the listening room: "golden ratio"?

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

Joeb,
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.
Joeb