Myth: "Studio monitor speakers must be set up in an equilateral triangle"

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Myth: "Studio monitor speakers must be set up in an equilateral triangle"


Postby Soundman2020 » Sat, 2020-Feb-15, 15:33

This one is a little trickier, and even some "experts" don't get it, so I'll try to explain it in simple terms, and also even simpler terms, with pictures, to try to make it fool-proof ...

The problem is that "everyone knows" you must set up your speakers and your head in a perfect equilateral triangle, to get "proper sound" (whatever that means...). You "must" have your speakers toed-in at exactly 30°, so that the axes intercept in the middle of your head at an angle of exactly 60°. That's the "right" way to do it. It must be: everyone says to do it like this:

triangle-4.png (4.37 KiB) Viewed 783 times
triangle-4.png (4.37 KiB) Viewed 783 times

Guess what? Its a myth! You should NOT do it like that in your room! (Or rather, you should, but not really... sort of :) )

That "equilateral triangle" thing is all over the internet, in all types of books, all over YouTube, many websites, some speaker manuals, and every place else you look. Any place that supposedly gives you advice on "how to set up your speakers in a studio" talks about the "equilateral triangle" as though i were sacred, carved in stone... But just because everyone talks about it, does not make it correct. The way it is normally interpreted, it would only be correct under two very specific conditions:

1) If the speakers and your head were set up some place where there is no room around them: out in the open, where there speakers are not loaded by the room, and there are no reflections or reverberant field. And:

2) For all people who have had their ears surgically transplanted onto their eyeballs! :shock:

Think about it. Every speaker manufacturer will tell you that the absolute flattest, cleanest sound from their speakers is "on axis": when your ear is lined up perfectly with the acoustic axis of the speaker. Even the pretty graphs with wiggly lines on them that they print in the manuals, show the "on-axis response", and usually a few extra squiggles, for various degrees of "off-axis"... and those off-axis squiggles are always far worse than the on-axis one.

Yet all of those "equilateral triangle" diagrams show the acoustic axes interesting in the middle of the engineer's head. ... which means that the ears are NOT on axis! The EYES are on axis... :roll: So if your ears are in your eyeballs, the equilateral triangle is the correct way to set up your speakers. For the rest of us, the speakers need to be set up so that the acoustic axes are aimed at the ears, not the eyes. See below for some very simple 3D diagrams that illustrate this.

In fact, there are many indications that show that the speakers axes (plural of "axis") should actually be aimed a bit outboard of the ears, not directly at them, since the head itself affects the sound as it approaches the ears, and also to create a wider sweet spot around the mix position. The best spot seems to be at the tip of your pinna (that's the technical term for the fleshy wrinkled folded thingy that sticks out the side of your head, normally called the "ear").

This is your "pinna". It sticks out the side of your head: Very useful for hearing:
Ear-pinna4-CRP.jpg (5.47 KiB) Viewed 798 times
Ear-pinna4-CRP.jpg (5.47 KiB) Viewed 798 times
That's the part of your anatomy where the speaker should be pointing, because that's the part that does the hearing! The body part shown below does NOT do any hearing, so it doesn't make sense to point the speaker at this:

This is NOT your "pinna". It sticks out the front of your head: NOT very useful for hearing:
eye3-SML.jpg (5.15 KiB) Viewed 797 times
eye3-SML.jpg (5.15 KiB) Viewed 797 times

Also, if you look at the polar response of the human ear, maximum sensitivity is at about 45° off the median plane, not 30°. (The "median plane" is an imaginary vertical plane running front-to-back through the middle of your head, poking out from the tip of your nose and extending out in front of you forever. And also behind you. Acousticians measure many aspects of hearing with reference to that imaginary plane. On the graphic below, the median plan passes through the 0° and 180° points of the circle, standing up vertically). And as I mentioned, your ears are most sensitive at and angle of about 45° from that plane:
human-hearing-polar-pattern-03.jpg (16.41 KiB) Viewed 798 times
human-hearing-polar-pattern-03.jpg (16.41 KiB) Viewed 798 times
That's why people often turn their heads a bit to one side, when they are trying to hear a very quiet or distant sound: because your ears are a bit more sensitive off to the sides, and a bit less straight ahead. So if you have the speakers 30° off from that plane, then that's not the most sensitive spot. However, this is not the main reason why the triangle is wrong.

So, if the axes (again: plural of "axis"), are aiming past the tips of your ears (pinna), then they won't intersect in the middle of your head any more! Thus, the triangle is wrong. Rather, the acoustic axes from your speakers should intersect at some point several inches behind your head, not inside your head.

