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1 week ago
#1

Equilateral triangles/ monitor placement.

Hey guys. Super quick question.

I’m treating my room right now 16’8”x 11’2”. If my math is right the 38% sweet spot rule of thumb should be 6’4”from the front wall.
My question is what is the equation to find an equilateral triangle from this point
1 week ago
#2
Lives for gear

Quote:
Originally Posted by Bolt audio
I’m treating my room right now 16’8”x 11’2”. If my math is right the 38% sweet spot rule of thumb should be 6’4”from the front wall.
My question is what is the equation to find an equilateral triangle from this point
Super quick answers: First, the 38% rule is not a rule, and does not guarantee a great mix position: It's a starting point, a guideline.

Second, the equilateral triangle is somewhat of a myth. Yes, it does work OK for most rooms, but like the 38% rule, it isn't a rule either. It's a starting point.

Those are the quick answers: now for the details:

Truth is, there's a process for setting up your speakers and mix position and then optimizing the locations and angles of both. Commonly, you'll end up with the speakers angled anywhere between about 25° and 35°, and the mix position anywhere between about 30% and 45% of the room length. It's a slow, tedious, boring process, but it works. It involves doing many acoustic tests while moving both the speakers and mic in a set of small increments, then checking the results to find the best spot.

So unfortunately there's no quick and simple answer to your question, if you are wanting to get a great setup.

- Stuart -
1 week ago
#3
Lives for gear

Quote:
Originally Posted by Soundman2020
Super quick answers: First, the 38% rule is not a rule, and does not guarantee a great mix position: It's a starting point, a guideline.

Second, the equilateral triangle is somewhat of a myth. Yes, it does work OK for most rooms, but like the 38% rule, it isn't a rule either. It's a starting point.

Those are the quick answers: now for the details:

Truth is, there's a process for setting up your speakers and mix position and then optimizing the locations and angles of both. Commonly, you'll end up with the speakers angled anywhere between about 25° and 35°, and the mix position anywhere between about 30% and 45% of the room length. It's a slow, tedious, boring process, but it works. It involves doing many acoustic tests while moving both the speakers and mic in a set of small increments, then checking the results to find the best spot.

So unfortunately there's no quick and simple answer to your question, if you are wanting to get a great setup.

- Stuart -
Very well said!
1 week ago
#4
Lives for gear

For more on this see: Speaker placement methods
6 days ago
#5
Lives for gear

Quote:
Originally Posted by Soundman2020

Second, the equilateral triangle is somewhat of a myth. Yes, it does work OK for most rooms, but like the 38% rule, it isn't a rule either. It's a starting point.
As a huge fan of EBU citing recommendations more often than not, you shouldn't say that.

https://tech.ebu.ch/docs/tech/tech3276.pdf

60 degree angle is the standard, not a starting point.

Quote:
Those are the quick answers: now for the details:

Seriously?

The trivial solution is to turn the speakers a little to the outside and still keep the equilateral triangle. Thats all well known. Actually a matter of taste, because some manufacturers recomend direct facing towards the listener. All not a big deal if the triangle distance is at least 1.75m, or as EBU recommends, not falling below 2 meters.
Attached Images

6 days ago
#6
Lives for gear

Quote:
Originally Posted by Bolt audio
Hey guys. Super quick question.

I’m treating my room right now 16’8”x 11’2”. If my math is right the 38% sweet spot rule of thumb should be 6’4”from the front wall.
My question is what is the equation to find an equilateral triangle from this point
I would simply stay on the equilateral triangle and move speakers along those axises until finding the optimum sound. This has less degrees of freedom to optimize frequency response but ensure correct imaging. If you deviate from this triangle, you are either increasing the mid signal versus the side signal or vice versa (thinking in M/S), meaning that you will not hear the mix how it was intended, either too wide/deep or too narrow / flat, hence the stereo image is distorted. The 60 degree angle is simply a common standard to ensure that all sound engineers will hear the same stereo image (but for different size of sound stage, depending on the triangle length).
6 days ago
#7
Lives for gear

Quote:
60 degree angle is the standard, not a starting point.
As I said before, it's a starting point. I don't know of many contemporary studio designers who always use 30° toe-in! Maybe 30 or 40 years ago perhaps, but today? The general rule we use is "anywhere between 25° and 35° toe-in, as needed to get the optimum results".

