View Single Post
Old 16th August 2019
Northward's Avatar

Originally Posted by Soundman2020 View Post
That's the entire point. As soon as you rotate the speakers, or move the mix position, there is no longer an equilateral triangle. Period. End of story.

If your speakers are toed-in at exactly 30°, but then you sit forward of the apex, then there is also no longer an equilateral triangle: the distance from each ear to the speaker is no longer the same as the distance between speakers, and the angle from ar to speaker is no longer 30° either. Thus the triangle is not equilateral: it is isosceles. Which is what I've been saying all along.

I really don't get why it is so hard for people to understand this: it is basic high-school geometry. Sit down with a piece of paper, a pencil, and a protractor, and you can prove it to yourself inside of a couple of minutes.

The equilateral triangle only exists when the distance between the speakers is the same as the distance from each speaker to your head, and the angle of the speakers is 30° toe-in. If you change ANY of that, then there is no equilateral triangle! This is just plain common sense. Move your hear, or turn the speakers, and there is no more "equilateral".

So I'll repeat, one more time, that the majority of contemporary studios do NOT have the speakers and mix position set up as an equilateral triangle! (see the photos I posted above, of several studios where there clearly is no such triangle). And even if they did have perfect triangles, as soon as the mix engineer leans forward a few inches in his chair to adjust something on the console, or slides his chair back a bit to stretch his legs and listen more comfortably, once again there is no such triangle.

The triangle does not exist: it's a myth.

So there's no need to chase a myth, and try to make it happen in a studio, because it never can happen. (Unless you bolt the engineer's chair to the floor, tie him down with straps, and lock his head immobile in a surgical neck brace, so he can't move it at all... )

QED There is no equilateral triangle.

- Stuart -
Well... I think you're again being a bit too black and white and playing on semantics. A rhetoric just to prove a point that isn't really meaningful as it's all about context.

There is a difference between the conventions and frameworks needed when engineering & planning a room, and the real life adjustments needed and expected for psycho-acoustic reasons and sometimes practical reasons. The latter being tiny variations if the engineering bit was processed seriously.

When starting a project from a blank page or from the plans of an existing empty space, as a designer / acoustician you have to understand and define what your technical constraints and goals are. That's the very first thing you're taught to do as an engineer.

When designing ground-up rooms like we do, once the structural and design variables are known (room type & design parameters, possible shell type, general layout, target net surface of each room, speaker type and mounting etc) you have to set a reference point in the space around which you will engineer your whole design.

If you were to describe what studio designers do in the least amount of words possible it would be that we work with time.

"Everything we do has to do with sound in time."

Hence our reference points in time / space are de facto Tx @ t(0) transmitter: the loudspeakers and Rx @ t(1): the target receiver (listener).

All the room variables are set within the following simple time limits:

Without EER variable: lim t(1)->t(1+n) since direct path speakers to ears is the fastest path so any reflection always arrive in t(1+n)

With EER variable: lim t(0)->t(0+n) since EER can arrive before direct path since sound travels a lot faster in solidians than in air and can shortcut air transmission that way (this time issue you fix by decoupling.)

You simply can't start drawing a studio shell if you don't have these particular time and hence physical space / location references. What we know is that all other things being equal a specific speaker setup statistically gives much better results: that's the area nearing a setup that is an equilateral triangle, as created between the speakers and a specific point in the room, whose dimensions will be dictated by a number of factors such as size of speakers (having to respect minimum distance vs. coherence / number of drivers), structural and other technical constraints, presence of a mixing console or not etc. (In some cases, like with a mixing console, there may even be a need to slightly elevate the speakers to control the interactions with the console's surface.)

You list your time constraints within your structural constraints, set your speakers up @30° in CAD on the draft plans and you draw an equilateral triangle.

The tip of the triangle is the reference point in space and time around which the whole design is going to be referenced. Speakers, 0° incidence (perfectly on axis) time reference point over the symmetrical axis of the room.

We already know that for psycho-acoustic reasons the engineer will need to sit a bit forward from this point, and we use that tip of the equilateral triangle reference point to then estimate precisely that exact location: we now have the theoretical sweet spot, which with an in-wall 3 way setup will be about 30cm+ / 1ft+ forward from the tip. How much forward is based on the specific HRTF and tastes of a given engineer. Like a finger print it is unique to every human being, so it's not a variable we can control 100%. The engineer will naturally sit where it's best for him, the difference between engineers being in the realm of centimeters / few inches.

In that sense, the equilateral triangle is a very real thing as it is the ideal and absolute reference point of a design.

Some designers do vary this of a few degrees (either the reference triangle itself or just toeing the speakers a bit) but for the serious ones it's always because they are facing structural constraints (e.g. room isn't wide enough for a given setup) or speaker constraints (on axis harshness etc). In that sense, it's a forced compromise, not something they would happily do out of the blue.

Visiting local studios when travelling to build sites, I often see all sorts of sub-par speaker setups (that also sound sub-par) I don't see why it means that the equilateral triangle isn't a solid reference, in our case, one that worked 100% of the times.

Debating whether the engineer actually sits at the tip of an isosceles or equilateral triangle is beyond the actual point and not really interesting.

The actual subject is studio design and engineering conventions and why the equilateral setup is the best possible reference point in that context.

Last edited by Northward; 16th August 2019 at 01:27 PM..