the listening room: "golden ratio"?

I too am about to build a listening room, actually, I'm building a garage and adding the room over the top. There seems to be a lot of advice to pay attention to the "golden ratio" which, essentially requires a room at least 25 feet long, by, roughly 17. this seems really "BIG". The rationale for the size is based on the theory that the lower hz frequency has a "wave length" of 25' or something to that affect. However, there are few speakers that reach down to that range. I have BW N804, whose freq. response is around 40hz. I was thinking of getting some N803's which add a bit, but still nothing close to 20hz. As nice as it might be to build a 25'X 17' room, I'd like to stick to somehthing around 15 X 12, roughly half the total size of the garage. How much would I "lose" in that size? The other consideration is the cost of heating this room, living in the north, my electronics would not like to spend the winter out there at -30 and electric base board heat would run up a hell of a bill.
I don't buy that rationale because your ears only hear part of a sound wave at any given moment as it propagates by you - that is why we have a "sweet spot". Anyway, my room is 15x13 and with simple acoustical treatments like covering windows and putting canvas paintings on the walls, the sound quality is lovely. I would check with the speaker manufacturer's recommendations on their correct placement and room. They will know best. Arthur
Look at this site and then you'll understand why things are the way they are it explains how to calculate room nodes and why they are important. If you have the means to have them design your room it would be a good idea- everyone has an idea how to make a room sound good(myself included), but these guys do KNOW how to make a good sounding room, in fact they do it for a living and in this field you would have to be good to make it. If nothing else look at the link I gave you and try the equations with all the possible room dimentions you are thinking.
You could--I'd say should--also consult F. Alton Everest, "Sound Studio Construction on a Budget" and/or his "Master Handbook of Acoustics, 2nd or 3rd Edition". Among much other vital info, you'll learn that there's no magic about the so-called "golden ratio", and you'll see why not. Bigger rooms run less risk of main resonant nodes being far apart, and so standing out, but it's a matter of degree, and 25' is definitely not mandatory, even among "golden ratio" advocates. Everest's books will also go into how to deal with problems your dimensions pose. If you can manage DIY projects, his book discusses many. I myself have designs for RPG-style diffusors and Argent Room Lens clones, not related to "golden ratio" issues but still relevant to good sound. I email them on request; feel free.
These are good resources above, there is one other that is also quite good. Russ Hershelman (I don't think I spelled his name right) does home theater architect columns in SGHT. He did one that showed a spread sheet on calculating room modes, inlcuding the transaxial and oblique modes. This can be very useful in trying multiple modes. However, one word of caution. Many of the references treat all modes equally, and they aren't. In fact even the axial modes, which are the most prominent, are weighted based on materials of the opposing surfaces and on surface area. Thus, these models, and golden ratios are not really so golden (slightly tarnished perhaps), but they do provide a good basis for a starting point--sometimes adjustments need to be made from them.
In fact the golden ratio is 1:1.4:1.9 which is based on the greatest resonant mode distribution. In short this ratio avoids harsh resonance at certain frequencies. The golden ratio has nothing to do with dimention, but has everything to do with relative proportions.

For example, by multiplying each number in the ratio by ten, you would get the following dimentions: the ceiling would be 10 feet high, the width would be 14 feet, and the length would be 19 feet. If your ideal room size is 17 X 25 feet, then your ceiling would have to be between 12 and 13 feet high. Most average homes have a ceiling height between 8 to 10 feet. An 8 foot ceiling would require a room dimention of 11 X 15. A 9 foot ceiling would require a room dimention of about 13 X 17, etc.

The formula for determining resonant modes is 1130 (speed of sound in feet per second) / a dimention of the room times two. Therefore the resonant mode for an 8 foot ceiling is 1130/16= 71Hz and every multiple of it ( 142Hz, 213Hz, etc.

The worst room dimention is 8 X 16 X 24 feet. Since they all are multiples of 8, they would all have the same resonant modes. This means that every frequency which is a multiple of 71Hz would be three times louder than surrounding frequencies. This causes all these frequencies to be extremely harsh.

