7:1 surround sound control room dimensions

[isol8]

Greetings
I am looking into the design of a surround sound training control room that can accommodate +/- 30 students.
We have certain space restrictions but can work within a maximum room size of put to 4.4 meters ceiling height, 7.5 meters width and 12 meters long. I am using the standard room ratios (Louden, Sephmeyer, Dolby etc) as a guideline (but appreciate they are not aways definitive ) .
However I need to consider that there will be a tiered/stepped section of seating (5 or 6 rows) which will reduce the effective room height at the rear to around 2.5 meters. (Thinking this should be solid concrete slab construction to avoid resonance / vibration)
This structure presumably negates the "golden ratio" approach or is there a way one can factor in the space occupied by the seating to determine an optimal room size?
As always experience shared is greatly welcomed . .

[Soundman2020]

That's a fairly large room, so I don't think modal issues are going to be too much of a problem. It's actually a bit larger than the largest size recommended for a control room 89m2 vs. 70m2, and 395 m3 vs. 300m3. But still usable, provided that it is treated properly.

In other words, you don't need to be worried about room ratios for a space that size, since it has modal support all the way down to 22 Hz., and above 59 Hz. it is pretty much all diffuse. So RT-60 actually has some meaning for a room that size. I'd be more worried about diffusion and absorption in there, and overall reverberant field control, intelligibility, and suchlike, rather than about modal resonances.There's actually no such thing as a true "golden ratio" in acoustics. There are good ratios and not so good ratios, but none of the good ones is spectacularly superior to the others.

That's going to be a very challenging design! A large room like that for 7:1, with multiple seats, raked upwards at an angle... that's a going to be rather complex to design. The math involved in that is definitely not for the feint of heart!

- Stuart -