I'd suggest that you start by buying the book "Master Handbook of Acoustics" by F. Alton Everest, which will give you the background you need to understand acoustics. Right now, you have found two pieces of advice and a couple of calculators on the internet, but you don't really understand what they are telling you. I'm not trying to be disparaging or belittling: just trying to point out that where you are right now is not where you think you are, and there's a long road ahead of you for understanding what you need to know in order to design a studio.
First, room ratios: There are MANY possible room ratios, and both Andy's and Bob's calculators are really good at showing you how the modal response of any room will turn out, based purely on its dimensions, and making no other assumptions (other than that it is a rectangular prism). There is no such thing as "the perfect ratio" or "the golden ratio" for rooms. There are merely good ratios, and not so good ratios. The only real rule you need to know, is that you should stay away from the not so good ratios, and try to get reasonably close to one or more of the good ones. That's it!
If your final room shape will not be a purely rectangular prism for whatever reason (for example, if you choose to splay some of the walls if you are following the RFZ design philosophy, or the NER or CID philosophy, or another related philosophy which relies on splayed walls), then starting out with a rectangular prism that has a good ratio is STILL a good idea, since the results for the surfaces that are still parallel, will still be valid, and the results related to surfaces that are not parallel any more, can still give you a rough idea of what the modal response will be. The tangential and oblique results will not be far off, and the axial results for the remaining parallel surfaces will be perfectly accurate. So starting out with a rectangular prism that has a good ratio, then modifying it as needed to splay your walls, is still a smart thing to do.
Now a typical controlroom has short sloping walls on the front(mixing position) and longer ones or none on the back
No it does not. A typical control room has whatever shaped walls are needed by the basic underlying design philosophy that the studio designer chose to use at the outset. Many designers prefer pain rectangular shapes. Some used to prefer the LEDE concept, but that is outdated now, and no longer used. Some use the RFZ design, which is an extension of LEDE and does indeed splay the front section of the side walls (or the side section of the front walls, if you prefer to see it that way). NER is a bit similar, but often incorrectly misunderstood as an octagonal shape, for some unknown reason. CID is sort of similar, but with many shorter wall segments. Etc. So there's no such thing as a "typical" control room that resembles your sketches. There are many different design concepts, some of which do have things in common with your sketches, but not all, and there are different reasons behind each of them.
But is there anyone who can tell me how to calculate the lenght and degree of those sloping walls keeping the rome mode calculation and ratio of sepmeyer in mind.
Not really. That's like saying "Can anyone tell me how much sugar to put in my coffee, keeping the temperature and size of the handle in mind". There simply is no relationship.
If you want to go with an RFZ design, which many modern studios are based on, then the angle for splaying the walls is determined by two things: first, then angle of the speaker soffits themselves, which will likely be in the region of 30° (but not necessarily, and that assumes that you will, in fact, flush-mount your speakers), and secondly by the technique called "ray tracing", to determine the angle of the walls that fill in between the edge of the soffit and the parallel part of the side wall. The actual angle depends on the room size, the room geometry, the specific speakers you will be using, how big you want the RFZ to be, the size of the console, the building materials that will be used to make the walls, and several other factors. Nobody can say what angle you will need without first knowing all of the above factors, then going through the process of ray-tracing.
Or is it just important to keep it symmetrical?
Yes, keeping the control room room symmetrical is VERY important! Regardless of which design concept you choose, symmetry is critical.
It seems (correct me if i'm wrong) there is no certainty in room ratio when building a sloped wall controlroom, and no easy way to calculate.
If your room is non-rectangular, then correct: room ratio calculators will not accurately predict the complete modal response of the room. But they will still accurately predict the modal response for the walls that are NOT angled! And they won't be very far off with the other predictions, especially if you use the maximum, minimum and average dimensions.
Room ratio depends on rectangular rooms. So sloping messes that up.
Partly true, but there is also no need to go crazy about room ratios! Modal response is only a small part of studio design. The room will need treatment in any case, no matter what shape it is, and you will have to measure the response in order to decide on the treatment, no matter what shape or size, so it really isn't that important to worry excessively about room ratios.
So why use them as starting point if you can't depend on them??
Because they provide a good approximation for most cases.
So i guess I'll just use the max of space I have available(comfortable) for my control/mixing/jam room and keep it symmetrical fr good stereo imaging and use a sloping for the flutter echos.
Splaying your control room walls to get rid of flutter echo is not a good idea. Firstly, flutter echo should not be a problem in a correctly designed control room anyway, and secondly even if it is a problem, it is very easy to deal with using simple treatment. Flutter echo is never a good reason for splaying walls.
Rather, you should first decide on which design philosophy makes sense to you, for your way of tracking / mixing / mastering, then you should use the concepts and "rules" associated with that philosophy to determine the shape and size of your room, and the angles (if any) of the walls, floor and ceiling.
- Stuart -