How many speakers make up a spatial sound setup?
Of course, it all depends on your definition of„spatial“, the level of immersion you want to achieve, and the purpose of your installation. In the scenario where you want to provide a continuous sound pressure level within the whole audience area, with no audible gaps when walking around, there are some rules of thumb that can help you plan your loudspeaker setup. Depending on the type of project and of the audio content, you might still need professional help to achieve a perfectly measured and calibrated setup, but in most cases, you can rely on a few handy tricks and plan it yourself without driving your project’s costs to the ceiling.
Loudspeakers surrounding the audience
Let’s start with the physical parameters of a space. In the example presented here, the room has a floor surface of 15 by 15 meters. The ceiling is 5 meters high. If we think of placing speakers all around the space, we might need 1 meter space to put the stands (or the truss); so let’s say the loudspeakers are placed with a distance of 1 meter to the walls.
The closer the loudspeakers are placed to the audience, the more you will need to try to avoid acoustic gaps. Hence one rule of thumb is to put the loudspeakers as far from the audience as possible. Within a rectangular space, its corners are definitely a good choice, and this is why we start with placing speakers exactly there.
Now the question arises: how many speakers are needed in between the four corners, alongside the walls? At this point, the audience area comes into consideration. The audience area is defined as the field where the listeners are going to experience a presentation. In our case the audience area a 10 by 10 meters in the center of the space. Its borders might be consisting of seating, for example. So the audience area has a distance of 2.5 meters to each wall, and a distance of 1.5 meters to the potentially closest loudspeaker.
Another rule of thumb to avoid acoustic gaps: The distance between two loudspeakers should be equal to the minimum distance of the audience area to a loudspeaker. This rule is very close to what you might already know from placing a stereo pair of loudspeakers: together with the listener position, it should result in an equilateral triangle. In our case it is 1.5 meters.
Now we have all information we need to calculate the number of loudspeakers. Sum up the length of each side where the loudspeakers would be placed, and then divide it through the distance between the loudspeakers. In our case that would be:
4 walls x 10 meters / 1.5 meters = 26,67 loudspeakers
Because this is a rule of thumb, the result is not ultra precise. Compared to the well known stereo triangle, here the distance between two loudspeakers tends to be a little bit too short. Which means that the calculated number of loudspeakers is a little bit over the amount of what you would actually need. So there is still a little margin to scale down the number. In this case I’d say 24 loudspeakers would be quite enough.
The calculation above is what you’ll need as a maximum reference value, every additional speaker is practically useless for the hearing experience – meaning that the audience is not going to really hear the difference if the speaker density was higher. From this point, you can now modify the speaker setup according to the project’s needs. Could you minimize the audience area? If you could resize the audience area to 8 by 8 meters, you would only need to put 16 loudspeakers in order to achieve the same sound quality. Or could you make a technical compromise and allow the effect of acoustical gaps? You could put one loudspeaker in each corner, and one in-between on each wall. Depending on your creative concept, that could also go a long way, and you would end up with 8 loudspeakers surrounding the audience.
In order to achieve a continuous sound pressure level when walking around within the audience area without perceiving acoustical gaps, 26 loudspeakers is the maximum amount of loudspeakers you would need in the example depicted here. Such a setup would make each loudspeaker acoustically disappear; when you close your eyes, you’ll be barely able to distinguish whether a sound comes from a certain loudspeaker, you just hear the sound in space. In many cases, you don't need to achieve this level of technical perfection, and a much lower loudspeaker density could make you create the sound experience you want.
Loudspeakers above the audience
In addition to the rules described above, there is another effect to be considered to figure out the amount and position of the overhead loudspeakers: spatial hearing is less precise when sound comes from above. This means that you need less loudspeakers on the ceiling than those surrounding the audience horizontally. Depending on what you aim to achieve artistically, you can multiply the distance between two loudspeakers with the factor 1.5 or even 2.
In our example, the ceiling height is 5 meters. With an average listening ear level of 1.7 meters for a standing audience, and subtracting the position of a loudspeaker hanging let’s say 0.8 meters below the ceiling, the minimum distance between the audience and the overhead loudspeakers is 2.5 meters. Multiplied with a factor of 1.5, the distance between the overhead loudspeakers results in 3.75 meters.
Now you can create a square grid of loudspeakers with a distance of 3.75 meters each, starting with the zenith position in the very middle. As depicted in the sketch, you’re going to end up with 25 overhead loudspeakers. Just like the horizontal loudspeakers surrounding the audience, you should do that with a pragmatic mind and stretch the grid in order to achieve an efficient audio resolution with no more loudspeakers than needed. Also, putting more speakers on the ceiling would barely make a difference in the sound quality. You could rather reconsider if – with regard to the content and creative intention – you really need such a high sound resolution on the ceiling. Five loudspeakers, one at the zenith, and four above each corner of the audience area, could also do the trick.
While subwoofers are uncritical in terms of their spatial position in a home theater or 5.1 studio setup, things get a bit trickier in larger spaces. While it is still true that one can barely locate the position of a subwoofer, when you start wandering throughout the space, you will perceive a higher sound pressure level when you come close to a subwoofer, and vice versa. In this sense, the question is not primarily about the spatial localization of a subwoofer, but about providing a more or less constant sound pressure level overall. In our example, four subwoofers would be adequate, located in the corners of the space. In case only one subwoofer should be available, you could try to place it on the ceiling close to the zenith. But there is an advantage of the four subwoofers in the corners: If you’re running your system with a crossover frequency of 80 Hz or even 100 Hz, a deep male voice might sound strange when you hear it from one of the horizontal loudspeakers, while the low frequencies are located on the ceiling. This effect becomes even worse when you put a single subwoofer on the floor. It’s not a no-go, but if you have the capacities, you will do better to distribute the low frequencies more or less in the directions where they belong to in your creative sound work.
As shown in our example, an audience area of 10 by 10 meters would be ideally served with 24 loudspeakers surrounding the audience, 25 overhead loudspeakers, and 4 subwoofers. Depending on the type of the content presented, you could scale down that system to 8 loudspeakers on the floor, 5 overhead loudspeakers, and 1 subwoofer.
To make the calculation easier, we prepared an Excel sheet (coming soon) enabling you to figure out the equipment and the budget needed. As an example, using the active loudspeaker MR5 Mk3 by Mackie with 108 € each (excl. VAT), and the subwoofer MR10S Mk3 also by Mackie with 293 € each, the price for a whole setup ranges from 1.697 € to (cables etc. on top)
Are you wondering how to find the perfect loudspeaker according to your individual requirements? You might be interested in reading the related blog article here soon.
Finally, feel free to share your knowledge in planning a spatial loudspeaker setup here in the comments, other users will appreciate it!