Searching for matching(?) Subwoofer solution

Ok Tim, first of all this is not my method. It a rule of acoustics and speaker design. I started applying it to subwoofers because I was having difficulty matching subwoofers to my Line source ESLs. So I created a horizontal line source subwoofer array which has the added benefits of being very efficient and greatly reducing reflected sound in the room because of the way a Line Source radiates. 
Now I have no experience doing Swarm systems around point source satellites. But I find it an interesting concept as I too have great performance using four subwoofers. Your numbers are about right. So, if you are crossing at 40 Hz you would want 14 or less feet from one sub to the next. Theoretically the drivers are now acting as one acoustically and are phase coherent. But, then you have to add the room into the equation which I think is Duke's message and I would like to understand what he is trying to describe better. With subs at various distances from walls and each other you have a very random pattern of reflections at different times (phase) and with dimensions in and around the wavelengths of the frequencies you are producing certain frequencies are going to resonate longer. Simplifying the situation, what Duke is saying is that placing subs randomly throughout the room creates a situation that smooths out the frequency response throughout the room. I am trying to understand how that happens. 
I would not say that the line array is better bass in all situations. It is better in my situation because I cross over much higher and I have line source satellites. If I put my subs around the room it would really screw up the image. In your case crossing over at 40 Hz  you can not tell where the bass is coming from. The question I have Tim is if you arrange your subs so that any gap is not longer than 14 feet can you detect any difference in the bass. 40 Hz is way down there. What you might try is playing a 30 Hz test tone. Many test records have test tones. You can even download them digitally. Play the tone and some music with deep bass before and after you rearrange things. It may not make any difference at all. 

Here is Earl Geddes explaining subwoofers
https://mehlau.net/audio/multisub_geddes/
Smoothing the bass frequency response in a room with multiple subs is a simple matter of overlapping nodes. He thinks that three subs is optimal the 4th adding little to the solution. He also wants the subs as far apart as possible. He would cross over somewhere below 80 Hz where he thinks bass becomes non directional. So his approach is radically different than mine. I cross over higher but still below the Schroeder frequency and create a line source. Funny thing is that he greatly favors directional speakers over omni directional speakers because they reduce room interactions in a way superior to room treatments. He does not say that in this paper but relates this strongly in other papers. My array does exactly this. Again, I have a sophisticated room correction system which is to some extent cheating. If I bypass it my speakers sound like crap because of the rising response of the transformers I am using. I can not separate the subs from the satellites in this regard. It is either all on or all off.
This paper was written for lay people so he does not use terms like minimal phase system. He may well use terms such as this in more scientific papers aimed at people who understand what he is talking about. I got as far as the Fourier wave equations and gave up.
So Tim, According to Earl Geddes I am wrong. You want to keep your subs as far apart as possible and throw the fourth one away. It is just taking up space. Or, you could try making a line array using all 4 subs and see what happens. Couldn’t hurt to try:)


Mike

Hello Mike,

    You stated: "Simplifying the situation, what Duke is saying is that placing subs randomly throughout the room creates a situation that smooths out the frequency response throughout the room. I am trying to understand how that happens. "

    Hopefully, Duke will respond, too. But as I understand it, the key to understanding how and why a distributed bass array (DBA) smooths out the bass frequency response is psychoacoustics, how the brain processes bass information in the room delivered through the ears, as well as through other body senses, and creates our perceptions of the bass.  
    The purpose of four independent, well distributed subs launching bass soundwaves into the room, with the full knowledge that these soundwaves can be relied upon to reflect off room boundaries and collide into themselves and one another until they run out of energy, is to create an abundance of bass room modes (bass peaks, dips and nulls) and then depend upon our brains to process, sort and make sense of the abundance of room modes in order to create an overall perception of the bass in the room. In other words and simpler terminology, psychoacoustic principles, which explains how the brain will sum the bass by frequency and average it out which results in our perception of the bass as smoothed out and natural.
    I believe psychoacoustics are the key to understanding why and how the DBA concept works so well. It seems to me that explaining how and why a line source bass array (LSBA?) concept works so well can be done more easily with just physics than the DBA concept can and the LSBA concept seems to rely much less on psychoacoustic dynamics than the DBA concept does.  I think psychoacoustic principles and dynamics are a bit esoteric and counterintuitive.
    I've never experienced the bass response performance of an LSBA system in any room. I know the first time I experienced the bass response performance of a DBA system in my room it was a revelation and uncanny how well it performed.  I'd love to experience a LSBA system some day soon since I believe it could also be a revelation.
     I share your curiosity about whether I would detect any difference in bass performance with my DBA by limiting the distance between subs to under 14 feet.  However, in 2008 I had a stroke and still don't have full mobility of my left arm and leg.  I also had custom length speaker wires made for all four subs and the wiring is all run and hidden in the crawl space below my room.  Due to these factors,unfortunately, I don't think it's practical for me to experiment anytime soon.  Perhaps I could recruit a fellow audio enthusiast friend as an experimental lab assistant and mover but no promises.


