specifics on the golden ratio...

I'm attempting to add an isolation booth in my existing project studio to record both vocals (singing) and loud amplifiers, though of course, not at the same time ;). I do not have a lot of space for this, roughly 5x6x8 ft, which, with walls and acoustic treatment, leaves me with a tight squeeze, but I'm comfortable with that. I know these are two very different uses, in a very tiny space, so I'm making it as dead as possible and not attempting any room noise. I have a number of questions about such a small booth and about some design rules I've read over and over, mainly the Golden Ratio: A - Golden ratio... which one?: Why are there so many different golden ratios? Wikipedia's got THE golden ratio, but this guy Louden has a couple of his own. Google has so far given me no less than six different golden ratios. B - Golden ratio limitations?: Does the golden ratio even apply to a room as small as I'm attempting to create? C - Golden ratio... orientation: Louden's ratio is 1 : 1.4 : 1.9. Does the 1 always apply to the height, or could I make a tall room where the 1 is the width? D - Golden ratio vs parallel walls If the golden ratio does apply in my case, how does the parallel wall issue fit in to this? If I splay a couple of my walls, then one end of the wall fits the golden ratio and the other doesn't. Do I turn the walls on their centers so the middle of the wall hits the golden ratio, or make the largest wall dimension hit the golden ratio?

In a room like that I wouldn't worry about ratios ;) your idea of making it dead is the way to go but DON'T have all dead surfaces or it will sound dull and lifeless. Use some slots to keep the top end alive and use the ceiling space for heavy acoustic treatment. Check out the first pics in update 4 here: http://johnlsayers.com/Studio/Mainpage/MP-Leftbank.htm for ceiling treatment. cheers john

Thanks John! So in a booth this size and this dead, parallel walls are still something to avoid? How non-parallel is non-parallel enough? 5 degrees difference between opposing walls? 10 degrees? 20?

When you say "use some slots", do mean add slot resonators? Can you get me started on how I would do that in this case? I guess I don't understand how adding flat timber within this space would keep from adding early reflections, and from just generally being very "live".

well if you were to add 703 to all surfaces you would end up with a dead room except the low mid frequencies (150hz - 500hz) will be liver than the highs because the 703 is not as efficient an absorber in the low end as it is in the high. Slots absorb the low mids ONLY!! they don't effect the high end so a balance can be found between high end absorption and low mid absorption. see attached cheers john

When you say that 703 won't absorb the low-mids as much as the rest of the audible frequencies, are you talking about a specific thickness, or all thicknesses of 703? Bob Gold's charts on absorption coefficients show a very different ratio of absorption across the frequency range between 4" of 703 and 1" of 703. Which thickness would you recommend for my case? And as far as the construction of the slot panels, the Helmholtz formula tells me that a panel made of standard 3.5"x.75" boards with .5" between them, 3" from the wall, for instance, will absorb 465hz. I know which frequencies I'm aiming for, but how do I construct my panels so they absorb a range of frequencies (the 150hz-500hz you mentioned)? Or does their angled position take care of that? I have noticed variations like Mark at Spark One varying the spaces between his slats and Joe at Egan varying the width of the slats. Sorry, there are a lot of questions there. :roll:

if you grab the Helmholtz calculator in the stickies, you can play with the settings to see the effect on the depth of the slats, the width of the slots, and the depth of the cavity. by varying the depth you change the range, and changing the slats/slots width/depth will also. by combining these alterations you can expand the range beyond just one method or another.

Hm, the only Helmholtz calculator I could find is the updated one here, and while it's been very handy, it doesn't specify anything about range. Really, I'd just like to know how to absorb the range John has specified, 150hz to 500hz. I understand how to pinpoint certain frequencies using the calculators, but how to vary the specific dimensions of the slats and slots to cover this range well is still confusing to me. Yes, I can change the height/depth of slats and distance in slots, but it's the details of the variances that I don't get... do I need 5 different sizes of slats and slots? 2 difference sizes, 10 different sizes? If I build slots exactly like John's side wall absorbers, will I be sufficiently absorbing that range?

Finished my design, have most hardware and supplies. Should I go with 2 inch or 4 inch 703 on the inside of this?

the 4" would be better on low end but 2" will work. two 2" layers with air gaps between tem will ensure the cavity behind the resonator doesn't ring. the resonator needs to have the acoustic cloth behind the slats and the insulation behind. it should contact but not be compressed as you want it to breath. the reason for the bandwidth of the slat resonator is many but the varying air gap, the slots/slats as a percentage of overall surface, slot depth, the materials, all play a role. a resonator will have a tight bandwidth if built with a single set of spacing, slats, air gap, slot depth, etc. adding the cloth and insulation reduce efficiency slightly in exchange for broader frequency range, and then adding the variations extends that more. adding individual chambers behind the resonator can add more efficiency but is more complex to build. generally speaking its range is about an octave plus or minus. so a 300hz target will give you about 150-500hz. anything above 350hz doesn't significantly affect eigenmodes in the room but can diffuse/absorb some mid ranges. efficiency at the ends is also lower so if you build with +/- half octave in mind you'll probably be comfortable with its performance.