Room Acoustics question:

For anyone with a fascination for numbers and curiosity about what George Cardas and others are promoting.

Read "The Golden Ratio, The story of PHI, the world's most astonishing number" by Mario Livio, Broadway Books, C 2002 (available in paperback).

This book covers the golden ratio from when it was defined by Euclid, through 2000 years of historical understanding. This ratio appears widely in nature and and has been reported used in architecture, painting, analyzing the stock market, and now the design of speaker cables and optimal listening rooms. Many examples and pictures of PHI in action.

1.61803... is a remarkable and mysterious number.

Magfan, writers/historians studying the Pyramids disagree on whether PHI was used in the design. According to Livio, it is possible either PHI or PI was used and more likely it was PI (see his book for the explanation). Just because there is a relationship between Pyramid elements that approximates PHI doesn't prove it was used. There is lots of controversy surrounding PHI.

A regular pentagon is made up of 5 isosceles triangles. The ratio of the longer side to the base is PHI. It is an irrational number, that is, it is a number that cannot be expressed as a ratio of two whole numbers. This really bothered early geometrical researchers.

PHI can also be constructed by taking the limit of the ratio of adjacent numbers in the series formed by summing integers:

1+1=2
1+2=3
2+3=5
3+5=8
5+8=13
8+13=21
etc.

Series is 1, 2, 3, 5, 8, 13, 21 etc.

2/1=2
3/2=1.5
5/3=1.666667
8/5=1.6
13/8=1.625
21/13=1.6153846...
etc.

A logarithmic spiral has the property of not changing its shape as it grows larger. The radius keeps increasing as the spiral grows just at the right rate and this is governed by PHI. This spiral is the logo for Cardas. Does PHI work in the design of cables and rooms? George clearly believes it does.

Adampeter, sorry as we seemed to have hijacked your thread. It started with a comment that your room dimensions seemed similar to the Golden Mean. I don't believe they are, however, if so, that would have meant that there was good reason to believe room modes would be fairly evenly distributed.

I think the size of your room is a positive for creating a large sound stage and image. You will be able to keep the speakers well away from reflecting boundaries and will have the space to move them to maximize bass performance. Every room has its challenges, but large rooms have more flexible solutions.

Do not worry about the concrete floor. Many great listening rooms have them, and you are avoiding the possibility of floor resonance and footfall issues on a TT. A thick carpet is just fine and will minimize high frequency reflections and help damp reflections.

I happen to believe there are many ways to design a good listening room and using the Golden Mean is one of the ways to approach good bass performance. I have done exactly that currently in my own room and it works extremely well. I don't know the limitations of your space (fireplaces, doors, windows etc.) but if you have the option to shorten the room with a new partition, here is one to consider.

Starting with 30 x 20 x 8.5

Go to 30 x 18.5 x 8.5 and fill the 1.5 ft space behind the rear wall with damping material. Put speakers about 3.5 ft in front of the short wall about 8 ft apart and 5 ft off the side walls. This is very close to what I had in a previous room which worked well.

If you are interested in this approach, it would be helpful if you described your room conditions in more detail.

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Magfan, You are correct, it was Herodotus who is credited to have said "the pyramid's base is square, each side is eight plethra long and its height the same". Translations of this statement have been reinterpreted by many, and somewhat twisted to say "the square of the pyramid's height is equal to the area of its triangular lateral side." If so, one could argue that the pyramid was designed such that the ratio of the height of its triangular face to half the side of the base is equal to the golden ratio. Not only is this a stretch, it fails because the actual pyramid measurements do not come close to those implied by the statement.