Quote:
Seriously?
Yup. Seriously. That is, in fact, the truth. Just because you didn't know it, doesn't mean it isn't true.

Quote:
The trivial solution is to turn the speakers a little to the outside and still keep the equilateral triangle.
Your understanding of geometry seems to be a bit flawed! (sort of like your understand of acoustics). If you turn the speakers as you say, then the toe-in angles are no longer 30°! Duh. And the apex intercept is no longer 60°. Thus, it is no longer an equilateral triangle. Ooops! Should I suggest a basic book on geometry and trig, to help you get a better grasp of these terms and concepts?

You should probably check back, and you'll see that exactly what I said: maybe you could make a better effort in the future, to read what others have written before commenting on it. Because when your comments show that you clearly didn't read it at all, that just makes you look foolish.

Quote:
Actually a matter of taste,
Nope! It's a matter of psycho-acoustics, actually. That seems to be something you aren't familiar with at all, so I'd recommend that you read a couple of books about that. I'd suggest Floyd Toole's "Sound Reproduction", and also Kliener and Tichy's "Acoustics of Small Rooms". Both of those should help you get a better grasp of basic acoustics as well.

Quote:
because some manufacturers recomend direct facing towards the listener.
... which, of course, puts your ears off axis...

The best practice here is to aim the acoustic axes slightly past the tips of the pinna, to intersect at some distance behind the head, maybe 12" to 24" back... give or take. Depends on the room, the speakers, and the treatment, but somewhere in that range it usually ends up.

Quote:
I would simply stay on the equilateral triangle and move speakers along those axises until finding the optimum sound.
No wonder you have such serious problems in your own room! I'm starting to understand why that is. But that's no reason to mess up the OP's room in the same way yours is messed up.

Rather, he should follow the usual procedure that experienced acousticians and studio designers use, which is as I outlined above. You could even try doing that in your room, and amaze yourself with the improvement...

Quote:
If you deviate from this triangle, you are either increasing the mid signal versus the side signal or vice versa (thinking in M/S),
Not true at all. And..... Newsflash! Speakers are nothing at all like crossed-pair mics. There's no relationship at all between how an M-S mic setup works, and how speakers work. Zero. Zip. Nada. Nothing. You should probably do some research on what M-S is, and why it works. If you wanted to try the M-S principle with speakers, you'd need two very different speakers: one would have to be a dipole, and the other would have to be a sealed box with rather narrow dispersion.... and you would have to set them up right on top of each other, rotated 90° from each other! Oops.... you failed again.

Quote:
meaning that you will not hear the mix how it was intended,
Ummmmm... We are not talking about listening rooms here! We are talking about CONTROL Rooms.... you know... the room where the mix is created? Where the guy sitting at the console decides what his intentions are, and imposes them on the mix? I had long suspected that you come form the crazy world of audiophiles, but I think you pretty much proved my suspicion here... only an audiophile would make such a silly statement.

Quote:
either too wide/deep or too narrow / flat, hence the stereo image is distorted.
Yup, true audiophile silliness, with no basis in reality. Try again.

Quote:
The 60 degree angle is simply a common standard to ensure that all sound engineers will hear the same stereo image
You should probably go visit a few real control rooms, in real pro studios, and check the speaker angles.... Then report back here with your findings. The real world is rather different from the world you imagine.

Let me save you the trouble: I'm attaching a few images from some real studios, so you can tell me again why studios only ever angle their speakers at 30° tow-in, never anything else...

