terms I know best, artistic...
imagine that whole rectangle is a canvas, as a painter it is beneficial to the overall naturalness of the image I will paint on the canvas to make the J point (in the diagram above) the center of the canvas instead of the actual center. I can then add to the composition by adding elements in the painting that fit the lines in the diagram, it is proven to look better overall...Architects use this equation...


http://www.mathopenref.com/rectanglegolden.html
http://en.wikipedia.org/wiki/Golden_rectangle

by the way I didnt read the article in question, if I am off base then I apologize but it is fun talking about this.

hearingimpared

Lsi9 wrote:

hehe...

I'll explain it in terms I know best, artistic...
imagine that whole rectangle is a canvas, as a painter it is beneficial to the overall naturalness of the image I will paint on the canvas to make the J point (in the diagram above) the center of the canvas instead of the actual center. I can then add to the composition by adding elements in the painting that fit the lines in the diagram, it is proven to look better overall...Architects use this equation...


http://www.mathopenref.com/rectanglegolden.html
http://en.wikipedia.org/wiki/Golden_rectangle

by the way I didnt read the article in question, if I am off base then I apologize but it is fun talking about this.

Duuuuuhhhhhh okay I get it now. . . is golden rectangle like golden showers?:D

SCompRacer

schwarcw wrote:

Extra points if you can post the 3D equation for the spiral in revolution.:D

I can show you that in 3D Studio MAX R2.

unc2701

Bringing it back to audio, the reason why this works is that it minimizes the ability of the system to create standing waves- what you're hearing is the bass having a lot less spikes & valleys due to phase cancelation when the waves bouce off your walls.

If you work through the equations & it turns into this nasty integral- that happens to be exactly equal to phi. It's amazing all the places that pops up.

dragon1952

I've been experimenting with this Cardas method the last couple of days and it's kind of bizarre because your speakers always end up at least 5 ft into the room and you end up sitting so close it's like they're right on top of you. It's so unorthodox that , even if you have the room you almost want to say 'screw it', even if it does sound better. I doubt if 90% of most people could even consider this as an option. BTW, the product info for my speakers says to go 1 ft off the back wall and at least 2 ft (or more) from the side. I've always thought that the farther from the back wall, the less bass but actually the bass is much less boomy and much more musical using the Cardas method. Having a little trouble getting the center focus just right, especially with the drums. And still not sure I want my speakers out in the middle of the room. For one thing, I'll probably end up knocking them over. Does anyone out there actually use this method?

mulveling

I've tried that. It's worth trying, but IMO optimal placement is still going to depend a lot on your specific speakers, ears, preferences, and room arrangements. No formula is going to always give you the optimal placement (or even close to it, sometimes). When I followed that formula, it ended up placing seating smack in the MIDDLE of my room, which is horrendous for bass nodes - just one of the many variables it doesn't take into account (unless you have the precise "golden" room dimensions).

Sometimes I've found I prefer placement on the long wall - sometimes that gives a wider sound stage and better imaging. With other speakers/rooms it's often sounded best on the short wall. You just gotta try a few different things if you can!

I can definitely say that speaker positioning is one of the most critical components of your system.

dragon1952

I know, I've been considering trying the long wall. That's probably my next experiment.

treitz3

I have no choice BUT to run the long wall. Any math for a long wall setup?

dragon1952

Scroll down the document and there are calculations for the long wall. Looks like more options that way.
http://www.cardas.com/pdf/roomsetup.pdf

bikerboy

Hi,
I have been using that for my sda-2 set up for years. I even have it in my sig. The cardas site has lots of good info and the calculator on the site is easy to use. I played with many other setups and have always gone back to the ratio suggested spot. Best bass and imaging. I could never get my speakers to sound great close to the wall. Its funny we can use something centurys old to place speakers. Cardas uses the ratio for wood blocks also. I removed the small riser from the bottom of the speakers and place them on 3 wood blocks. Helped the speaker connect to the concrete floor better. Imaging is better, mid bass is cleaner. The tweaks never end.

dragon1952

OK...well I guess this is finally it. I think I've finally dialed it in. This system works incredibly well and it's really too bad that it isn't able to be implemented in most people's systems. If you've got a dedicated listening room you need to try this. If I had been able to do this earlier I probably wouldn't have swapped out speakers and components like I have. And it totally invalidates a lot of reviews, if not most, because without optimally placed speakers your observations aren't necessarily valid. Having said that, I'd like to return to some of my previous systems to see what would happen.

Hawkeye

I set up my 2 channel this way the results are outstanding. The difference is night and day.

However, when the wife saw the speakers in the middle of the room she raised some "colorful discussion". They went back into the corners where she thought they belong.

When it's time to do some serious listening, she relents and they come back out to the spots where I think they are supposed to be. I put little dots on the floor (wood floors) for the repeatable correct placement. On occasion I've "forgotten" to put the speakers to bed so to speak. The more I forget, the more she gets used to seeing them out in space.

Gordo

tryrrthg

treitz3 wrote: »

I have no choice BUT to run the long wall. Any math for a long wall setup?

The Audio Physic method.

http://www.immediasound.com/Speakersetup.html

http://www.audioasylum.com/scripts/d.pl?audio/faq/audiophysic.html

dorokusai

I've never found it difficult to setup loudspeakers.....ever. Hmmmm, oh well.

Face

I found better imaging setting them up in the middle of the room, but bass suffered. I'll be shoving the monkey coffins back into the corners again soon.

phuz

Spiral out, man.

No toe in? Pffffffft.

reeltrouble1

now that sounds kinky Phuz, the spiral I can handle but getting the toe in is going to be a bit of trick.

I dont know, I just sort of plop down in between them and hit play, sounds good, if I sip Rum they can sound a bit better.

SKsolutions

No dedicated listening room, so I have to shuffle stuff about. I have two pieces of marker tape on the hardwood, and the double recliner at the far end has felt slides on it. When I really want to get on it, I pull the speaks out to the tape, slide the couch back to a couple of feet from the rear wall, and listen. The image stability and stage of this setup works wonders. Bass detail comes faster and cleaner without the extra loading, harmonics are amazing, and I find that the sub in the front corner, when used, blends much easier when it's almost 5' behind the speaks. Around 13x17x8 Speakers are at 67'' from rear, and around 30'' when put to bed.

It's a bit of a procedure, but when I'm changing stuff around, it's the best way to qualify better/worse. The guest room, dining room, and changing room, all have awful dimensions, or the setup would be in there.

tommyvo09

Nice work--thank you for sharing-
Thanks so much for this. I appreciate the effort. It really helps a lot.
Glad to read such a nice piece of information.
This is exciting news.

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BeefJerky

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