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MultiWay Conventional loudspeakers with crossovers 

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15th March 2009, 09:31 PM  #1 
diyAudio Member
Join Date: Jan 2009

√½ instead of the golden ratio
Do any speakers use it? Any pics?

15th March 2009, 10:00 PM  #2 
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Join Date: Jun 2007

As far as I've been able to discern there is an Architectural Golden Rule and a Acoustical Golden Rule. I always use the Architectural model because that is what was contained in the first speaker design book I even used.
But is is for visual appeal, not acoustic perfection, though it comes very close to acoustic perfection too. The rule is simple  1.4:1.0:.707 If you divide 1 by .707 you get 1.414. So, the actual ratio is 1.414 : 1.00 : 0.707 The also correspond to trig functions, and are also the SqRt(0.5) and the SqRt(2). So, a visually appealing cabinet would have the ratios of 14" H x 10" wide x 7" deep, or 24" x 20" x 14". My cabinets are 26" x 18" x 13", which is slightly off from the ratios at 1.44 : 1.0: 0.722, but I don't think we need to haggle over a few fractions of an inch. The perfect dimensions would be 25.45" x 18" x 12.73"; I figure I'm close enough. Notice that using this ratio, the depth come extremely close to being a multiple of the height. Steve/bluewizard 
15th March 2009, 11:07 PM  #3 
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Join Date: Jan 2009

Yeah I had noticed .414 before in other things. I had always thought of it as 22.5 tan though. Same with √½ I always think of it as 45 sine.
My monitors (wharfedale diamond 8.2) I believe use the golden ratio or are close being 364MM x 212MM x 322MM . And if you take a program like Atrise Golden Section you can kind of see how they used it in the placement of the phase plug and tweeter. I had always used both just as a way to be less cliche than the rule of thirds. It's not used as much as the rule of thirds in photos and designs. But I also notice these numbers come up in dsp and audio processing. 
16th March 2009, 12:17 AM  #4 
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16th March 2009, 03:02 PM  #5  
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Join Date: Nov 2003
Location: Brighton UK

Quote:
AFAIK its more like ~ 0.6 : 1.0: ~1.6, if they are x, y, and z then z/y needs to equal y/x = 0.618 : 1 : 1.618. sreten. 

16th March 2009, 03:15 PM  #6 
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Join Date: Jan 2009

He was doing √½ not the Golden Ratio.
√½= .7071 
16th March 2009, 03:20 PM  #7  
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Join Date: Nov 2003
Location: Brighton UK

Quote:
Quote:


16th March 2009, 04:05 PM  #8 
diyAudio Chief Moderator
Join Date: Oct 2002
Location: AthensGreece

I have used 0.7 when 1.618 wasn't applicable due to constrains. It works. Still less ripple on impulse graph than near symmetry. Unfortunately haven't saved any photos. Not as good as with 1.618. Near enough though.

16th March 2009, 04:07 PM  #9 
diyAudio Chief Moderator
Join Date: Oct 2002
Location: AthensGreece

P.S. Better use Edge software. There are many possibilities on a baffle, certainly more than those two.

16th March 2009, 04:22 PM  #10 
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Join Date: Jul 2007
Location: South Worcestershire

Why the golden ratio?
In some cases, there is mathematical justification for choosing the golden ratio.
If we want the sequences of modes in the two directions to have few near coincidences, we want to avoid a simple rational ratio, but instead want the most irrational one we can get. One specific way of defining "the most irrational", is to say that it is the number with continued fraction expansion that converges most slowly. Any exact rational has a finite continued fraction expansion over the integers, but for an irrational the expansion carries on. If we want the expansion to converge slowly, we should never divide by a large number. So if we consider g = 1/(1+1/(1+1/(1 ....... which looks like the most slowly converging expansion possible, then you can show that g = 1/2 + sqrt(5)/2 Neat, huh? 
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