According to you, all of those studios must be total flops, because none of them have speakers set up in equilateral triangles with perfect 30° toe-in. None of those places could ever hope to produce a good mix, because their sound stages and stereo imaging must all be totally useless, unacceptable... And yet, there's some pretty good studios there, that turn out pretty darn good mixes. That's hard to explain... (for you, at least...)

Quote:
(but for different size of sound stage, depending on the triangle length).
Ooops! And now you have established that you also don't understand what the term "sound stage" means!

Keep digging that hole... you might get to China soon...

Anyway, trying to get the OP's thread back on track: There is no need at all to use the mythical equilateral triangle. Rather, you should use the normal procedure that is used by most acousticians and studio designers, as well as most home studio builders who understand acoustics: set up the speakers against the front wall ( to minimize SBIR issues), spaced about 30% of room width apart form each other, with the test mix position about 35% of room length, and start testing there. Move the mix position forwards and backwards in small steps, testing at each position, then compare all the tests to see which location was the best. Then do the same with the speakers. move them further apart in small steps, testing at each step, then compare again to find the best spot. You'll find that the speakers and mix position will be set up as an isosceles triangle, not an equilateral triangle. But don't worry about that: the equilateral triangle is not necessarily the best layout: that's a myth for beginners to use, but experienced acousticians, studio designers, and studio builders don't fall for the myth. Rather, they use the above procedure to find the REAL best layout.

- Stuart -
Attached Thumbnails

6 days ago
#8
Lives for gear

Quote:
Originally Posted by Soundman2020
As I said before, it's a starting point. I don't know of many contemporary studio designers who always use 30° toe-in! Maybe 30 or 40 years ago perhaps, but today? The general rule we use is "anywhere between 25° and 35° toe-in, as needed to get the optimum results".

Yup. Seriously. That is, in fact, the truth. Just because you didn't know it, doesn't mean it isn't true.

Your understanding of geometry seems to be a bit flawed! (sort of like your understand of acoustics). If you turn the speakers as you say, then the toe-in angles are no longer 30°! Duh. And the apex intercept is no longer 60°.
I shorten this up a little bit. Do you pretend to be silly and play the clown here?
You turn the speakers (rotate!!!!) them a little outside and then they will hit your ears instead of your eyes (lol!).

You can still maintain an omnidistant triangle. If that is not clear to you, go back to school (if you are not a teenager) and study some simple geometry.

There is no need to move the speakers. You rotate the speakers on their stands and you get a slight off-axis response. This is the intention. And if you wish you can then correct the triangle by some 3 cms. But 3cm is neglibile. If you use a triangle of 1.75m of bigger that its not even worth to discuss because the change is very small, unless you are using your awfull 1.2m triangle for your setup as you suggested ("as a starting point", nobody would ever do that).

IF (!!) you are using MORE than one speaker set, a second pair of speakers or a third pair, then you have no choice than to go for a smaller angle.

But as you see in the image, there is always a pair with perfect 60 degree angle. You need at least ONE PAIR perfectly aligned to 60 degree, especially if it is the only one, 20 years ago and now.
6 days ago
#9
Lives for gear

Quote:
Originally Posted by Synthpark
You turn the speakers (rotate!!!!) them a little outside and then they will hit your ears instead of your eyes (lol!).

You can still maintain an omnidistant triangle. If that is not clear to you, go back to school (if you are not a teenager) and study some simple geometry.
The triangle is formed perpendicular to the front face of the speaker's cabinet. Hence if you rotate the cabinet, you don't have an equilateral triangle anymore.

(This used to be a very civil and informative subforum and is becoming pretty childish lately.
Please stop trying to disprove every bit of advice Stuart gives on this forum, it is becoming really annoying to read through all of this nonsense and get to the actual useful information.)
6 days ago
#10
Moderator

We typically stick to the 30° equilateral setup while designing. With good speakers, it's going to be the optimal setup in terms of perception of stereo, phantom center image and depth in 100% of the cases.

