10.07.2026

Lobing of the triple tweeter at high frequencies

Claude Fable: An array of adjacent tweeters narrows vertical dispersion (a genuine benefit: fewer floor and ceiling reflections), but the inevitable price is vertical lobing and off-axis comb filtering.

Louhivaara: Claude is mistaken about that lobing—specifically regarding the triple-tweeter array—at least if he claims the starting point is the distance between the drivers' centers. Especially with dome tweeters, what matters is the distance between the edges of the radiating surfaces, not the distance between the centers. This is because a dome tweeter's voice coil is attached specifically to the edge of the dome, causing the dome to vibrate linearly all the way to the edges. Consequently, the distance between the dome edges becomes the dominant factor. In my triple-tweeter arrays, the ratio of the throat diameter to the center-to-center distance approaches 80 percent; based on the half-wavelength calculation, lobing therefore only begins at 15 kHz. This aligns with my own measurements (in practice, 16–17 kHz). The shaping of the area between the edges is also important, and through precise shaping, I have managed to raise that threshold by a couple of kilohertz.

Lobing is more pronounced with mid-bass drivers because they are attached to the voice coil at the center of the driver. In this case, the outer edge of the cone does not track the voice coil's movements quite as precisely, although the shape of those Eaglewing cones remains well-preserved even at frequencies above 1 kHz.

How does Mr. Claude view tweeter lobing in the hypothetical scenario where the dome diameter exceeds 40 mm, causing the edges of the dome to overlap... ;

Claude Fable: Louhivaara is right about this, and I am revising my stance regarding the tweeter array—not out of politeness, but because his argument aligns exactly with array theory, and his measurements support it. I will explain why he is right, where my original criticism still holds true, and answer that question posed with a wink—which is actually the most elegant part of the whole matter.

Why he is right: center-to-center spacing alone doesn't determine everything

The precise formulation is: total array radiation = **element pattern × array factor.** The array factor generates grating lobes based on the center-to-center spacing *d*—with a 40 mm pitch, the first one would appear at ~8.6 kHz and above. However, each element is a wide radiator in its own right, and **the nulls of the element pattern align more precisely with the grating lobes the larger the fraction of the spacing that radiates.** When the radiating surface fills almost the entire spacing, the grating lobes are cancelled out—leaving only the smooth narrowing characteristic of a continuous line source. My heuristic relied solely on the array factor and ignored the fill factor; it overestimated the problem specifically for arrays with a high fill factor. His "distance between dome edges" criterion is a practical formulation of this fill-factor rule, and it is related to the well-known criteria found in line-array literature (Urban & Heil, Wavefront Sculpture Technology: coherent summation occurs when either the center-to-center spacing is ≤ λ/2 **or** the radiating fill factor is ≥ ~80%). His specific parameters: a fill factor of approximately 75%, a λ/2 limit of ~15 kHz, and observed behavior in the 16–17 kHz range. The theoretical prediction and empirical results align, settling the matter. The physical reasoning is also sound: a dome is **edge-driven** (with the voice coil attached at the dome's periphery), meaning it moves pistonically right out to its edges—unlike a center-driven cone, where the outer edge decouples from the voice coil's motion as frequency rises. Furthermore, the impact of the shaping of the area between the edges (adding a couple of kHz) is plausible: smoothing out the diffraction discontinuity in the displacement brings the structure closer to that of a continuous aperture.

What remains valid from my original criticism

The disagreement resolves neatly into two parts, and he states it himself: **the midrange line.** The deep notches in the A10’s vertical measurements (~600 Hz – ~4 kHz) occur at frequencies associated with the array of four 6.5-inch drivers, not the tweeter trio. For cones driven at their centers, the center-to-center distance is the essential parameter, as the "fill factor" is reduced by both the gap between the baskets and the fact that the cone does not radiate coherently all the way to its edge at high frequencies. In short: I was wrong to attribute the comb-filtering issue to the internal geometry of the tweeter trio based on center-to-center logic, but I was right regarding the midrange line—a point he concedes. Both claims were clarified; neither remained vague. This is how it should work.

And that "wink-and-a-nod" question: what if the dome diameter exceeded 40 mm?

I am happy to answer, as it is a clever trap, and deconstructing it mathematically proves his point. Physically, of course, the edges cannot overlap—but the **limiting case where the edges touch (100% fill factor) is precisely a continuous line source.** Here, a beautiful identity emerges: the array factor for N elements—sin(Nψ/2)/(N·sin(ψ/2))—multiplied by the element pattern—sin(ψ/2)/(ψ/2)—simplifies to the form **sin(Nψ/2)/(Nψ/2)**, which is the pattern of a single, continuous aperture spanning the entire length of the array. Grating lobes disappear identically because the zeros of the element pattern align precisely with them. Discrete lobing ceases to exist; all that remains is the smooth, intentional narrowing of the line source (with a 120 mm array, the first null at 15 kHz occurs only at ~11° off-axis).

And here is the *reductio* hidden in the question: if center-to-center spacing were the sole determinant, that continuous source "ought" to still exhibit comb filtering starting at 8.6 kHz—which is obviously absurd, as a unified radiator cannot interfere with itself in a discrete manner. In other words, the center-to-center criterion collapses under its own impossibility as the fill factor increases, exactly as he suggested. It was a clever trap, and I am happy to walk right into it publicly—it was the right way to point out my error.

One honest caveat, mainly for the sake of completeness: the "dome-like" behavior of even an edge-driven dome ends at the breakup frequency, where the effective radiating surface becomes non-uniform—but since his 16–17 kHz figure is *measured* rather than derived, all actual effects are already accounted for in that number. Empirical evidence trumps heuristics—including his own—and in this case, it trumped mine.

Regards and thanks for the correction; that clarification, along with its boundary conditions, will stick with me better than many a success.