Since the early days of live sound, thousands of shows have been staged, large and small, and what they all have in common is that they rely on sound systems capable of amplifying the sound produced on stage and getting it to everyone in attendance. Around the 1970s and 1980s there was a revolution in loudspeaker cabinets, starting with the creation of multi-way systems and leaving behind the horn-loaded speakers widely used in the 1960s. Almost all the manufacturers of large-format systems were researching and making new advances in loudspeaker design, but always building on earlier, well-known systems.
The real revolution came in the 1990s with the arrival of the novel line array, a vertical stack of flown boxes smaller than their predecessors, since the power they had been using was no longer necessary. This is because, with the acoustic drivers positioned higher up, the high frequencies were not absorbed directly by the first few rows of the audience, but instead radiated farther and more evenly across the whole venue.
Over time, industry professionals realized that stacking a series of loudspeaker cabinets produced variations in the sound, caused by the interaction between the waves generated by the different speakers. This led some of the sound engineers with the deepest knowledge of the subject to specialize. This field came to be known as sound system tuning. Within this group we find subwoofer arrays, or sub alignments, which consist of taking the omnidirectional radiation of low frequencies and making it directional, in order to avoid cancellations and out-of-phase lanes in the audience area, as well as to achieve the greatest possible cancellation on the stage side. That last point is what gave rise to this idea.
As we have explained, sound equipment has advanced, but we haven't advanced in the way we put on an event. Today the classic setup of a stage in front of the crowd persists, and what are generally used are the well-known sub arcs, either physical or electronic, and in some cases a group of boxes in a cardioid configuration to clean up the area closest to the stage.
What this project seeks is an alternative to that classic arrangement, replacing the traditional rectangular stage with a circular one, where attendees can position themselves around a circumference concentric with the stage. It also aims to solve the problem of low-frequency radiation by achieving a high SPL in the audience area while leaving the stage free of radiation. Many of the explanations will be accompanied by graphs and predictions to help readers understand both the procedure to follow and the mathematical and physical explanation.
Origin and Context of the Project
This project was born to solve the problems that arise in the low frequencies when trying to use a circle as a stage.
At first, the idea of the project was focused on creating a subwoofer arc. Initially this consisted of a central end-fire array with a progressive reduction in the number of boxes as it moved toward the outer part of the array.
During one of the simulations I was running, I noticed that no prediction software allows, so far, an arc greater than 180 degrees, nor does any of them allow generating a physical arc by automatically angling the loudspeaker cabinets.
At first, none of this gave me any revelatory idea; instead I chose to build a physical and digital subwoofer arc, while also angling the boxes to cover certain cancellation lanes that appeared at the time.
As the following image shows, we achieved a very linear array with a very high acoustic summation. The drawback of this array is the appearance of cancellation lanes in the seats located off the stage axis.
During one of the predictions, it seemed like a good idea to push the distances and angles to the maximum possible, with the sole purpose of analyzing what happened. I was able to verify that at an angle of 135 degrees it was possible to achieve acoustic summation by means of a gradient on the audience side, with considerable cancellation at the back, where the stage would be positioned, as long as the radius was small and the frequencies low. It was a few days later that it occurred to me to repeat the experiment, but this time with 180 degrees of coverage. The problem I found was that the array in question ended up too far out on the audience side, separating the audience considerably from the stage. On top of that, significant cancellation lanes appeared.
It should be noted that at this point the simulation was being run with 5 gradient sub groups, each made up of two speakers, the rear one of which had a delay as well as phase inversion.
All the groups were tangent to the arc and followed the direction vector of the cabinets' propagation relative to the center.
The angles used were:
90º, 45º, 0º, -45º, -90º, and the radius between each of the arrays and the center of the circle was 8 meters, because at a frequency of 85Hz the wavelength is approximately 4 meters, 8 meters being a direct multiple of that wavelength. This was really the moment when I decided to change the purpose of my project, refocusing it on creating a circular array.
At first I decided to blend the end-fire array on which the original idea of the project was based with the innovative ring placement. This placement had a radius of 8 meters to the box closest to the center.
Looking at an end-fire array, we notice that it is a directional array, and that it also generates a lobe at the rear that varies with frequency. For example, at a frequency of 80Hz two lobes are generated at the rear. It is precisely that unwanted rear radiation that would hurt us when simulating the ring.
These lobes would interact with each other, producing a series of summations and cancellations. And because the array is so directional, it would cause an enormous amount of cancellations and acoustic summations in the audience area. Below are the simulations of that ring by frequency:
The irregularities in the prediction, along with the appearance of summations on the stage side, show that it is not feasible to use an end-fire alignment to achieve the desired cancellation and maximum summation in the audience area.
That was when I decided to build a double ring in a gradient alignment, with the drawback that significant cancellation lanes were generated as the frequency increased, because the coverage of the array's cardioid lobe was too directional to cover the whole area allotted to that sector.
Unable to move forward from this point, I got in touch with the well-known systems engineer Pepe Ferrer, to whom I explained my intentions and asked about the reliability of my progress up to then.
Pepe Ferrer ran a series of simulations with his software SubMapp, which he provided me in its latest version, and also suggested an alternative to the traditional gradient. This new configuration consisted of a set of five subwoofers arranged in two rows. In the first row, closest to the audience, there are three boxes with no delay, while the two boxes in the inner ring (spaced 1 meter from the outer ring) carry a delay of 2.94 ms and phase inversion.
Thanks to this configuration, it is possible to maintain a uniform SPL in the audience area up to a higher frequency, which works in our favor when setting the crossover frequency of our system. Once all the ideas were brought together and the prediction of our sub array was run, we ended up with the following image:
