Room Ratio: Golden or Optimized

Picking a Room Ratio

The vast majority of folks attempting to develop a well isolated acoustically correct room will stumble on a few phrases that often make the process of moving forward difficult.

One of these phrases will be “room ratios”. Why even consider the dimensions of a room and how it relates to sound?

Since it does relate to sound, the idea is that these room ratios are very important when in fact, as important as they are, it is simply a small aspect of the build.

The rooms size and shape will determine the modes (wave length and frequency associated with your rooms dimensions).

Small rooms are known to have issues with low frequency since a small room will accumulate longer low frequency waves that will overlap and build up in corners if they cannot locate an exit from the room.
This always presents a challenge to overcome without some understanding of what you are up against.

In some cases, as in using an existing room in your residence, it may not be possible to move any of the existing walls!

So you move forward, knowing that you will have to face this issue down the road, the issue being the existing modes the room might present.

The Golden Ratio

Reference: http://en.wikipedia.org/wiki/Golden_ratio
Golden ratio – Wikipedia, the free encyclopedia

The golden ratio is an irrational mathematical constant, approximately 1.618.

The golden ratio has fascinated Western intellectuals of diverse interests for at least 2,400 years.

According to Mario Livio:
Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties.

But the fascination with the Golden Ratio is not confined just to mathematicians.

Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal.

In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics

Room dimensions typically start from the ceiling hard boundary.

If we use the golden ratio then this will produce a room with dimensions based on the ceiling height, then to the width of the room and next the depth of the room.

With an eight foot tall ceiling, based on the Golden ratio we would use 1: 1.62: 2.62, this would be a room with a ceiling height of 8 foot with a width of 13 feet and a depth of 21 feet!

WOW!

That is a lot of room which is certainly good for the music to expand but you may not have this kind of floor space or money to build something so large.

Imagine if you were lucky enough to have a ten foot ceiling, the room would be so large as to become too expensive to build.

Optimized Room Ratios:

Room ratios have been around for decades and rooms in general have been designed to be pleasing visually and sonically by many builders/ architects.

You only have to look around the building you are in right now to recognize this is not something new, it has been around you all your life you just were not aware of this.

Rectangular rooms have been a staple of residential houses since the late 1800’s due to ease of construction when more room is required but a square room means more material and that means more cost per square foot.

The inclusion of room ratios for an acoustical environment is different in that the ratios used have been tested so that the builder has a better starting place than a typical room ratio that a typical builder might use.

Alton Everest ( Master handbook of Acoustics – 4th Edition) presents 3 of the most widely used ratios developed by L.W. Sepmeyer (1965) and M.M. Louden (1971)


			Height	Width	Length
____________________________________
Sepmeyer	A.	1.00		1.14		1.39
		B.	1.00		1.28		1.54
		C.	1.00		1.60		2.33

Louden	        A	1.00     	1.4		1.9
		B	1.00		1.3		1.9
		C	1.00		1.5		2.5

It must be noted that when these ratios were being tested, a ten foot tall ceiling height was assumed. In some detail, we will find out why this was an important aspect to this particular testing procedure.

Based on Loudens first ratio “A”, 1.00, 1.4, 1.9 with a ten foot tall ceiling this would produce a room with the interior finished ceiling height of 10 feet with a interior finished width of 14 feet and a depth of 19 feet.

This room will have a volume of 2,660 cubic feet.

Plenty of height for the sound to expand and develop and exceeds the 1500 cubic feet room volume limit determined to be the least amount of volume a quality audio environment should have.

(C.L.S. Gilford, Affiliation: British Broadcasting Corporation,“The Acoustic Design of Talks Studios and Listening Rooms” circa 1979, maintained that a “small” room based on the research done would be a room with a volume of 1500 cubic feet.

Further he states “It is shown that a distinctive characteristic is that, because their dimensions are comparable with the wavelength of low-frequency sound, the sound field is characterized by strong simple standing-wave patterns which cannot be eliminated without eliminating the reverberation itself.

It is shown also that for the audible effects are confined to those associated with simple axial modes and that, by careful adjustment of dimensions, provision of diffusion and the proper distribution of absorbing material, the worst faults can be avoided.”

An interesting thing happens when we look deeper into these ratios, when we look at the single components of the room and not the end result.

The speed of sound at sea-level is considered to be 1,130 feet per second and in order to get the fundamental frequency of the height or width or length we have to use the equation F=1,130/2xD.

The height of ten feet using the above equation will produce: 1,130/20=56.5Hz.

This is important to know since 56.5 Hz relates to the note A1. It actually falls 1.5Hz past the frequency of 55Hz.

The width of 14 feet using the equation F=1,130/2xD (1,130/2×14(28)) = 40.36Hz which closely correlates to 41.20Hz or E1 on a midi keyboard.

The remaining length measurement 19 feet X 2 = 38 produces 1,130/38=29.74Hz, relates closely to 29.14 (A#0/Bb0).

Using the 8 foot ceiling height and Loudens first ratio produces a room 8 feet tall, 11 feet and a few inches wide and 15 feet and a few inches deep.

That is about the size of a typical bedroom or the living room in some homes.

The consideration for having a balanced proportional room is valid and worth the effort to use in any sound related type room.

A few things to consider along the way. The measurements that are obtained from the ratios define the interior side of the wall.

In order to use these measurements, you must determine how much and of what thickness your interior sheathing will be.

This allows you to step out the placement of the sheetrock or MDF/OSB or whatever combination you may use, in order to establish were the actual framing will be placed on the floor of your build.

[needs graph on this stepping out procedure]

To that end, ratios are not scalable…they cannot be modified and expect the same results: http://www.acoustics.salford.ac.uk/acoustics_info/room_sizing/
Room Sizing Tutorial | Acoustics, Audio and Video | University of Salford