Now due to e.g. the space between our ears, we recommend the engineers sit a bit forward from the triangle tip, usually 30cm forward, which provides the best representation of stereo and optimizes the sweet spot area. We account for this in the design.

You get "out of field stereo" width, yet with a lot of depth and a strong phantom center and everything in-between: you can pin point every source precisely, even out of field info.

It's also impossible to fool around with angling speakers once they're in-wall, and since we only work in-wall... Question answered. Same when you work quasi-flush mount (speakers stuck against the front wall) where the objective is to keep the front wall/speaker relationship as close to minimum phase as possible. Having a differential between the angle of the front wall and the speakers, even of only 5°, degrades the response immediately audibly and on measurements.

I did notice that angling the speakers away from 30° (reducing the angle) tends to degrade the stereo and center relationship - creating more of a strict "LCR" image with little info in-between and damages the depth a lot.

Angling the speakers further (augmenting the angle) also creates more of a "LCR" image and the center tends to collapse, headphone style.

YMMV.
6 days ago
#11
Lives for gear

Quote:
Originally Posted by Northward
We typically stick to the 30° equilateral setup while designing. With good speakers, it's going to be the optimal setup in terms of perception of stereo, phantom center image and depth in 100% of the cases.

Now due to e.g. the space between our ears, we recommend the engineers sit a bit forward from the triangle tip, usually 30cm forward, which provides the best representation of stereo and optimizes the sweet spot area. We account for this in the design.

You get "out of field stereo" width, yet with a lot of depth and a strong phantom center and everything in-between: you can pin point every source precisely, even out of field info.

It's also impossible to fool around with angling speakers once they're in-wall, and since we only work in-wall... Question answered. Same when you work quasi-flush mount (speakers stuck against the front wall) where the objective is to keep the front wall/speaker relationship as close to minimum phase as possible. Having a differential between the angle of the front wall and the speakers, even of only 5°, degrades the response immediately audibly and on measurements.

I did notice that angling the speakers away from 30° (reducing the angle) tends to degrade the stereo and center relationship - creating more of a strict "LCR" image with little info in-between and damages the depth a lot.

Angling the speakers further (augmenting the angle) also creates more of a "LCR" image and the center tends to collapse, headphone style.

YMMV.
Isn't it also a question of semantics?
If you suggest sticking to 30 degrees and sit closer, you could also interpret that as changing the angle, depending on which point you choose to measure the triangle. Because you moved one point of the triangle while the others remain fixed, no?
6 days ago
#12
Moderator

Quote:
Originally Posted by Jamie Mac
The triangle is formed perpendicular to the front face of the speaker's cabinet. Hence if you rotate the cabinet, you don't have an equilateral triangle anymore.
I think that what he means is that while keeping the distance between speakers cabinets and engineer an equilateral triangle, you can slightly toe in or out a speaker.

For a while it was quite common to do this especially in Mastering studios with a specific brand of free standing speakers that were common in the 90s' up to mid 00s' that had quite harsh tweeters.

The engineers would toe out the speakers a bit to soften the tweeters, their slight off-axis response being a bit smoother. They could work longer hours that way.

In short, instead of physically moving the speakers cabinets on the ideal "circle" and changing the equilateral setup to an isosceles one which degrades the imaging a lot more, they simply slightly rotated in place the speakers cabinet.
6 days ago
#13
Lives for gear

Quote:
Originally Posted by Northward
I think that what he means is that while keeping the distance between speakers cabinets and engineer an equilateral triangle, you can slightly toe in or out a speaker.

For a while it was quite common to do this especially in Mastering studios with a specific brand of free standing speakers that were common in the 90s' up to mid 00s' that had quite harsh tweeters.

The engineers would toe out the speakers a bit to soften the tweeters, their slight off-axis response being a bit smoother. They could work longer hours that way.