But I bet you are thinking "I can do that and still get an equilateral triangle! I'll just slide my chair a foot or two forward!". Yes you can, but you'd be forgetting point number 1 above: the room. There are good locations for the speakers in the room, and there are bad locations. There are also good locations for the mix position (engineer's ears) in the room, and bad locations. In most rooms, creating the traditional "equilateral triangle" puts the speakers in a bad location, or it puts your head in a bad location, or both. And if you put them both in good locations, then you no longer have an "equilateral triangle"! My answer to that is: "So what?" There's no logical or acoustic reason why the distance between the speaker cones must be identical to the distance between the cone and your ears. Yes, the distance from the left speaker to your left ear must be the same as the distance form the right speaker to your right ear, in order to ensure that the two sounds arrive in phase and at the same intensity: Absolutely. That's the key to getting a good stereo image and sound stage. But that has nothing at all to do with the distance between the speakers! In what way does that distance between the speakers cause the sound to be better or worse? Answer: Not a lot of effect at all!

OK, I'll qualify that: the distance between the speakers is somewhat important, as that's what helps set the width of the stereo image you hear, and the limits for the sound-stage. You can change that speaker separation distances, as long as the distance between the speakers is within a reasonable range. You cannot go to ridiculous extremes. This does not apply to crazy things, such as having both speakers right next to each other, side to side, with no distance at all between them, nor does it apply to having the speakers spread out at 180°, against the side walls, on either sid of your head. But if you keep the separation within reasonable limits, then the actual angle is not a problem. I'll get back to defining those "reasonable limits" below. It's more about angles than it is about specific distances.

So it's a myth! The "equilateral triangle", as it is usually interpreted, is wrong. Not true. Not even necessary. Sure, it's nice if you can actually get your speakers set up like that in your room, but there's no essential life-or-death necessity for doing so.

The truth is that the speakers should be set up at the best point in the room for your speakers in your room, and your head should be set up at the best location for your head in your room, then the speakers should be angled correctly such that the acoustic axes of the speakers intersect several inches behind your head, usually around 8" to 16" back. Perhaps as little as 6", and perhaps as much as 24". All rooms are different.

"But", you say: "that means they won't be angled at 30° any more! :shock:" Yup. My answer, again, is: "So what?" There is nothing magical about 30°. It just happens that 30° is the angle you need to create an equilateral triangle, but once you abandon that myth, then you are automatically abandoning the need for a 30° angle: Yes, both speakers must be angled exactly the same, so the angles on each side are identical, but it does not have to be 30°. Anywhere from 25° to 35° is just fine, and under certain circumstance you could even go as far as 20° and 45°. Not more than that, though, for other reasons that I don't have time to go into here. So those are the "reasonable limits" I mentioned above: 25° to 35° is fine. (And maybe even 20° to 40° in some cases, if you know what you are doing and understand the consequences).

But you don't have to take my word for it: try it out for yourself! Set up your speakers in the classic text-book "equilateral triangle", 2 feet away from the front wall, 1/3 and 2/3 of the room width, angled exactly 30°, with your chair set up so that the axes pierce your eyeballs and intersect in the middle of your head, then carefully listen to your favorite music like that (flat EQ: don't adjust). Listen to a few songs that you know really well, and pay attention to the bass tightness, accurate definition in the mids, clarity in the highs, as well as the width of the sound stage, and clarity if the stereo imaging. Move your head side to side, and forwards / backwards, to see how that changes, and how big your "sweet spot" is. Then quickly and silently (all sounds turned off, so as not to lose the mental reference of what you just heard) move everything around to set it up the way I normally do it: speakers up against the front wall, spread apart by about 55% of the room width, mix position about 1/3 back in the room (35% to 40% of the room length), speakers angled to point at a spot about 8" behind your hear... and listen to the same songs again, at the same volume, once again paying careful attention to all of the above.

Then tell me which setup works best... 8) Which one gives you the best stereo imaging, clearest sound-stage, and broadest sweet-spot, as well as the tightest bass, best definition in the mid range, and clearest, detailed high end? :)

Don't believe all of the "one size fits all" hype about how so set up your room. All rooms are different. All need different setups. Very seldom does the best setup work out to be a 30° equilateral triangle. Unless your ears are in your eyes! ...

The reason why so many places insist on the "equilateral triangle", is supposedly because of "standardization". The theory is that if all control rooms have the speakers angled 30°, then they should all sound the same: The belief is that all the sound stages should be identical, and all the stereo images should be perfect copies of each other, and all the sweet spots should be the same size and shape.... and of course, that is pure, total, utter, complete, absolute garbage! Even for rooms where the speakers are set up spot-on for the "equilateral triangle", it is very evident that they don't all sound alike, the sweet spot is not the same, the stereo imaging can be different, and the sound-stage too. So this is not a valid reason. a 30° angle alone does not make all speakers and all rooms sound the same.

