√½ instead of the golden ratio - Page 2 - diyAudio
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Old 16th March 2009, 04:59 PM   #11
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I've only recently started using the golden ratio heavily. Any irrational number will usually do.

One has to be careful not to use root(2) twice in the same box. The ratio of the dimensions in the box in post 2 (0.707:1:1.414) can also be expressed as 1:1.414:2. That is the kind of ratio you want to avoid.

dave
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Old 16th March 2009, 06:51 PM   #12
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Default Re: Why the golden ratio?

Quote:
Originally posted by PigletsDad
In some cases, there is mathematical justification for choosing the golden ratio.
...

which looks like the most slowly converging expansion possible, then you can show that
g = 1/2 + sqrt(5)/2

Neat, huh?
Just a quick clarification.

Is that -

g = [0.5 + SqRt(5)] / 2

or...

g = 0.5 + [SqRt(5)/2]

Just curious.

As I said in my initial post, I got my formula out of a speaker design book, but again it said this was for aesthetic appearance. From an architectural perspective, this is a shape that is visually appealing.

Now keep in mind, this ratio seems to be from the 'bookshelf' era. Modern tower speakers seem to have abandon these ratios all together, though perhaps not the concepts the rule is based on.


Also, can we have a consensus that this -

0.618 : 1 : 1.618

is indeed the correct and true Golden Ratio.

Steve/bluewizard
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Old 16th March 2009, 07:17 PM   #13
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Agreed. From a technical standpoint, any irrational fraction will do. i.e.

Golden Ration / Fibonacci ==> 1/phi ==> 1/1.618.....

natural exponent ==> 1/e ==> 1/2.71828....

Pi ==> 1/pi ==> 1/3.14159....

Any of these will ensure that room / reflection nodes are not reinforcing, but the Golden ratio tends to be the most convenient to work from.
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Old 17th March 2009, 12:35 AM   #14
GM is offline GM  United States
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Quote:
Originally posted by planet10
I've only recently started using the golden ratio heavily. Any irrational number will usually do.

One has to be careful not to use root(2) twice in the same box. The ratio of the dimensions in the box in post 2 (0.707:1:1.414) can also be expressed as 1:1.414:2. That is the kind of ratio you want to avoid.

dave
To play the Devil's Advocate, according to Mssrs. Bolt, Barenek, and Newman, their published nomograph of acceptable room ratios, ergo speaker box ratios, shows a 1.0:1.5:2.0 mean, putting the 1.0:1.414:2.0 Architectural ratio well within acceptability and rather surprisingly when I first saw it, the 1.0:1.618:2.618 Golden Mean well outside.

Since I typically design high aspect ratio cabs, this issue only applies to its width/depth where the Golden mean is one of many acceptable ratios, so typically suggest it as it's apparently the most familiar.

GM
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Old 17th March 2009, 06:01 AM   #15
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Not 45sine/cosine but I the way they used the rule of thirds on these.
Avantgarde UNO PICCO, DUO PRIMO, and Basshorn
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Old 17th March 2009, 11:49 AM   #16
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The golden ratio is ( 1 + sqrt(5) ) / 2

See http://en.wikipedia.org/wiki/Golden_ratio

A more detailed explanation can be found at http://en.wikipedia.org/wiki/Continued_fraction with the specific property I mentioned at http://en.wikipedia.org/wiki/Continu...n_ratio_.CF.86
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Old 18th March 2009, 12:51 AM   #17
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So what about speaker placement? I just eyed this setup to where the height of my head is and put it off center so it wasn't a third but where I guessed the golden section of the room was.

Today I was curious as to how close I was and wanted to check other dimensions that I didn't even think about or consider - height and width.

The Golden section of the height of my room is 58.7" and I checked and my phase plug is a fraction of a centimeter away from 58".

The Golden section of the width of the room is around 73. And damn if that isn't my favorite spot to listen to the speakers in - a little in front of the sweet spot. I in no way did this on purpose with the set up. if I was shooting for that spot I would have probably put the speakers too close to the wall. That was my only aim with where I set them was to get the bass boost out of the speakers and pull them off the wall.

Now the one I did sort of guess at was the length. I was off about 8". The golden section is 102" and I am at 110".

I was just curious. I think I like where I have my speakers set, but do you think you derive benefit in the same way from speaker placement within the room as you do from the dimensions of the box and placement of drivers?

Oh and I think the dimensions of my room might be close to 45sine+1 or the golden ratio.
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Old 18th March 2009, 01:23 AM   #18
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Quote:
Originally posted by Key
...do you think you derive benefit in the same way from speaker placement within the room as you do from the dimensions of the box and placement of drivers?
The AES did a study to come up with a reference rectangular room, and where speakers and people go in it... a lot of phi turned up in that.

dave
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Old 18th March 2009, 07:24 AM   #19
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Old 18th March 2009, 09:36 AM   #20
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Hello,

For what it's worth, you'll find in attached file a graph I draw many years ago. This graph resulted from a study I did of the Rayleigh formula for the resonance modes of rectangular boxes (including rooms).

The colors and yellow numbers give the maximum value of the difference of frequency between 2 following resonances (we want to minimize that parameter).

Points on the red line corresponds to optimal values. You should try to design your boxes and room with such length/heigh and width/heigh ratios corresponding to a point on the red line.

Best regards from Paris, France

Jean-Michel Le Cléac'h
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