In short, instead of physically moving the speakers cabinets on the ideal "circle" and changing the equilateral setup to an isosceles one which degrades the imaging a lot more, they simply slightly rotated in place the speakers cabinet.
Hi Thomas, I understand.

I just think there is some confusion about what defines the equilateral triangle and how it is measured: whether or not to account for the toeing in or out as changing the angles of your traingle. Or simply defining the triangle as the distances between speakers and engineer.
6 days ago
#14
Lives for gear

Quote:
Originally Posted by Northward
I think that what he means is that while keeping the distance between speakers cabinets and engineer an equilateral triangle, you can slightly toe in or out a speaker.

For a while it was quite common to do this especially in Mastering studios with a specific brand of free standing speakers that were common in the 90s' up to mid 00s' that had quite harsh tweeters.

The engineers would toe out the speakers a bit to soften the tweeters, their slight off-axis response being a bit smoother. They could work longer hours that way.

In short, instead of physically moving the speakers cabinets on the ideal "circle" and changing the equilateral setup to an isosceles one which degrades the imaging a lot more, they simply slightly rotated in place the speakers cabinet.
Thanks for clearing this up with other words.
6 days ago
#15
Lives for gear

Quote:
Originally Posted by Jamie Mac
(This used to be a very civil and informative subforum and is becoming pretty childish lately.
Please stop trying to disprove every bit of advice Stuart gives on this forum, it is becoming really annoying to read through all of this nonsense and get to the actual useful information.)
I agree with you. You have to see that sometimes one can be "sucked in" in a discussion he actually doesn't want to have. And it happens that some let's say novice comes in and gets some answer which might be rather weird, nobody intervenes. What to do then? But you are right that these childish excesses should be kept to a minimum. Anyway, I am out for a while, also since I am not a long-term fellow here. Thanks.
6 days ago
#16
Moderator

Quote:
Originally Posted by Jamie Mac
Isn't it also a question of semantics?
If you suggest sticking to 30 degrees and sit closer, you could also interpret that as changing the angle, depending on which point you choose to measure the triangle. Because you moved one point of the triangle while the others remain fixed, no?
You have to sit a bit forward, among other things due to spacing between your ears, but also because moving out of the tip degrades stereo a lot more than moving a bit in.

Since engineers will change position while working, the ideal spot is a bit forward at the average working position. That way the changes are very small if the engineer leans back on his chair for a bit, or leans forward to adjust an EQ etc.

Same with lateral movement.
Attached Thumbnails

Attached Files
GS triangle speakers.pdf (41.7 KB, 27 views)
6 days ago
#17
Lives for gear
Thank you Thomas.

Jens wrote a nice post here (as usual)...worth reading as well.

Monitors placement/room acoustic
6 days ago
#18
Lives for gear

Quote:
Originally Posted by Northward
I think that what he means is that while keeping the distance between speakers cabinets and engineer an equilateral triangle, you can slightly toe in or out a speaker.

For a while it was quite common to do this especially in Mastering studios with a specific brand of free standing speakers that were common in the 90s' up to mid 00s' that had quite harsh tweeters.

The engineers would toe out the speakers a bit to soften the tweeters, their slight off-axis response being a bit smoother. They could work longer hours that way.

In short, instead of physically moving the speakers cabinets on the ideal "circle" and changing the equilateral setup to an isosceles one which degrades the imaging a lot more, they simply slightly rotated in place the speakers cabinet.
That is funny. I was just thinking about those when I read this.
6 days ago
#19
Lives for gear

Stuart and Synthpark need to go for a drink together, and hash things out. Jeez

Y'all sound like a married couple. And while the humour of it all can be amusing (I see myself a lot in Synthpark - always being rebellious and going against the grain), it's tedious and s turning the place bitter. Can you guys hug it out?
6 days ago
#20
Lives for gear

Quote:
Originally Posted by Jamie Mac
The triangle is formed perpendicular to the front face of the speaker's cabinet. Hence if you rotate the cabinet, you don't have an equilateral triangle anymore.
+1. Thank you! It's good to see that some people around here really do understand geometry!