Conclusion: it's a myth that the equilateral triangle is the only possible way to set up your speakers: it isn't. It's merely a good starting point, and works for most rooms, but is NOT necessarily the best for any room at all! It is nothing more than a simplified misrepresentation of how it should actually be.


OK, the above is a simple explanation in words: I've tried to make it as simple as I know how.... but even some "experts" don't seem to understand those words. So here's a more visual, detailed explanation, that ANYONE can understand: (even the "experts", hopefully...)

The normal diagram you see everywhere for the equilateral triangle setup, is something like this:
That is the supposed "best" and "correct" layout, with the speakers at the top two corners of the triangle, and your head (indicated by the circle) at the apex (tip) of the triangle.

Now let's add some numbers, showing the actual angles, and typical distances for a small home studio:
There you have it: the angle for each corner of the triangle is 60°. Equilateral. The speakers are 50" /127cm) apart in this hypothetical setup, and the distance from each speaker cone to the apex of the triangle is also 50". Equilateral. I chose those distances for simplicity, because in most small home studios, that's about the way things commonly end up.

Let's add in another angle here, which is the "toe-in" angle for the speaker:
That's how much you would have to rotate your speaker to get this setup, if you started with the speaker aiming straight down the room, not angled at all. For the famous "equilateral triangle" setup, the toe-in angle is 30°, as you can see above.

Now, instead of having a circle to represent the head, let's put a REAL head in there:
Maybe you can see the problem with this setup now.... but maybe not, and this is where those stubborn experts don't seem to be able to visualize things clearly, so instead of doing it in 2D, let's take a look in 3D:

OOOPS! And there you have it! The speakers are NOT aiming at your ears, but rather at your eyes! As I said above, this is a great setup for all humans who have had their ears surgical transplanted onto their eyeballs...

So how can you fix that?

Easy! Here's how: First, DON'T MOVE THE SPEAKERS OR YOUR HEAD! Keep them exactly where they were in terms of distance, but just change the angles a bit. Forget about the equilateral triangle with 60° corners, and instead rotate the speakers just a little, usually by about 5°, so that the spot where the axes intersect is a bit behind your head, not in the middle of your head. Like this:
in this case, I changed the angle by 5° (If you are mathematically minded, the triangle is now isosceles, not equilateral... the sides are still the same length, but the base is not.).

In other words, I decreased the toe-in angle from 30° to 25°, as you can see here.
and also note that the tip of the triangle is now a little more than 10 inches (25 cm) further back than it was... behind your head.

Let's put the head back into the picture, to make this more clear:
As you can see, the speakers are now pointing at your ears, not your eyes! Your EARS are now on-axis to the speaker. Where they should be.

So here's the same thing in 3D, so that even the most stubborn "expert" can get it:

Bingo!! Each speaker axis is now pointing where it should be: at the tip of the pinna (foldy wrinkly fleshy ear thingy). Because we humans listen with our ears, not our eyes... And because the flattest speaker response is "on-axis", not 5° off axis.


"But!" you say: "The sides are all different lengths! That's not equilateral any more!". Actually, yes it is... it just doesn't look like it... but you'll see that it is... keep on reading...

"BUT! BUT BUT!" Scream the experts.... "That's wrong, because the ears-to-speaker and speaker-to-speaker distances are not the same! They are all messed up! The triangle sides are now 59 inches, not 50 inches! Bad boy! You got it all wrong now!" . Ummmm .... Nope! Not true.... "But! BUT! BUT!!!!" They shriek even louder... "The word 'equilateral' means "same sided", so the sides must be the same length!". .... That part is true, yes... but look CLOSELY! In fact, when you do it like this, those distances are they same! They are now CORRECT! Take a closer look:
See that big purple number on the side? That's the actual distance from the speaker cone to the pinna. What does that number say? "49.1 inches". Bingo again! So in fact, your ears and the speakers are NOW set up almost perfectly in an.... (drum roll please...) ... "EQUILATERAL TRIANGLE!!!! Yup. Look closely: the distance from speaker to speaker is 50" (127cm), and the distance from each speaker to the relevant ear, is 49.1" (125cm). So if you slide your chair back roughly the width of a matchbox, you will once again have your perfect equilateral triangle, but done the RIGHT way, not the wrong way, with the speakers pointing at your ears, not your eyes. 8-)

End of story.

So why is this myth so widely spread, even in speaker manuals and text books, if it isn't correct? Because it works for most rooms... Sort of reasonably well. It's that simple. However, it is NOT OPTIMAL FOR ANY ROOM! It works, and that's all you can say for it. However, if you are trying to set up your studio to be the best it can be, then ignore it, and set up your room for optimal performance, not mediocre "text book geometrical" performance. Do you want your speaker setup to be the best it can be, or just sort of reasonably OK... Take a look at my signature line, and I think you'll see which way I lean... :)

- Stuart -

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