The Key of B

Seeking acoustic Nirvana: the drawing is done! March 26, 2009

I finished the quadratic equations, resulting in the drawing you see below.

Why the quadratics? Well, look at the double door on my drawing (near topmost part of room). Now find the corner just above and to the right of the door. Where, precisely, is that corner? Keep in mind: when I started, I had only the lengths of the walls, and this corner in question is the only one where neither wall is nicely horizontal or vertical, so all we know is that it’s 177 inches from the point next to the keyboard, and it’s 16-3/8 inches from the edge of the top horizontal wall. Euclidially (if that’s a word), we have the intersection of two circles, folks, and that is a quadratic equation.

Later on, a second such equation surfaced, and I only dodged a third by noticing (at the last minute, whew!) that I could intersect two lines instead of two circles. Bisecting the big angle was another story: slopes and inverse tangents. And, of course, that angle’s vertex is MIA, so first I had to find it. Then, the speakers are on a line normal to the bisector, forming the recommended equilateral triangle with the listener … by the time I was done, 1985 seemed like only yesterday!

Friday, when I go out to do errands, I will get this thing scanned (’cause what you see here is a camera photo, not great for printing), and then I will send it off to Auralex Acoustics for a professional analysis. I’m sure they’ve seen it all! (I hope they’ve seen it all …)

Click the image to get an enlargement you can actually read, in a new window.

Bee squared minus four ay cee March 17, 2009

Acoustic analysis of a room starts by taking all the measurements and finding symmetric locations for the main speakers. In most rooms, this means measuring length, width, and ceiling height, then plunking down the speakers one or two feet from the side walls, about 1/4 of the way from the room’s front.

My studio, however, is shaped like a large fragment of a triangle, stuck onto a similarly-sized rectangle. In other words, as any fifth grader could tell you, it’s not even a real trapezoid.

Now, normally, I’m one to ignore all the fine calculations and just do it anyway, but when I first moved in to this room, I couldn’t even play a CD without being blasted by what studio technicians call “boomy bass,” and I was unable to make acoustic recordings with sound quality I considered decent.

With a little bit of reading, I was able to solve a lot of the trouble myself. Turns out, corners are the worst place to put speakers (who knew?), and I made an incredibly makeshift vocal booth out of spare blankets and about $18 of Home Depot products.

Yet, I hunger for more. At Auralex Acoustics, pro engineers will analyze your room for free. That’s because they want to sell you their acoustics products. But I’m okay with that if they’re prepared to make a good case.

So, I broke out the tape measure, and it was easy enough to measure all the walls. But then I started plunking down the speakers, and you know what? Before long, I wanted to know where was the main axis of symmetry. So I figured, I just needed to bisect the angle of the main triangular region, except the triangle’s actual vertex is not on the map (its tip is truncated asymmetrically by not one, but two, line segments) … and there is one corner between walls that are not orthogonal to anything, so … where exactly is that point? The (x,y) coordinates came out, and they brought their friend, the point/slope formula, then Mr. Pythagoras showed up, looking shifty, and before I’d wised up, there was a quadratic equation!!

But I recovered, and then I remembered that I actually like this stuff. Plus, I’ve got Apple’s “Numbers” application to do all the heavy lifting—how nice is that? So, now I’m almost done with an awesome little map of the place, and this time I really know where to put those speakers!

I will post the map in a bit.
(Update: here it is!)