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Since I can't see the image, I can't talk about anything you wanted to show in it!
I feel I need to get the building right first and then the acoustics will fall into place with the proper treatments. Right?
Nope! That would be doing it totally backwards. The acoustic response of any room depends mostly on the size and shape of the room. By carefully adjusting those to be good, you control the basic acoustics. No amount of treatment can fix an inherently bad room, and a room that was good to start with will need less treatment than a room that was not good, due to having unsuitable dimensions.
Right now I am only focusing on the construction aspect and not the acoustic treatment.
Instead, you should focus on the overall design. When I design studios for my customers, I start by looking a the overall space and taking into account the limitations imposed by the building itself, such as the locations of doors, windows, structural columns, stairs, pipes, and other things that cannot be moved for whatever reason, then figuring out a layout for the rooms that fits in with those restrictions and still provides the best functionality. By "functionality" I mean that there can be good sight lines between rooms, doors that don't open into each other or obstruct other things, and are not located at points where acoustic treatment will be needed, simple short routes for load-in / load-out of equipment and instruments, simple logical routes for movement between rooms, good shape and size of each room, the locations where treatment will be needed in each room, good geometry and layout of the control room, such that the speakers and listening position will be in the optimum locations acoustically, practically, and aesthetically, and that the needed treatment can be in the correct locations, of the correct size, and of the correct thickness. Once I am done with all that, and have a good workable arrangement with good acoustics, only then do I start worrying about construction. That's the point where I will decide how to build the walls, ceilings and doors, what materials to use, what techniques to use, etc. The question of "how to build it" only comes AFTER the functional and acoustic aspects have already been determined.
If you forget about acoustics and only design for construction, you will end up with rooms that sound lousy. This is a studio, so the very first thing you should take into account is the acoustics: That's the entire point of the building! To have good acoustics so you ca record and mix in there properly. The building should be centered around that, not around construction.
Start by designing he acoustics response that you need for each room, then work forwards from there to the question of how to build it in order to get that response. Not the other way around.
Concrete floor/foundation with thin acoustic closed layer foam underlay and laminate floor. (do not want to raise the surface).
Excellent! That is, indeed, one of the best way to do studio floors. Raising the floors would be a big mistake.
Decouple the walls (air gap and rock wool?) as well as the ceiling using the 2 leaf MSM system.
Yes! That's the right approach, for sure.
How much insulation between each leaf? 30cm thick walls, 50cm?
How much isolation do you need, in decibels? That's the key question.
we don't have an issue with neighbors and the sound (but the wife might be irritated if it was too loud
You need to put numbers to that: how many decibels would be "irritating for your wife"? How loud are hte external sounds around your place that you need to sop from getting in? How loud will your recording sessions be inside? You need to answer those questions with real decibel numbers.
The majority of the studio can have high ceilings but I had hoped to put the control room above the drum and storage room
That would make your construction very much more complicated, and expensive. It would also have a negative effect on functionality, since there would be no visibility between the CR and the other rooms. Having a room that needs acoustic isolation on an upper level makes it hard, complex, and expensive. That's why most studios are built on the ground level.
I would switch things around, so all of your acoustic spaces are on the ground, and all your auxiliary spaces are above: But your storage room, the toilet, and the green room (band room) upstairs, and put your live room, control room, drum booth and vocal booth downstairs, where you can easily get good isolation and also have good sight lines between rooms.
Having the CR and LR on different levels is also impractical for setting up mics: running up and downs stairs twenty times to adjust the positions of mics, then go listen in the control room to see if it is good, then run back again to move it a bit, then run again to listen.... that gets very tiring, very quickly. That's part of "functionality": keep the LR and CR right next to each other, with simple, short path between them.
Having said all that, you only have 5m of height to work with. Your floor is going to be at least 30cm thick, leaving 470cm. HVAC ducting will take up no less than 30cm, minimum, leaving 440 cm. You want your control room at least 250cm high, so your rooms upstairs are going to have very low ceilings: around 190 cm. That's an important aspect to take into account. Since your LR needs a very high ceiling to make it usable, acoustically, I would suggest that you should not put any rooms above that, or maybe just a small storage "loft", so you can keep it at least 3.5m high, inside.
What does a system like this cost?
It's impossible to say, without first knowing what system you need! That's like asking "How much does a car cost?": Without knowing anything about your needs for that car, it is impossible to say which car would be good, or how much it would cost. It might be that a US$1,000 small used car is all that you need, or you might need a US$ 20,000 new typical family car, or you might need a US$ 150,000 luxury car, or maybe a US$ 300,000 sports car, or perhaps what you really need is a million dollar limousine. Until we know what your needs are for the VAC system, it is impossible to say how much it will cost.
There are not so many options when one only has 4.5x10m to work with.
Right. Considering that you need about 20m2 for a decent control room (for good acoustics), and that the live room needs to be about three times the size of the control room, I'd say that you have a problem! You will have to sacrifice acoustics to fit in just those to rooms alone. You can probably squeeze in a usable control room to maybe 15m2, leaving 35m2 for your live room, drum booth and vocal booth. That is unworkable: Forget the vocal booth, and do any vocal recordings in the CR. 35m2 for LR plus drum booth is VERY tight. This is going to be a very small studio, and you won't be able to get good drum sounds, simply because the drum both will be very minute. Hardly big enough to fit in a typical drum kit. Since drums sound terrible in a room with a low ceiling, try to keep the ceiling in there as high as possible, with no rooms above.
Drum room 2.5x2.5m

That is SQUARE! That's the worst possible dimensions for an acoustic room, since all the room modes in the "length" direction will line up perfectly with all the modes in the "width" direction. The modal response will be hell. Bad idea.
Live room 4x5m
Small, but usable.
storage room 1.5x2.5
Toilet and sink 1x2m
Band Room 2.5x2.5m
Upstairs. There is no room for those downstairs.
I have attached a rough sketch up drawing
Unfortunately my main computer crashed and is in for repairs, so I'm using a very old computer where I can only install up to Version 13 of SketchUp, and your model is in Version 16, so I can't open it. If you want to save it as version 13 and post that, then I'd be happy to take a look at it.
This is a tricky program to get all the lines
Not once you get used to it, and learn how to use all of the features! It's a very powerful program, and placing walls, windows, doors, treatment, furniture, etc. is actually very simple. Take a look at one of the many tutorials on how to use it, on YouTube. The trick is to make each object that you create into a "component" as soon as you create it....
- Stuart -