October 19, 2020 3 Comments

In mathematics, if two numbers have the same ratio as the ratio of their sum to the larger of the two numbers, they’re said to be in the “golden ratio.” If that sounds like Greek, don’t worry. The “golden ratio” in sound – more specifically in acoustics, doesn’t require you to understand the mathematical term and all its implications.

Instead, this ratio is related to set of ratios that tend to lead to the best acoustic response in a room, with a minimum of acoustic interference anomalies such as comb filtering, nodes, peaks, or dips. Knowing these ratios can help you to look for the best room in a house to put your studio or rehearsal space and are especially useful if you’re building a new space and can control the dimensions of the room.

The Ratios

It turns there are more than one set of ratios that have proven useful to acoustics experts over the years, besides the classic golden ratio – they’re all related to the golden ratio – here are a few:

  • 1 x 1.60 x 2.56 – The classic “golden” acoustic ratio.
  • 1 x 1.14 x 1.39
  • 1 x 1.26 x 1.59
  • 1 x 1.28 x 1.54
  • 1 x 1.30 x 1.90
  • 1 x 1.40 x 1.90
  • 1 x 1.50 x 2.50
  • 1 x 1.60 x 2.33

Any of these room ratios will prove much better for minimizing acoustic issues, and in some cases could nearly eliminate the need for acoustic treatment – depending on your usage.

For the most part, we consider the fixed number the height of the ceiling, which is normally 8 feet. So for example, a room built to the classic golden ratio would be 8 feet high by 12.8 feet wide by 20.48 feet long. A big room!

Many rooms built to spec opt for 10-foot ceilings instead, which would yield a room 16 feet wide by 25.6 feet wide when using the classic ratio. It’s not common to have that much space, so some of the other ratios are often used, for example 8 feet by 9.12 feet by 11.12 feet – a much more normal size.

Unfortunately, most existing rooms are not built to these specs, and are often built with evenly divisible ratios, which is a headache for amateur and professional acousticians alike. This is why learning a bit about smart acoustic treatment is so crucial.

Of course, it is possible to adjust a room’s dimensions – at least to some degree. An existing room is hard to make bigger, but it may be possible to make the room slightly smaller by adding a false wall on one or two sides, or even a false ceiling. For example, take the room this article is being written in. 16.5 feet long by 8.5 feet wide with an 8-foot ceiling. Dividing the length and width by 8, we can see that the ratio of this room is 1 x 1.06 x 2.06. Not ideal, but at least not evenly divisible.


3 Responses

Keith
Keith

October 21, 2020

Interesting post. I will try to apply this formula when I am able to put together a studio space. Thank you for sharing this.

Kirk Smith
Kirk Smith

October 21, 2020

Very interesting. I’d always heard that you didn’t want your room dimensions to be integer multiples of each other, but I had never heard any advice on what they really ought to be or why.

Wayne Handzus
Wayne Handzus

October 21, 2020

Greetings from San Francisco Ca.
Great article on the golden ratio.
Thank you for typing that for us musicians
I didn’t read the whole article yet. I shall come back to it later. Been up most of the nite.
Was looking for an example of the golden ratio where 2 numbers have a sum that is the same ratio with the larger of the 2 numbers.
I’m not sure if there is a formula to use to figure the golden ratio, something like , maybe, the cubed root of 2 ?
Or something
Like the 12th root of two that brings us to the next half step or next fret on the fingerboard.
First time I calculated the12th root of 2 I had to guess. New calculator has a button for the x root of y.
Thanks people
Wayne

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