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 -
4 days ago
#21
Lives for gear
Quote:
Originally Posted by Jamie Mac
The triangle is formed perpendicular to the front face of the speaker's cabinet. Hence if you rotate the cabinet, you don't have an equilateral triangle anymore.
Quote:
Originally Posted by Soundman2020
As soon as you rotate the speakers,[...] there is no longer an equilateral triangle. Period. End of story
My take :

Following Northward illustration, if speakers are angled of 30°, the direct signal from speaker (0°) (represented in black line with arrow, added by myself) is on the same line as d (added by myself in this illustration).

If you rotate your speakers around its axis point, you still have your equilateral triangle.

Overlaying both images from Northward:

d is still equal to d as you can see. The triangle doesn't move.

You only change the direct signal (0°) direction.

d and the 'direct signal' paths are now in different directions.
Difference is equal to the angle difference between your two compared positions. Here 5°.

If we overlay both (30° and 25°) direct signals.

So, equilateral triangle is not a myth. And it's NOT defined by the rotation of your speakers but only by d (distance between 2 axis point of your 2 speakers).
Attached Thumbnails

Last edited by JayPee; 3 days ago at 10:54 PM.. Reason: Spelling
4 days ago
#22
Gear Maniac

Quote:
Originally Posted by VenVile
Stuart and Synthpark need to go for a drink together, and hash things out. Jeez

Y'all sound like a married couple. And while the humour of it all can be amusing (I see myself a lot in Synthpark - always being rebellious and going against the grain), it's tedious and s turning the place bitter. Can you guys hug it out?
4 days ago
#23
Moderator

Quote:
Originally Posted by Soundman2020
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; 4 days ago at 01:27 PM..
3 days ago
#24
Lives for gear
Here's what I did.

How I got pretty good sound from three absorbers

Worked pretty well. Still need to get around to optimizing it by testing multiple small variations. But I post it just to point out that using some of these "rules" as starting-point guidelines, and not getting caught up in minutia or millimeters, gave me a quick start at half decent sound.
1 day ago
#25
Lives for gear

Quote:
And it's NOT defined by the rotation of your speakers but only by d (distance between 2 axis point of your 2 speakers).
This is actually very simple: what is the distance between the speakers? What is the distance from each speaker to your ear? If those two are not the same, then you do not have an equilateral triangle.

This isn't about where you put the aim point for the speakers, or anything similar. It's about the speakers, and your ears. That's what matters. That's what the triangle is all about, because at the end of the day what matters is what you are hearing, not how nice the lines look when you draw them on paper, or which way the speakers happen to be pointing: What matters is the acoustic axis of each speaker, and the location of your ears. Measure the distances, and if they are not equal, then you do not have an equilateral triangle. Point the speakers straight back, at each other, toed in, toed out: that's not entirely relevant (although it does matter, of course). What is relevant to having an equilateral triangle, is the way your ears see it, period. As far as I can determine, the justification for the equilateral triangle is that it gets the sound waves arriving at your ears at an angle of 30°, and the ONLY way you an do that is if the distance from each ear to the relevant speaker, is the same as the distance between the speakers. If you angle your speakers at 30° toe-in, but then sit forward of the apex, the distance from each ear to the speaker is LESS than the distance between the speakers: thus, you do not have an equilateral triangle any more. On the other hand, if you toe-in the speakers slightly LESS than 30°, such that the apex is further back in the room, you can then sit inside the apex and actually get an equilateral triangle, with respect to your ears: the distance from ear to speaker can be the same as the distance between speakers, even though the physical toe-in angle is no longer 30°, the angle from ear to speaker is 30°.

