Recommended minimum variance in room dimensions?

[chrispire]

As you are probably aware, the worst possible shape for an acoustically balanced room is a cube. OK, scratch that, a sphere would presumably be worse.

So we know that our studios are better if they have width, length and height dimensions that all differ.

My questions is, by how much should room dimensions differ in order to avoid an accumulation of room modes? For example, let's say I'm designing a room that will be 9 feet high, 18 feet long and 18 feet wide. The length and width are the same which is not ideal. Would changing the length to 19 feet make a significantly positive difference to the room, or would it simply leave me with two room modes that are close in value causing a broad null or peak in the room's frequency response? Would changing the length to 20 feet be enough? 21 feet?

I'm aware that so called "acoustically ideal" ratios like the Louden ratio exist, but I'm not really looking to explore those golden ratios. I'm just trying to find out what the recommended minimum variance in room dimensions is.

Scientifically proven evidence preferred, but wild conjecture is also welcome at this point.

[Soundman2020]

Excellent question! There's been a lot of research done on that, and different sources have come to similar conclusions. According to the ITU, these are the conditions that a rectangular room should meet in order to provide "a reasonably uniform distribution of the low-frequency eigentones of the room": (Eigentones is just a fancy technical term for room modes):

First condition: 1.1 w / h ≤ l / h ≤ 4.5 w / h – 4
Second condition: l / h < 3
Third condition: w / h < 3

Where:
l=Length
w=Width
h=Height

Another rule of thumb says that the integer multiples of the dimensions should differ by more than 5% at least, and preferably more than 10%. So in your example, with 9 foot height, the width should be greater than 18'11" or less than 17'1", which is a difference of 5%, and the length dimension should then be more than 5% different with respect to both the height and the width.

There are other similar rules, but this one is plenty good.

- Stuart -

[chrispire]

Question asked and answered! Thanking you!