Maybe I can summarize and comment on some previous posts:
Comb filtering: Numerous people have suggested that multiple tweeters are avoided (in nearly all cases) because it leads to comb filtering. This arises when the spacing between radiators is on the order of the wavelength of sound radiation, leading to alternating constructive and destructive interference of the pressure field. There is no way to prevent this in the crossover, other than to filter all but one radiator at wavelengths below the tweeter spacing. What is not so clear is how to correlate comb filtering with subjective preference of the results. I suspect if high-frequency comb filtering was really a desirable characteristic, we'd see many more speakers with multiple tweeter arrays. Instead, we see the opposite -- a strong emphasis on avoiding this effect throughout the entire operating range of the loudspeaker.
Tweeter dispersion: This is a more general comment, not necessarily relevant to Tekton. There was some suggestion that more tweeter dispersion is better, but this is not necessarily the case, particularly for 2-way systems. Current trends and research data suggest that matched directivity between radiators is important to maintain smooth power response and avoid an excess of high-frequency energy. This accounts for the popularity of waveguides and ring (annular) domes which increase the tweeter directivity. Its easy to see why this is desirable: if the tweeter (in a 2-way design) is radiating as a monopole, and you are standing 90 degrees off axis, the direct sound reaching your ear will be have a huge mid-band hole.
Expectation bias: Anyone without significant hearing impairment who has visited a high-end show will know that many well-respected, high-cost designs are both flawed technically and (unsurprisingly) sound mediocre -- or worse than mediocre. Yet, those who own these systems (and this includes professional reviewers) seem predisposed to a certain blindness with respect to flaws or limitations. Even DIYers who design their own systems are subject to this bias. Leo Beranek expressed this sentiment more than 60 years ago:
Comb filtering: Numerous people have suggested that multiple tweeters are avoided (in nearly all cases) because it leads to comb filtering. This arises when the spacing between radiators is on the order of the wavelength of sound radiation, leading to alternating constructive and destructive interference of the pressure field. There is no way to prevent this in the crossover, other than to filter all but one radiator at wavelengths below the tweeter spacing. What is not so clear is how to correlate comb filtering with subjective preference of the results. I suspect if high-frequency comb filtering was really a desirable characteristic, we'd see many more speakers with multiple tweeter arrays. Instead, we see the opposite -- a strong emphasis on avoiding this effect throughout the entire operating range of the loudspeaker.
Tweeter dispersion: This is a more general comment, not necessarily relevant to Tekton. There was some suggestion that more tweeter dispersion is better, but this is not necessarily the case, particularly for 2-way systems. Current trends and research data suggest that matched directivity between radiators is important to maintain smooth power response and avoid an excess of high-frequency energy. This accounts for the popularity of waveguides and ring (annular) domes which increase the tweeter directivity. Its easy to see why this is desirable: if the tweeter (in a 2-way design) is radiating as a monopole, and you are standing 90 degrees off axis, the direct sound reaching your ear will be have a huge mid-band hole.
Expectation bias: Anyone without significant hearing impairment who has visited a high-end show will know that many well-respected, high-cost designs are both flawed technically and (unsurprisingly) sound mediocre -- or worse than mediocre. Yet, those who own these systems (and this includes professional reviewers) seem predisposed to a certain blindness with respect to flaws or limitations. Even DIYers who design their own systems are subject to this bias. Leo Beranek expressed this sentiment more than 60 years ago:
"It has been remarked that if one selects his own components, builds his own enclosure, and is convinced he has made a wise choice of design, then his own loudspeaker sounds better to him than does anyone else's loudspeaker. In this case, the frequency response of the loudspeaker seems to play only a minor part in forming a person's opinion"
Let me add a further point, which is probably the most interesting one in relation to Tekton
Arrays: Presumably, in the design of the various Tekton models, there is some optimization of the tweeter amplitude coefficients (at high frequency) to overcome the worst case of comb filtering (that would occur at equal amplitudes). Most of the literature concentrates on a linear array, and in this case a very general result is that the pressure can be written as
where the x(l) are the amplitude coefficients and A is the directional response of a single tweeter. Perhaps the most well-known example is the 5-element Bessel array for which x=[0.5,-1,1,1,0.5]. The attribution to Bessel comes from the use of the generating function for Bessel functions in the development of the theory, such that he amplitudes x are approximately proportional to J_n(1.5), where n=[-2,-1,0,1,2]. I am not aware of a useful 3-element Bessel array. In the limiting case of M -> infinity, the sum above reduces to a pure phase factor so that the array exactly inherits the directivity of a single tweeter. Also, a crossover can be further used to "revert" the amplitude coefficients at low frequency to x=[1,1,1,1,1] thereby achieving the gain of a simple low-frequency array. My final point, however, is that if an advanced method of selecting the array coefficients is being used by Tekton, its not really apparent from the product literature.
NOTE: the equation is taken from https://doi.org/10.1121/1.428305
Arrays: Presumably, in the design of the various Tekton models, there is some optimization of the tweeter amplitude coefficients (at high frequency) to overcome the worst case of comb filtering (that would occur at equal amplitudes). Most of the literature concentrates on a linear array, and in this case a very general result is that the pressure can be written as
where the x(l) are the amplitude coefficients and A is the directional response of a single tweeter. Perhaps the most well-known example is the 5-element Bessel array for which x=[0.5,-1,1,1,0.5]. The attribution to Bessel comes from the use of the generating function for Bessel functions in the development of the theory, such that he amplitudes x are approximately proportional to J_n(1.5), where n=[-2,-1,0,1,2]. I am not aware of a useful 3-element Bessel array. In the limiting case of M -> infinity, the sum above reduces to a pure phase factor so that the array exactly inherits the directivity of a single tweeter. Also, a crossover can be further used to "revert" the amplitude coefficients at low frequency to x=[1,1,1,1,1] thereby achieving the gain of a simple low-frequency array. My final point, however, is that if an advanced method of selecting the array coefficients is being used by Tekton, its not really apparent from the product literature.
