When you say
"...it will turn into a rec-room..." do you mean that you're going to set it up as a music space now, but eventually it will be lose that functionality or possibly be turned into a multi-use room? If it's the former, why bother with any treatments at all? If it's the latter you would be wise to figure out which portions of the room are usable for music purposes and which, specifically against walls, will not be viable for treatments.
No there isn't. That's how it's presented, but there are no opinions about this at all. There is a set of pretty easily understood facts governed by physics that will guide you in the right direction based on the physical room space and what you're trying to do with it.
Good, that will save your budget and mental health.
You haven't provided enough information to know how to do this effectively. Firstly you need to identify where you have problem frequencies as different treatments work better in certain ranges. Secondly you need to identify if you have a wide range of problem frequencies, or a small handful of specific ones. Thirdly you need to identify how the room will be setup so you know where to place said treatments.
- Are you going to be using this as a room to simply play music?
- Will you be recording yourself in this room?
- Will you be mixing in this room?
- If you will be mixing will it be done via monitors or only ever with headphones?
- If you'll be mixing with monitors will a subwoofer be involved?
Without knowing any of the above information you certainly need bass trapping above all else. Bass trapping is most effective in corners. If your room is a rectangle with a flat ceiling you have 12 corners. 4 vertical wall-wall corners where you'll likely place most if not all of your bass trapping, 4 horizontal wall-ceiling corners where you may place some bass trapping even though it's far less common, and 4 horizontal wall-floor corners where almost no one places any bass trapping. All three conditions work identically well. At the very least place corner traps in the 4 vertical wall-wall corners either by using a corner trap from a reputable manufacturer (GIK, RealTraps, Auralex, etc.), by building a DIY superchunk style corner trap, or by using a broadband absorber from a reputable manufacturer or one DIY'd 4-6" of Owens-Corning 703 or the Knauff equivalent skinned with a breathable fabric placed so that it straddles the corner. The closer to the full wall height you can get on these the better. Most off the shelf products will be designed for 8' ceilings, and for your needs I wouldn't sweat that last foot. You can save some floor space over a straddled corner by placing panels at 90-degrees and flat to the walls on both sides of the corner. In this arrangement the panel will need an air gap roughly equivalent to the panel depth between its back side and the face of the wall it's mounting to (i.e. a 4" panel needs a 4" gap for optimal performance). The performance will be virtually identical to a straddled corner and will save you some floor space, but comes at the penalty of requiring twice the number of treatments and thereby a higher cost.
Your builder only knew enough to be dangerous by the sound of things. Specifically the insulation. Blown foam, whether open or closed cell actually hampers low frequency isolation compared to fiberglass insulation. Low frequencies will be your largest problem in terms of isolation and by using a foam product rather than a fiberglass one your builder has actually made things a little worse in total isolation not to mention foam being a substantially more expensive product. On the plus side of things the thermal benefits of foam, if installed correctly, are greater than that of fiberglass so at least there's one potential silver lining.
I see in a later post you mentioned "stand-off brackets" installed by the builder. This to me suggests a method of decoupling, but without knowing exactly how this was done it's unclear whether or not it will be at all effective. It would be good to get more information on what product was used and how it was installed to know whether or not your contractor spent your money wisely. I'm not saying this to poke fun, but for your benefit. I've seen some instances where people were able to recoup some expenses from contractors with no sound isolation background who wasted their money. I'm not saying that is the case here, but it's shocking how often it happens. An example scenario; If he used a simple RISC1 channel mounted to the stud and then attached the drywall to the channel, AND this was done for all walls and the ceiling not just a select few, AND there was no habitable space below this room you would gain a modest STC improvement assuming the drywall has a gap at all sides that was then sealed with permanently flexible acoustic sealant. Remove any of those variables from my hypothetical and all that happened is that you lost a bit of floor space and some dollars in your wallet.
This will kill some midrange and treble frequencies while still allowing the majority of low frequencies to be reflected. It's a step in the right direction, especially if combined with bass traps as outlined above.
You've got a few nasty room modes based on those dimensions, largely associated with the nearly square floor plan. Mathematically the 9' ceilings help you a bit, but not by a ton. There's nothing you can do about it at this phase (i.e. the room is already built), but it will help you to understand where treatments could be better utilized.
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First-off it's called sound isolation. Soundproofing is a misnomer. Secondly in terms of acoustic treatments and how the room sounds the supposed sound isolation will have no bearing on that, so don't sweat it.
Your first sentence describes an environment that is anechoic. Without spending a ton of cash you're not going to get there, so don't sweat it. Start with bass trapping as outlined above regardless of what you'll be using the room for musically, and then expand on the questions I asked above to get better advise on treatments moving forward so you can maximize their effectiveness as well as minimizing the impact to your wallet.