Joeb, your second choice of 12 X 15 would be close to ideal if your ceiling is 8 feet in height. Also, with the length of the room being 15 feet, you will be able to fully develop sound down to 37Hz. Not Bad!
Yes, I found the same info on resonant modes/room dimensions in Robert Harley's "High End Audio" suggested here by others. Hence, this fits into my budget nicely. The exact dimensions for an 8' ceiling is: L 15.2' X W 11.2' X H 8'.
That at least minimizes bass "boom" and other resonant modes. frequency modes. Other than that, I need good accoustical construction, which was mentioned but not really explored well in that book. I will have to purchase another book mentioned here; Alton Everst's book.
Thanks for your help
You're right about "High End Audio" not having much on acoustic construction. However, it did mention ASC's Walldamp acoustic construction method on page 115. I checked out ASC (Acoustic Science Corp.) on the internet which provided a wealth of information on acoustic construction methods. As a matter of fact, I just received
all their wall damp mateials needed to construct a 13 X 17 foot sound room. Not only will the room sound great when conpleted, but all that insulation will keep the room warm during cold winter weather. Another method you might try in making your room more cost efficient for heating is putting
your sound room in the center of the second floor with the extra outer room space used as a heat buffer.
Hi Joeb. I am a bit late on this one, but thought it worth adding that the Golden Ratio is a way of fixing the natural problem of parallel walls and ceilings parallel to floors. But if you are building a separate unit (ie. your garage with room over the top) then you can do better still by having the room boundaries curved or just not parallel. You still need to do some maths about nodes, but risks are reduced. The only issue of course is how a non-uniform structure adds to cost. But I would go that way if I were in your shoes.

The other piece of maths you need to do is about where you want your speakers to be. This will require some research about where others have positioned your chosen speakers, to get a rough guide - mainly to figure out how far from room boundaries you will have to have the speakers before they open up. But what I am getting at is that the distances from woofer to room boundaries are best to be in a golden ratio too. Again, non-parallel surfaces reduces the risk of encountering problems.
To those of you still watching this thread; I have been researching more and getting closer to starting my project. I have decided on the basic materials needed for sound isolation properties; layers of 1)sheetrock/2)soundboard/and 3)sheetrock attached to the studs with resilient channel on ceilings and walls. I might use 2 X 6 plates with offset 2X4 studs so that the front and back of the wall aren't able to transmit any vibration through the studs. Floor: sheetrock/soundboard/ particle board and carpet. I would like to float the floor joists using a foam "U" device but don't think I can because these floors need to be attached to the first floor and I can't afford to do a separate floating floor joist method, unless I cut out the depth of the "U" foam, but then I'd still have to nail through it into the floor.
The room dimension issue is still a bit fuzzy. In order to meet the golden ratio requirement exactly for an 8' height, I need the room to be 15 X 11.2. The 11.2 seems a bit narrow and I'm wondering if I can stick to an even 12' without a noticeable audible increase in "resonant mode distortion". In other words, how precise to you have to be? How much variance from the golden ratio before you get a noticeable difference? I could even go longer without a noticeable increase in cost, but increasing the height gets pricey.
You might consider opening the ceiling to the roof (cathedral). I have a second floor listening room over the garage that is 18'W x 28'D with 9' walls and a 13' peak. It is very close to the golden ratio. The extra height really opens up the sound stage vertically. I used the Cardas formulas for speaker placement from the side walls, but kept the speakers at 5' from the rear wall. The image is phenominally wide, deep and high and forward of the speakers. This room is one of the best I have heard.
Zargon, Great Idea. I have already thrown out the previous dimensions, way too small, I am going with a L22 by W15. the only question is to go with a 8' or 10' ceiling. Probably the 10'. The previous question remains to be answered however, re: the frequency resonant mode dispersion. with a 10x15x21 there is a pretty good balance across the fr. span from say 25hz to 300 hz, but some bundling in the low mid and hi mid range. I still don't understand how much variance of frq. dispersion transalates to sound distortion. Does say a gap of 25hz next to a mode make a "BIG" difference? Or does it require a 40hz span? etc. If anyone was really interested I could post the exact figures.
thanks, Joeb
Golden ratio is :
Phi = 1.618033..
Phi*Phi = 2.618033..

That will give you with 8ft ceiling approximately


However the I would go with higher ceilings if possible
Nar, com, Now I'm really confused, I thought the ratio was:
1: 1.4: 1.9 where 1= height etc. And why, if 8x13x21 is the "gr" would you go with a higher ceiling?

The golden ratio is the irrational number that is equal to (sqrt(5)+1)/2 = 1.618033989...
Just do search on the Net for GR and you will find more info than you need.

GR is only one of the ways to build the room and I’m sure rooms with other dimensions could sound wonderful. I’m not an acoustical expert and not pretending to be even close to one. If you are not sure what to do, you’d better consult someone who knows better or start reading books on acoustics.

As to higher ceilings I feel that it will give you more open sound plus I personally fill better in rooms with ceilings higher than 8ft.