Tim  

Tim, in this case I don't think psycho-acoustics is the reason. An example of psycho-acoustics is masking. MP3 compression strategies operate on this principle. The normal undistorted music masks the distortion because or brains can only pay attention to the loudest noise. If you don't want to hear your car rattle, turn on the radio.
Nodes form in rooms below what is called the Schroeder Frequency which depending on the size of the room is somewhere around 130 Hz.
Where the nodes are depend on the frequency, room size and the position of the woofer. By  positioning the woofers at different places in the room you create nodes in different places which overlap at different phases creating what I think Duke is referring to as a minimum phase system. This is a bit of a tough one to explain but I will give it a shot. Draw a sine wave on paper now draw another one 10 degrees out of phase with the first. Keep drawing sine waves 10 degree off from the last one until you come around a full 360 degrees. Now lets say these sine waves represent volume. The very bottom is zero dB and the very top is 20 dB. If you average all of these sine waves what you get is a flat line at 10 db. Or as Duke implies a minimum phase system. Geddes seems to think that just three sine waves is enough to create reasonably flat response and you can do this at any frequency below 80 Hz because below 80 Hz you can not locate the source. I personally think that should be below 60 as I know for a fact me and my audiophile friends can locate a 60 Hz test tone. The problem with this approach is what about the frequency band up to the Schroeder Frequency? By absolute coincidence I cross over at 125 Hz just below the Schroeder point. So my subs have to deal with all the room nodes from 125 Hz down. Above the Schroeder Frequency nodes do not form. My way of dealing with the node problem is to limit the dispersion below 125 Hz by forming a line source that is right up against the front wall. Now there are only reflections off the ceiling and rear wall. In my case the rear wall is broken up or there really is not a rear wall. The nodes that do form are easily managed by room control. I am not sure this approach would work well with point source speakers. Such an array may overwhelm them. 
When a concept is counter intuitive it usually means it was not explained well.

mijostyn: "Tim, in this case I don't think psycho-acoustics is the reason."   "when a concept is counter intuitive it usually means it was not explained well."

  Hello mijostyn/Mike,

    I think we have different ideas concerning what qualifies as psychoacoustics.  Psychoacoustics is the scientific study of sound perception and audiology—how humans perceive various sounds. More specifically, it is the branch of science studying the psychological and physiological responses associated with sound (including noise, speech and music).  I think you're right, masking and volume could be construed as part of that definition, they're just not the primary examples that I usually think of.
    I also believe my explanation of the DBA concept and the psychoacoustic dynamics involved was sufficient.  
    When I stated the DBA concept is counterintuitive I was referring to the method of creating more bass peaks, dips and nulls in the room to eliminate the perception of all of them in the room, with our brains being used as a sort of natural room correction software and hardware.  
     Do you think the DBA concept is intuitive?  
     Don't you think the cognitive dynamics involved with the DBA concept fall within the definition and realm of psychoacoustics? 

     You're correct, Geddes has stated that good in-room bass response can be attained over a wider area using as few as three subs and good at a single listening position using just two.

     Hopefully, Duke will respond to the bass phase issues.  

    You have no rear wall in your room for bass soundwaves to reflect off of? You must have very good bass performance along with very high heating and cooling costs.


Tim