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.
thoughts?
joeb
joeb
Look at this site and then you'll understand why things are the way they are http://www.rivesaudio.com/listroom.html 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!
Red,
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
joeb