So we’ve established our target: shortish decay time (~0.75 seconds) that is flat across all frequencies, and that is the same no matter where in the room an audience member is. As few resonant frequencies as possible, and those resonances should be “weak”.
Weak? Huh? The short explanation of that: a simple resonance is one where the sound bounces back and forth between two walls that are exactly as far apart as the sound wave is long. Since sound moves at 340m/s, a 5m long room would resonate at 68Hz, which is approximately C#2. (It would also resonate at multiples of that, but we’re going to stick with the simplest option here.) Now if the room is also 5m WIDE, we have a second 68Hz resonance on top of the first, making it stronger. If the room is 5m TALL, we get a third. In the other direction, if we were to add material to the walls to damp the reflections, it would be weaker. Yes, this is oversimplified, but you get the point.
We’ve all been in theaters that are more or less shaped like a scallop shell. Angled sides, curved rear wall? Those angled sides don’t reflect sound at each other, so no resonances can form between them. If that back wall is constructed correctly, sounds go there to die – no reflecting back into the room. It’s easier to build one very absorptive wall than 4. I’ll bet the floor and ceiling aren’t parallel, either. Sound will still bounce around a bit, but we want a little so that’s OK. Yes, there are very good shape options other than this one, but it’s the one I understand best. The Troy Savings Bank Music Hall has parallel walls, and I have no idea how that works.
There’s more to it than just shape, though. This is also where my expertise gets very thin, so here we start to gloss a bit.
What if the walls resonate? Or the floor? Or a space on the other side of the wall? That can pass energy back across the wall the same as it got there in the first place. There’s a great story about the acoustics at Carnegie Hall in New York where a renovation in 1986 was said to have “diminished the famed acoustics”. Turned out that there was a slab of concrete poured in under the stage causing the problem, and when it was removed in 1995 things were much better. (See: this New York Times article from 1995) So it’s possible that such resonances are bad, but equally possible that they are good or even necessary.
Then we can get in to the use of resonators to tune the room. The Troy Savings Bank Music Hall has small cavities built in to the ceiling for exactly this purpose. In modern design, this sort of thing is generally used as “bass traps”, to damp down low frequency resonance, but I have no doubt there are other uses.
All of this, from the shape of the room to the wall materials to building in resonant cavities must be planned before construction starts. It can be retrofitted later, but it’s cheaper to do it right the first time from the beginning. The lesson to be had here is: When you start a construction project on a theater, whether you are building new or repurposing something existing, bring in your architect and an acoustics expert at the beginning, and design it right. Then build to that. You’ll be glad you did.