That's the issue that folks seem to be avoiding here, or not wanting to see: what matters is your ears and the speakers: If you want an equilateral triangle, then that's where it should be.

Boggy has been saying this for years. So have many others: Use whatever physical toe-in angle you need to get the listening position where it needs to be. There's no need to follow the old-school rigid, strict but unjustified "rule" of using exactly 30° and placing your head exactly at the apex. That's the way things were done 40 years ago, before the science of psycho-acoustics, and the research, and the lab testing, showed how our hearing actually works, as opposed to how it was thought to work back then, when the "triangle" first originated. Science moves on, and there's no need to stick to the myths of the past.

To throw another item out: it turns out that 30° isn't even the bet angle for hearing anyway! If you look at the polar pattern for ear sensitivity, our hearing is most sensitive somewhere around 40° to 50° off the median plane (it varies by person, and by frequency). So maybe an angle of 45° would not be too bad either!

- Stuart -
23 hours ago
#26
Lives for gear

Quote:
Originally Posted by Soundman2020
As soon as you rotate the speakers, or move the mix position, there is no longer an equilateral triangle. Period. End of story.
Quote:
Originally Posted by Soundman2020
This is actually very simple: what is the distance between the speakers? What is the distance from each speaker to your ear? If those two are not the same, then you do not have an equilateral triangle.

This isn't about where you put the aim point for the speakers, or anything similar. It's about the speakers, and your ears. That's what matters. That's what the triangle is all about, because at the end of the day what matters is what you are hearing, not how nice the lines look when you draw them on paper, or which way the speakers happen to be pointing: What matters is the acoustic axis of each speaker, and the location of your ears. Measure the distances, and if they are not equal, then you do not have an equilateral triangle. Point the speakers straight back, at each other, toed in, toed out: that's not entirely relevant (although it does matter, of course). What is relevant to having an equilateral triangle, is the way your ears see it, period. As far as I can determine, the justification for the equilateral triangle is that it gets the sound waves arriving at your ears at an angle of 30°, and the ONLY way you an do that is if the distance from each ear to the relevant speaker, is the same as the distance between the speakers. If you angle your speakers at 30° toe-in, but then sit forward of the apex, the distance from each ear to the speaker is LESS than the distance between the speakers: thus, you do not have an equilateral triangle any more. On the other hand, if you toe-in the speakers slightly LESS than 30°, such that the apex is further back in the room, you can then sit inside the apex and actually get an equilateral triangle, with respect to your ears: the distance from ear to speaker can be the same as the distance between speakers, even though the physical toe-in angle is no longer 30°, the angle from ear to speaker is 30°.

That's the issue that folks seem to be avoiding here, or not wanting to see: what matters is your ears and the speakers: If you want an equilateral triangle, then that's where it should be.

Boggy has been saying this for years. So have many others: Use whatever physical toe-in angle you need to get the listening position where it needs to be. There's no need to follow the old-school rigid, strict but unjustified "rule" of using exactly 30° and placing your head exactly at the apex. That's the way things were done 40 years ago, before the science of psycho-acoustics, and the research, and the lab testing, showed how our hearing actually works, as opposed to how it was thought to work back then, when the "triangle" first originated. Science moves on, and there's no need to stick to the myths of the past.

To throw another item out: it turns out that 30° isn't even the bet angle for hearing anyway! If you look at the polar pattern for ear sensitivity, our hearing is most sensitive somewhere around 40° to 50° off the median plane (it varies by person, and by frequency). So maybe an angle of 45° would not be too bad either!

- Stuart -

So ...

Are you now accepting the fact that you can "rotate" (toe in/out) speakers and still manage an equilateral setup?
20 hours ago
#27
Lives for gear

imo stuart got a point or two:

i'm mixing quite a few things in 5.1 (and very few things in 7.1.4) these days: when setting up speakers in one of my studios or for temporary installations (where some of my mixes get played) and when evaluating options purely in terms of listening, i almost always seem to prefer wider angles for front speakers, certainly for any format above 2.0 or 2.1 - not sure whether it's got to do with my use of coax speakers...