NOTE: the equation is taken from https://doi.org/10.1121/1.428305
Did anyone actually look at the patent?
The introductory B.S. leads me to the thought that the gentlemen at the US Patents Office must have been either drunk or bribed..
US9247339B2 - Loudspeaker design
- Google Patents
The introductory B.S. leads me to the thought that the gentlemen at the US Patents Office must have been either drunk or bribed..
US9247339B2 - Loudspeaker design
- Google Patents
An excerpt from the patent:
Is the guy who came up with this stuff actually delusional, or simply laughing all the way to the bank?
-Gnobuddy
Neither, I suspect. It's just marketing reality. A patent is a useful tool to help sell product, simple as.
I'm curious if you have any "solid" evidence about what sort of array algorithm(s) they might be using. The Quadratic Phase Array is presumably better than the Bessel approach for line arrays with many elements (the asymptotic efficiency is higher, as described in the 2000 JASA paper by Aarts). However, there is no indication from the product literature, or from the patent text linked to by others, that a sophisticated array algorithm is being employed by Tekton. The patent text is actually too painful for me to read carefully, but a cursory glance gives no hint of a non-trivial array algorithm. Of course, that doesn't mean they are not using one. Also note that Tekton is using 2D arrays, which makes a (careful) analysis even more difficult.
I always presumed that Eric was simply using either
a/ the sextuple tweeter arrangements in series-parallel to cover the upper midrange & the single central tweeter for the HF. Or
b/ running 5 apiece of the hexagonal arrangements in a series-parallel arrangement for the upper mids, then handing over to 3 tweeters for the HF.
No firm evidence for that or any other arrangement of course, just supposition. I doubt it's particularly complex though.
Depends what you're doing with them & how much 2nd harmonic you're willing to put up with. A single Satori can take a hell of a low XO frequency (I've done it) if you chuck proper impedance compensation & a reasonably steep filter at them. No real issues there. From the hints in reviews I doubt the Tekton has either of those, but there's 10 - 12 of them, which is about as much Sd as a 5in cone. I'd guess they've probably gone for 2KHz or thereabouts; I'd prefer (significantly) lower myself but you really need a more complex filter to do that well.
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My interpretation of the potential advantage of this design is that using multiple tweeters allows the use of a lower crossover frequency allowing more midrange to handled by the tweeter. This is by dropping the tweeter excursion. I believe that at higher frequencies the central tweeter takes over alleviating array combing problems in the highest octaves. So this is somewhat similar in some respects to a waveguide in that here horn gain allows extension of the lower frequencies for tweeter operation into the midrange, with potential superior sound over the woofer in this range.
I did distortion measurements on a woofer years ago, and below the fundamental resonance frequency, the distortion I measured was almost entirely 3rd harmonic (not 2nd).
This makes perfect sense when you think of the "S" shaped force vs position curve of a good spider or voice coil surround - you're snubbing both positive and negative excursion peaks symmetrically to try and keep the voice coil within the magnetic field, so no even harmonics are generated.
I would assume the same is true of tweeters if you try and drive them to large excursions at (relatively) low frequencies.
Obsessing about one particular technical problem while ignoring other bigger ones seems to be a hallmark of eccentric one-person engineering designs. In this case, obsessing about lowering midrange moving mass (a non-problem) seems to have been traded for an excessively large midrange sound source (which is a real problem, as it causes erratic frequency response and uneven directionality.)
And that's without even considering the quite unnecessary cost of the plethora of expensive tweeters.
-Gnobuddy
There is a theorem in math that says that there always exists a polynomial of order (n-1) that will exactly pass through n points in a plane.
If you have, say, three drivers, there will be no difference between the Bessel function (Jo, zeroth order Bessel function of the first kind) and a plain old quadratic; a quadratic is already a polynomial of order (n-1), where n=3, and the higher-order coefficients that differentiate the Bessel function from a simple quadratic will all be zero.
In a nutshell, with 3 drivers, there will be no difference at all between a quadratic and Jo(x) Bessel fit.
As you say, if you have "many" drivers, there may be some slight difference between Jo(x), and a plain quadratic (x*x).
But I suspect that, for a practical number of drivers, this is going to be more a case of gilding the lily than a revolutionary improvement. I would be very surprised if there turn out to be significant benefits.
-Gnobuddy
I am not sure there is such a theorem about polynomials intersecting planes. What you may be referring to is the Lagrange polynomial, which is the polynomial of least degree passing through the n points (x_i,y_i) with i=1,n. Indeed, this polynomial is unique and has order n-1.
I don't understand your point. In particular, I don't know what you mean by "fit", or how this relates to Bessel arrays, which are not fits to J0(x) by any meaning of the word "fit". A Bessel array uses properties of the generating function for Jn (not just J0) to obtain a phase factor with (nearly) constant amplitude. For a 5-element Bessel array, these amplitudes are Jn(1.5) where n=-2,-1,0,1,2. The choice of 1.5 is, in essence, arbitrary but is chosen to get as close as possible to integer amplitude ratios. The argument 1.5 is a fixed quantity and does not refer to the location of the array elements.
This is not the difference Bessel and Quad. Phase arrays (QPA). A QPA modifies the generating function to give better efficiency at the cost of a slightly worse (irregular) polar pattern.
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