Golden Ratio

[kayagum]

Do you buy this? From Sweetwater's "Word of the Day"

Golden Ratio
As first determined by the ancient Greeks, the Golden Ratio is a theoretical ratio for room dimensions that results in "perfect" room acoustics. This means that no matter where you are in a room, the sound will be balanced and natural, with little interference from standing waves or ringing that may occur in less-than-ideal rooms. The ratio, named phi, of height to width to length of a room to achieve optimal sound in a room is approximately the width 1.6 times the height and the length 2.6 times the height, and was named for the Greek sculptor Phidias. In theory, minimal acoustic treatment should be needed in a room with dimension ratios that matched the formula. However, it may be desirable to acoustically treat one end of the "Golden" room, to be able to have a place in the room where there are fewer reflections, resulting in a less "live" sound. If it's not possible to have a room that fits the ratio perfectly, there are ways to achieve similar results. For example, if a room should have a 5-foot ceiling to match the ratio of the wall length and width, apply acoustic treatment to the walls above five feet.

Ladies and gentleman, start your room dimension calculators!

PS By this method, my basement is pretty darn close to the 6.5' x 10.4' x 27.04' ratio- cool! It actually does sound better than it should....

[Professor]

Well I don't recall that the Golden Ratio and the Golden Mean were originally intended for acoustics but rather for visual aesthetics - creating buildings and spaces which were the most pleasing to the eye. And of course, beyond being simply eye-pleasing, it's also among the most architecturally stable ratios for constructing buildings, second maybe to pyramids? The ratio that was stumbled upon from that direction proved to be similar to it's relative pi, both in the simplicity of it's origin (ratio of a cirlcle's diameter to it's circumference) and the absolutely mind-boggling way it appears everywhere in nature.
As the most mathematical of the arts, it's only logical that pi and phi would be visible in all sorts of applications around music and sound in general. The linear nature of the overtone series, the geometric relationship of octaves, the logrithmic nature of amplitude, the cyclical nature of frequency itself, all inter-relate around those ratios. So I guess it would seem almost natural that applying those ratios where it's possible to do so in acoustic designs is at the very least not going to be harmful, and quite possibly will be helpful to whatever you are creating.
Similarly, applying Fibinaci numbers (which create golden ratios) or the quadratic equation to acoustic treatments such as diffusors is done all the time for a very good, and a very ancient reason.

Of course, the very simplified length/width/heighth ratios apply easily to rectangular rooms, but rectangular rooms are not necessarily the best for tracking live instruments. They may prove to be the most evenly resonant spaces, but the parallel surfaces and resonances that prove so pleasing for simply listening to an instrument in a room can prove difficult when trying to recording an instrument in that room. But then you can apply some golden ratio diffusion.

-Jeremy

[Ethan Winer]

Kay,

> the Golden Ratio is a theoretical ratio for room dimensions that results in "perfect" room acoustics. <

If only.

> no matter where you are in a room, the sound will be balanced and natural, with little interference from standing waves or ringing that may occur in less-than-ideal rooms. <

OMG, what a total load of crap.

> In theory, minimal acoustic treatment should be needed in a room with dimension ratios that matched the formula. <

Clueless, totally clueless. Do you happen to know who at Sweetwater wrote this drivel?

--Ethan

[kayagum]

Here's the actual article: http://www.sweetwater.com/insync/index. ... 03/21/2006

I think they have an editor who compiles this, and they have changed around some in the last couple of years.

I figured it's one of those "if it sounds too good to be true, it probably is."

[RodC]

I thought the Golden Ratio was the ratio of F to M attending a gathering. Too much of the latter and it becomes a sausage fest.

[thethingwiththestuff]

yeah, immortalized in that beach boys lyric: "1.6 girls for every boy"..

seriously, who do i believe? the auralex dealer who says the right room ratio will eliminate the need to purchase treatment, or the guy who sells treatment but is always here to help out the TO community?

my dialectical reasoning is jamming up.....

ethan, what do you think about jeremy's points about diffusion and practical acoustic uses for "phi?" obviously i cant just build a standard drywall rectangle with those ratios and expect it to make a flat room, but do you think this formula can be useful at all?

[vsr600]

The golden ratio is just a number. Like pi, it's defined for a specific geometric property in mathematics. It pops up in many forms of geometry especially when pentagonal symmetry is involved. Anyway if you really want to check this out wikki it or check mathworld at wolfram: http://mathworld.wolfram.com/GoldenRatio.html

[wedge]

The golden ratio appears in nature everywhere, and it's presence seems to create things that most humans would regard as beautiful. The Greeks figured this out, and used it in their architecture to good effect.

For instance, studies have been done which show that faces that most would regard as attractive -- both male and female faces -- have features that relate to each other with the ratio of phi (golden ratio) in very tight fashion.

The length of the bones in your fingers relate to each other with phi -- first digit to second, and second to third -- and this is just one example... The more tightly body parts relate to each other with phi, the more attractive these body parts will seem to others. It's really most bizarre. Phi seems to be the mathematical language of natural beauty, in other words...

How this might relate to sound, who knows?

