..and following bdp24’s suggesting to google beaming characteristics, I continued my previous discussion with chatgpt.  It seems to ring true, however bdp24 would be a better referee. @bpd24 if any of the A-i info is incorrect..let me know and I’ll delete/correct it. No point in publishing poor info.

Also..the sections where formulas are presented don’t transfer well. I’ll try to replace these with images. If you see the formulas garbled, I haven’t replaced them yet with images. 

The re are two discussion sections with regard to the speaker crossover axis at or behind the listener or in front of the listener. This isn’t an option for me at least, however the logic is useful to read/understand. 

There are a couple questions asked of chatgpt. The first is a general question, the second is more detailed discussion.

Note, as bdp24 has stated, (now in chatgpt-speak..and my takeaway) A radiating surface becomes directional (beams) when its radiating dimension is on the order of the wavelength it’s reproducing. So, in basic terms, the midrange transducer isn’t beaming when the frequencies are low..200Hz, 500Hz..etc though progressively beam to a greater extent as frequencies rise up to the limit at the crossover frequency of 10,000hz, where beaming is very apparent. 

 

ChatGPT basic discussion start: 

Give me an explanation of driver and linear field transducer size to resulting beaming characteristics.

answer:

You’re absolutely right—driver size vs wavelength → dispersion (beaming) is the lens that makes your LFT-8b setup “click.”

Let’s tie the physics directly to what you’re hearing and why crossing in front works with mid-inside / tweeter-outside.

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🧠 The governing rule

A radiating surface becomes directional (beams) when its radiating dimension is on the order of the wavelength it’s reproducing.

• As frequency ↑, wavelength ↓ → more beaming for a given size

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📏 What that means for the LFT panels

1) Tweeter panel (narrow)

• Small lateral width

• Stays relatively wide dispersion through most of the treble, then narrows only at the very top

Implication:
Off-axis, you still get a lot of tweeter energy.

---

2) Midrange panel (much wider)

• Significantly larger lateral dimension

• Starts to beam earlier (lower frequency) in the crossover region

Implication:
Off-axis, the midrange falls off faster than the tweeter.

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🎯 The consequence at the listening seat

Because the panels are side-by-side, your ears are never equidistant/on-axis to both at the same time.

So at your seat you’re hearing:

• Midrange: more directional, angle-sensitive

• Tweeter: less directional, fills the room more

👉 That mismatch creates:

• Phase shift (arrival time difference)

• Amplitude mismatch (one driver louder than the other at your angle)

• → comb filtering in the crossover band

---

🔀 Why orientation matters (what you discovered)

Midrange INSIDE (what you switched to)

• Mid panels closer together → stronger, more coherent center

• Tweeters farther apart → wider HF spread

But now:

• Each ear is slightly more off-axis to the mid

• While still getting plenty of tweeter

👉 This can actually improve integration, because:

• The mid’s beaming is “tamed” by slight off-axis listening

• The tweeter fills in smoothly

That’s why your sound got:

• Denser

• More stable

• Better imaged

---

🎯 Now the crucial part: toe-in = dispersion matching

Toe-in is doing two things at once:

1) Changing arrival time (phase)

• Small distance differences between panels

2) Changing relative dispersion

• How on-axis you are to each driver

---

🟢 Why crossing in front works (this is the key insight)

When you toe-in so axes cross in front of you:

Geometry effect:

• You become slightly off-axis to both speakers

• But:

  • Midrange (which beams more) is brought closer to its main lobe

  • Tweeter (wider dispersion) stays strong

Result:

👉 Better amplitude match in the crossover region

AND

👉 Reduced phase audibility (less comb filtering)

---

🎧 What you hear when dispersion matches

When mid and tweeter “agree”:

• No dip or peak around crossover

• Vocals become solid and continuous

• Treble doesn’t “sit on top” of the sound

• Snare = body (mid) + snap (tweeter) at the same instant

👉 The system sounds like one driver, not two

---

⚠️ What happens at wrong toe-in

Too little toe-in (axes behind you)

• You’re very off-axis to mid → it drops too much

• Tweeter dominates

👉 Sound:

• Thin upper mids

• Wide but vague

• Slight “hole” in presence region

---

Too much toe-in (axes far in front)

• You’re too on-axis to tweeter

• Mid/tweeter balance shifts again

👉 Sound:

• Bright / etched

• Narrow stage

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🧠 The deeper takeaway

This isn’t really about “phase” in the strict sense.

👉 It’s about matching dispersion + timing in the crossover region

Because:

• Phase problems are most audible when amplitudes are similar

• If dispersion is mismatched, phase artifacts become obvious

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🧾 Final mental model

• Mid panel = flashlight (narrow beam)

• Tweeter = lantern (wide spread)

Toe-in = aiming the flashlight so it overlaps the lantern at your ears

👉 When overlap is right:

• No holes

• No glare

• Just one coherent source

---

✅ Bottom line for your setup

With:

• Midrange inside

• Tweeters outside

👉 Best result usually comes from:
Axes crossing slightly in front of you

Because it:

• Compensates for mid beaming

• Keeps tweeter energy smooth

• Minimizes audible comb filtering

---

If you want, I can estimate the exact toe-in angle based on your speaker spacing and listening distance—that lets you get very close without trial and error.

ChatGPT second question, more detailed:

ok, lets try again. The LFT-8b or LFT-8c has a 3-way crossover at frequencies 180Hz and 10,000Hz. The midrange transducer is 3.5 inches wide. The tweeter transducer is 0.375 inches wide. There is 3.5 inches of space (midrange outside edge to tweeter inside edge) between the midrange and tweeter transducer. The midrange transducers are on the inside relative to the listener position.  Please explain the transducer beaming characteristics with respect to speaker toe in (toward listener), minimizing comb filtering and optimizing the speaker presentation of soundstage, imaging..etc. First discuss a constraint of the speaker axis crossing at or behind the listener position and then discuss why the axis crossing in front of the listener might be optimal. 