...and in the lede cr i've spent the most time working (for 25+ years), i've setteled for smaller angles than 30° with its large 2.0 system a long time ago (after working for a couple of years with speakers at 30°).

so: two of my five control rooms do not use speakers set up in an equilateral triangle; no science behind it but taste/personal preference (in those rooms).
also: if you get to work in a multitude of studios, you get to experience nearfields being positioned on the meterbridhe in all sorts of ways, forming vastly different triangles: some sound ok, some weird, some exhibt width one would think is not possible from their physical position.

___

for the majority of folks around here on gs, running diy studios not using specifically shaped walls but working in rectangular rooms, i recommend moving speakers/compare different speakers in different positions - could be they get happy (and achieve better results) with a setup different from the equilateral triangle/30° starting point!

___

p.s. the soundstage one can create by using immersive formats both in the studio and in live sound is far beyond what can be achieved with more traditional surround setups (for obvious reasons) - interestingly enough, live rigs do not need to consider angles much and main hangs usually just get spaced across the width of the stage (so we're talking about narrow angles and large overlaps) yet achieve estonishing results regarding localisation for a large part of the audience/over a very wide area and hence appeal to a lot of people (while setting speakers up in a studio with very narrow angles did not work at all and the soundstage/width pretty much collapsed...)

Last edited by deedeeyeah; 7 hours ago at 01:17 PM.. Reason: edited/info added
9 hours ago
#28
Lives for gear
Stuart, I think no one said that (equilateral) triangle is formed with 2 speakers and the ears. If we want to be picky, 2 speakers and 2 ears don't form a triangle

(Equilateral) triangle is just a geometric form helping positioning the listening point into the triangle into the room.

Adding to my previous message : note that the difference between 25° and 30° (named δ1 and δ2 is getting bigger when distance d gets longer.

Difference measured between on-axis and off-axis depends on polar plot and distance d.

In a small acoustic space, difference should be very minimal. Since d is 'short'. Specially if polar plot shows very minimal differences between on-axis and 5° off-axis.

As I said, in a big perfectly treated room, like Northward's ones, difference should be more noticeable. But I can't say more about it. I never saw a polar plot from ATC.

But let's go back to the subject.

Now, we've been talking about only one axis (horizontal). Things get more funny if we want to rotate speakers on vertical axis. More on this later .
Attached Thumbnails

8 hours ago
#29
Moderator

Quote:
Originally Posted by JayPee
Stuart, I think no one said that (equilateral) triangle is formed with 2 speakers and the ears. If we want to be picky, 2 speakers and 2 ears don't form a triangle

(Equilateral) triangle is just a geometric form helping positioning the listening point into the triangle into the room.
... Case in point.

It is also a reference point for mixing: a de facto standard in studios that allows the mixes to translate and be reproductible with their artistic intent outside the studio.

It is a compromise. All speaker setups are a form of compromise. The typical +30°/-30° equilateral setup for stereo happens to be considered and experienced as the best compromise. Statistically, a narrower setup means the width suffers, a wider setup and the phantom center suffers.

See AES, EBU and ITU recommendations on screenshot.

There can be deviations, again mostly due to a specific context, or simply tastes.

Quote:
Originally Posted by JayPee
I never saw a polar plot from ATC.
Some public info on ATC mid domes. Which is a fantastic piece of engineering. Their new dual suspension tweeter is also pretty phenomenal.

http://www.troelsgravesen.dk/ATC-SM75-150.htm

All wide dispersion.
Attached Thumbnails

5 hours ago
#30
Lives for gear
The reason of the 30°: the bad directivity off axis.

A speaker with a perfect directivity could work fine at 0° with a perfect backwall and sidewalls

It seems than a range of 60° of diffusion sign a good speaker.

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