[nclayton]

I don't think you're any more likely to "find" the golden ratio in nature than you are to find 5/3 in nature, or pi/2 (both of which are close enough to the ratio to be confused with it given some rounding errors), or 1/2 or 10/1, or any other ratio you can name and the people who think that the the golden mean and the fibonacci sequence are somehow special or magical have the same credibility as fortune cookie fortunes that tell you that your eight lucky numbers between 1 and 20 are such and such, and then you reallize that, you know, four of those have important properties to you, like for example you have two testicles or whatever.

Still, despite what professor said up there earlier about harmonic sequences and etc. I think if you are going to have a rectangular room then the golden ratio isn't a bad one for the length of the walls if only because despite it's name it's actually irrational, and so if you get it right the lengths of your walls are not going to be harmonically related at all, in any way, right up to infinity hertz, which is not a bad place to start if you eventually want to eliminate standing waves. It's probably a good stopping point between 1:1 (which would be horrible) and 2:1 (which would also be really bad).

I think.

Ned

[analogcat]

Architecture specifically for acoustics was built on these principles, but usually it would be based on Pythagorean ratios listed above. The Cluny Abbey in France was one (gone now).
It was suppose to sound pretty good for chanting.



We're not so far from the Middle Ages these days.

[wedge]

I don't think you're any more likely to "find" the golden ratio in nature than you are to find 5/3 in nature, or pi/2 (both of which are close enough to the ratio to be confused with it given some rounding errors), or 1/2 or 10/1, or any other ratio you can name and the people who think that the the golden mean and the fibonacci sequence are somehow special or magical have the same credibility as fortune cookie fortunes that tell you that your eight lucky numbers between 1 and 20 are such and such, and then you reallize that, you know, four of those have important properties to you, like for example you have two testicles or whatever.

Do your research. There's tomes after tomes written about this by respected researchers/mathematicians/scientists. It's not something pulled randomly out of someone's uniformed ass...

[Ethan Winer]

> who do i believe? the auralex dealer who says the right room ratio will eliminate the need to purchase treatment, or the guy who sells treatment but is always here to help out the TO community? <

ROF,L. You should believe the person whose explanations make the most sense. As I see it, Sweetwater is not trying to convince you not to buy acoustic treatment. Rather, they're trying to appear knowledegable so you'll buy whatever they tell you to buy when you call them for advice. And who here has a "perfect" room ratio anyway? So right there that retains 99 percent of their potential customers.

Here's my favorite line from that mini-article:

if a room should have a 5-foot ceiling to match the ratio of the wall length and width, apply acoustic treatment to the walls above five feet.

This is so totally stoopid I don't even know where to start.

> what do you think about jeremy's points about diffusion and practical acoustic uses for "phi?" <

I'm not much of a math guy, but the goal of a diffusor is to scatter sound in all directions. I don't think it matters how the diffusion is implemented. Only that it works well. In the grand scheme of things, all rooms need as much bass absorption as possible. Diffusion is more like icing on the cake if you have a suitably large room. Many people have rooms too small to benefit from diffusion.

--Ethan

[vsr600]

I don't think you're any more likely to "find" the golden ratio in nature than you are to find 5/3 in nature, or pi/2 (both of which are close enough to the ratio to be confused with it given some rounding errors), or 1/2 or 10/1, or any other ratio you can name and the people who think that the the golden mean and the fibonacci sequence are somehow special or magical have the same credibility as fortune cookie fortunes that tell you that your eight lucky numbers between 1 and 20 are such and such, and then you reallize that, you know, four of those have important properties to you, like for example you have two testicles or whatever.

Do your research. There's tomes after tomes written about this by respected researchers/mathematicians/scientists. It's not something pulled randomly out of someone's uniformed ass...

Umm I'm a researcher/scientist working on a Phd in physics actually and I agree that it's just a number, nothing magical. It's not pulled out of someone's uniformed ass either (whatever that means) it has some neat properties. Helps with 5 fold symmetry in crystals and it is the most irrational irrational number. But I guarantee you if you go hunting through Kinsler and Frey Fundamentals of Acoustics (a bible for any physics based acoustician) you will not find the number phi. You will see phi's in there but they represent phase angles and not the golden ratio.
Anyway wikki does have some interesting info about the golden ratio and the wolfram link i posted earlier is a little more on the math for anyone interested.

[nclayton]

Do your research. There's tomes after tomes written about this by respected researchers/mathematicians/scientists. It's not something pulled randomly out of someone's uniformed ass...

Yeah, I definitely know there are tomes and tomes out there, which to be honest is probably more the cause of my reaction (overreaction?) than anything said here, so I definitely do owe an apology for bringing off thread baggage into thread. Fibonacci magic is sort of a pet peeve of mine. I DO think it's overhyped in pop pseudo science culture, but obviously phi has a mathematical basis, and is cool just for the fact that it was (if I'm remembering right) the first number that greek mathematicians were able to recognize as irrational, which totally mind fucked them and is probably one of the major causes of its being still thought of as particularly magical today, right?

Still, I think my explanation (not a new idea, and I don't mean to "claim it as "mine" just because I used the word "my") for why a golden section room might sound ok is probably more sensible than anything that can be got from the actual legitimate phi math. I mean, 1.618 is probably a little better than 1.5 or 1.75, you know?

Any opinions on room dimension ratios of 1:2.72? e is way magicker than phi, so surely it's a good room dimension?

Sorry for the clutter.

Ned

[supafuzz]

to help everyone remember the Golden ratio

1.6 is the lonliest number

thank you