My in-room measurements of large line-source-approximating dipole speakers versus monopole speakers agreed with Kates, but were made many years ago with a borrowed real-time analyzer and not recorded so I cannot present them here. Earl Geddes disagreed with Kates, and I think that was over the two-dimensional modelling Kates used (which I had forgotten about). Perhaps behavior approximating a line source plays a much bigger role than I had appreciated in the (ime) superior in-room bass smoothness of a large dipole versus a monopole, in which case my example of "two monopole subs back-to-back" was a poor illustration of a large dipole panel speaker's behavior in the bass region. Thanks for pointing that out.Kates’ paper used 2D modeling, which omitted vertical modes with monopoles, and that made them look lumpier than they really are (Kates assumed dipole bass is line-source-like and has no vertical modes), and the paper attracted criticism for that.
I agree with Toole that two well-placed subs will have smoother bass than one.Also, why jump to 4 monopole subs? Just because 4 monopole subs in bad locations and phase and positioning will look like a dipole bass pair? Toole showed how much smoother the bass can be with 2 well-placed subs than with one
Four is not a magic number, but four well-placed subs are better than two for the same reason that two well-placed subs are better than one. Geddes articulates the underlying principle:
"The use of multiple source locations in the modal region will globally yield a response curve that is closer to the natural power response of the sources and the room. Said another way, if we use multiple source locations the frequency response at any given location in the room will become closer to the true power response (read smoother) the more sources that are used. Basically if I have one source which has a variance, V, of the frequency response (the variation of the response from the average or smooth response) of say 6 dBs, by adding a second source we will reduce this variance by half to 3 dB. Adding a third source reduces this to 2 dB, etc. Basically the variance goes as V/N where N is the number of “independent” sources. A key requirement here is “independent”. If the added sources are close to the first source then they are not independent. And two sources in opposite corners or symmetrical locations are not as independent as two sources placed in non‐symmetrical locations. It is impossible to have two sources that are completely independent at LFs in a small room, so the effect is never as good as the formula suggests." (Emphasis Duke's)
If by any chance you might be attending the Axpona show in a few weeks, I hope you will stop by Room 709. There will be a distributed multisub system in that room, and whether or not we agree on its merits I'd enjoy meeting you.
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