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Multi-Way Conventional loudspeakers with crossovers

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Old 15th March 2009, 08:31 PM   #1
Key is offline Key  United States
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Default √ instead of the golden ratio

Do any speakers use it? Any pics?
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Old 15th March 2009, 09:00 PM   #2
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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
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Old 15th March 2009, 10:07 PM   #3
Key is offline Key  United States
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Yeah I had noticed .414 before in other things. I had always thought of it as 22.5 tan though. Same with √ 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.
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Old 15th March 2009, 11:17 PM   #4
Key is offline Key  United States
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I thought this one was kinda cool for the golden ratio
Diamond 9
the guide is set to golden vertical 1.618034
Click the image to open in full size.
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Old 16th March 2009, 02:02 PM   #5
sreten is offline sreten  United Kingdom
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Quote:
Originally posted by BlueWizard


The rule is simple -

1.4:1.0:.707

Steve/bluewizard
Hi,
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.
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Old 16th March 2009, 02:15 PM   #6
Key is offline Key  United States
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He was doing √ not the Golden Ratio.

√= .7071
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Old 16th March 2009, 02:20 PM   #7
sreten is offline sreten  United Kingdom
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Quote:
Originally posted by Key
He was doing  not the Golden Ratio.

= .7071
Quote:
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
Hi, its the Golden Ratio for visual appeal and acoustics, /sreten.
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Old 16th March 2009, 03:05 PM   #8
Salas is offline Salas  Greece
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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.
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Old 16th March 2009, 03:07 PM   #9
Salas is offline Salas  Greece
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P.S. Better use Edge software. There are many possibilities on a baffle, certainly more than those two.
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Old 16th March 2009, 03:22 PM   #10
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Default 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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