"Perfect" Room Ratios: Golden vs. Louden's

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James Romeyn

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"Perfect" Room Ratios: Golden vs. Louden's
« on: 28 Aug 2003, 06:58 pm »
There appears to be a significant difference between two known & recommended ideal room dimension ratios.  This is important to anyone contemplating a dedicated media room, meaning the difference between:

1. Adapting a pre-existing room with a minimum 8' 8-1/2" ceiling (reasonably easy to find)

OR

2. Being required to build a new dedicated room with 10' ceiling.

The "Golden Ratio" freqeuntly sited by acoustical engineers is .62x1x1.62.  It is said to ensure the smoothest, widest distribution, & least lumping of resonant modes.  It is considered the ideal ratio for internal speaker dimensions having parallel walls.  I assume that the goals for room ratios are the same.

Julian of Sedona Sky Sound, posted on Fri Aug 22: "When I built my room, my sole objective was getting the best possible sound.  The room is based on Louden's Best Ratio, which means the room is 14'x19'x10'."  In ascending order the dimensions are 10x14x19.  If 14=1, then Louden's Best Ratio is .71x1x1.36 (10/14=.71, 19/14=1.36).

If Julian's 14' middle dimension = 1 in the Golden Ration, we have 8.68x14x22.68 (14x.62=8.68, 14x1.62=22.68).

The differences between the two ratios are substantial: the Golden Ratio is 13% smaller in the smaller dimension, 19% larger in the larger dimension.

Where is my math wrong?  If not, explain the pros & cons of both ratios, & justify your personal preference.  The Golden Ratio seems ideal yet Julian obviously knows this subject upside down.  Ouch my head hurts!  Where is Karnak when we need him?  "Lucy, 'splain!"

Andrikos

"Perfect" Room Ratios: Golden vs. Louden's
« Reply #1 on: 28 Aug 2003, 07:20 pm »
This is fascinating since right now I'm reading a book called "The DaVinci code" (FASCINATING BTW, HIGHLY recommended)

Anyway, one of the subjects of the book is the golden ratio that Ribbon is mentioning. Its mathematical symbol is the Greek letter phee (or phi for fraternity dudes). This phee is the number 1.618 and is EVERYWHERE in nature. It's amazing, nobody can explain it that's why it was given the name "Divine Number". If you take a shell and divide the distances of the turns, you get phee. If you take a sunflower and do the same you get phee. It exists in animals, flowers, humans, gems, crystals, etc. etc.
Also the Parthenon in Athens was built by using those golden numbers.
I even used those numbers to design the dimension of my DIY speakers (9", 14.562", 23.561") that give me an internal volume of 42.6liters which is EXACTLY the recommended internal volume for the drivers I'll be using (Fostex FE206E).

Andrikos

"Perfect" Room Ratios: Golden vs. Louden's
« Reply #2 on: 28 Aug 2003, 07:20 pm »
...

dubravko

handbook
« Reply #3 on: 29 Aug 2003, 06:19 pm »
There's a very nice book which is now in it's 4th edition, Master Handbook of Acoustics by F. Alton Everest. Basic knowledge of math and physics makes easy to understand what's in there, and it can be useful in explaining many issues regarding room acoustics. When building from scratch, main objective regarding room size and ratios is to have modal frequencies distributed as evenly through the spectrum as possible.

My choice was a Golden rule for my room (as close as I could follow it) which ended with 1 : 1.60 : 1.64 (2.9x4.65x7.65m), with a part of the ceiling sloped. It don't recall Everest particularly recommends Golden rule, but I had a good experience with similar room, and it was convenient for other reasons. Besides, there are other factors which make good acoustics, and since it is not completely rectangular, all of the philosophy falls off. My primary objective was also to put the speakers as much from the sides as possible (conclusion drawn from previous experiences, although it seems a less issue with VMPS), so speakers are at the long wall. Room sounds nice to me. The biggest improvement from almost a bare room was a step towards LE-DE configuration, meaning I placed seven  0.65x1 m absorbers along the wall behind the speakers, and two at the sides, near to those seven mentioned.

There are actually more than two 'optimal' ratios, you can check this link for the PDF with the basic info on that subject. This is the usual info that goes around, but I find it much better organized and explained in books.

http://www.nonoise.org/quietnet/tcaa/smallrooms.pdf

JoshK

"Perfect" Room Ratios: Golden vs. Louden's
« Reply #4 on: 29 Aug 2003, 07:07 pm »
Jim,

My guess is this.  The Golden Rule is a ratio of nature, it is also closely related to the fibonacci sequence also seen vastly in nature.  However, my guess is that Louden's Best Ratio is more based on minimizing standing waves of certain frequencies within the audio range (which isn't infinite).

James Romeyn

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• Posts: 3282
• James Romeyn Music and Audio, LLC
"Perfect" Room Ratios: Golden vs. Louden's
« Reply #5 on: 29 Aug 2003, 10:34 pm »
Quote from: JoshK
Jim,

My guess is this.  The Golden Rule is a ratio of nature, it is also closely related to the fibonacci sequence also seen vastly in nature.  However, my guess is that Louden's Best Ratio is more based on minimizing standing waves of certain frequencies within the audio range (which isn't infinite).

Thanks for the input.  Josh's post above makes sense.  My estimate is Josh's "certain frequencies" are from the low-midrange down (below 200Hz).  It occurs to me that the lower the frequency, the more audible is the room mode, & the more difficult it is to control.  If so, then possibly Louden's Best Ratio damps bass modes better than the Golden Ratio. The Golden Ratio may provide more linear damping throughout the entire audio range.  In practice Louden's may result in better audio performance, with modes more prominent in the upper ranges, where they may be easier to control vs. the bass range.  In any case, 10' celings are rare.  Meaning Louden's Best Ratio room will likely require custom construction or major modification.  It could be very costly to convert a pre-existing 8 or 9' ceiling into a 10'

dubravko

"Perfect" Room Ratios: Golden vs. Louden's
« Reply #6 on: 5 Sep 2003, 02:13 pm »
Quote from: JoshK
Jim,
My guess is this.  The Golden Rule is a ratio of nature, it is also closely related to the fibonacci sequence also seen vastly in nature.  However, my guess is that Louden's Best Ratio is more based on minimizing standing waves of certain frequencies within the audio range (which isn't infinite).

Both ratios work within the audio band in the same way, neither ratio is more 'audiophile' than the other. The difference is only in how they group and distribute axial, tangential and oblique modes. Besides, this influence matters only up to some 200Hz, the rest of the audio band is much more a question of other conditions. More important is that these rigid calculations are valid only for perfect rectangular rooms. When any other factor gets in (slopes, openings, more than 4 angles, furniture etc.), things become incalculable. That's why good acousticians know they can rely on experience more than calculations, so they work with precalculations, but finish the task only through trials and errors.

JoshK

"Perfect" Room Ratios: Golden vs. Louden's
« Reply #7 on: 5 Sep 2003, 02:25 pm »
dubravko,

I think we are in perfect agreance.  My answer was mostly a simplistic one.

I am no acoustician, but I am an applied mathematician.  Its pretty obvious that there is no unique solution (for the lehman, no one pefect solution) but a number of good rules helps to start with as Dubravko said.  Much like we applied mathematicians usually start with good offhand approximations of solutions to start solving for a more precise specific solution.

Val

"Perfect" Room Ratios: Golden vs. Louden's
« Reply #8 on: 7 Sep 2003, 12:53 pm »
I am fascinated by the Golden Ratio and Fibonacci numbers myself (there is a link at my website), but just at a practical level regarding small rooms, I believe GR is just a bit better than Louden's because the middle dimension is larger and thus allows for a slightly wider speaker placement away from sidewalls. I have had to move many times in my life and I remember only two naturally good-sounding rooms, both close to Golden Ratio.