Answer:

Great—now we can pin this down quantitatively and tie it directly to what you hear from the Eminent Technology LFT-8b.

---

🧠 1) The numbers → what they imply

Given

• Mid width (D_m approx 3.5")

• Tweeter width (D_t approx 0.375")

• Gap (mid outer edge → tweeter inner edge) (= 3.5")
  ⇒ center–center spacing (s approx 3.5 + 1.75 + 0.1875 approx 5.44")

• Mid–tweet crossover (f_x approx 10, ext{kHz})

---

🎯 2) Beaming at the crossover

A radiator beams once (D gtrsim lambda).

• Mid (3.5") ≈ 2.6 λ → strongly directional

• Tweeter (0.375") ≈ 0.28 λ → very wide

👉 At ~10 kHz:

• Mid = narrow “flashlight”

• Tweeter = wide “lantern”

---

🧩 3) Spacing → lobing / comb filtering

👉 Very tight angular structure: small changes in listening angle (or toe-in) move you between lobes and nulls in the crossover band.

---

🧠 4) What toe-in actually controls

Toe-in changes two coupled things:

1. Amplitude balance via dispersion

• Mid falls off quickly off-axis

• Tweeter falls off slowly

2. Which lobe you sit in (phase pattern)

• With (s sim 4lambda), moving a few degrees shifts you across peaks/nulls

👉 You’re not “fixing phase”; you’re choosing a lobe where the two drivers sum smoothly and their levels match.

---

🔵 PART A — Constraining axes to cross at or behind the listener

A1) On-axis (axes meet at your head)

Geometry

• You’re near the acoustic axis of both panels

Dispersion

• Mid: maximum output (you’re in its narrow beam)

• Tweeter: also strong (it’s wide anyway)

Interference

• Because both are strong and (s) is large, lobing is fully expressed

• You’re likely sitting near a rapidly varying lobe/partial null structure around 5–12 kHz

What you hear

• Very high apparent detail

• But:

  • etch / glare in upper mids

  • small head movements change tone (classic comb filtering)

  • image can be “hyper-outlined” but not stable

👉 On-axis maximizes information and the audibility of the interference pattern.

---

A2) Axes cross behind you (reduced toe-in)

Geometry

• You move off-axis, especially relative to the mid (which beams)

Dispersion balance

• Mid: drops quickly

• Tweeter: stays strong

Interference

• Reduced, because the two sources are no longer equal in level

• You’re effectively “de-weighting” the mid in the crossover band

What you hear

• Smoother, less edgy

• Larger, more relaxed stage

• But:

  • presence region thins (mid < tweeter)

  • center image loses density/lock

👉 You traded interference for imbalance.

---

Best within this constraint:

A slight toe-out from on-axis—just enough to take the edge off, but before the mid loses body. That’s the point where:

• lobing is a bit less exposed

• mid/tweet levels are still reasonably matched

---

🟢 PART B — Why crossing in front often works best

Now allow axes to cross in front of you.

What changes

Because your mids are inside and tweeters outside:

• Toe-in puts you:

  • closer to mid axis (keeps mid strong)

  • slightly off tweeter axis (trims tweeter a bit)

👉 This intentionally counteracts the natural dispersion mismatch.

---

Combined effect

1) Amplitude matching

• Mid (narrow) stays strong

• Tweeter (wide) is gently reduced
  → Levels become closer in the crossover band

2) Lobe steering

• With (s sim 4lambda), the main lobe direction is angle-dependent

• Crossing in front steers a smoother summation lobe toward your seat and pushes sharper nulls off to the sides

---

What you hear

• Crossover “disappears” (no dip/edge)

• Center image densifies and locks

• Stage is wide and focused

• Treble integrates (no “HF halo” separate from mids)

👉 You’ve aligned dispersion + lobe direction at the listening seat.

---

🧠 The unifying picture

• Mid (3.5") is already beaming at 10 kHz

• Tweeter (0.375") is not

• Spacing (~5.4") is several wavelengths → strong lateral lobing

Therefore you must use angle to:

1. Match amplitudes (dispersion)

2. Choose a favorable lobe (interference geometry)

• On-axis: correct levels, wrong lobe (too much interference)

• Behind: smoother lobe exposure, wrong levels (mid too weak)

• In front: best compromise—levels matched and lobe aimed at you

---

🧾 Bottom line

Within your exact geometry:

• You can’t eliminate comb filtering

• You can only place yourself in the least offensive part of the interference pattern while keeping levels balanced

👉 Constraining to at/behind:

• Aim for just-off on-axis (slight toe-out)

👉 Allowing in-front crossing:

• You can simultaneously:

  • tame tweeter excess

  • keep mid energy

  • steer a smoother lobe to your ears

→ That’s why it often sounds clearly “right” when you hit it.

FWIW...I have my LFT-8b axes crossing about 2-3 feet (hard to estimate unless I get really anal about measuring it) behind my head (where there is open space as I’m sitting on the open side of a balcony). The ChatGPT discussion suggests a steeper increase or decline in sound quality than I actually hear..it’s more of a gently slope.  I did notice the toe in increments I mentioned above (yesterday)..so it is somewhat sensitive, but the changes are fairly minor. The key is to get in the right ballpark and then fine tune, like any other setup. 

@douglas_schroeder 

The LFT-8 series imo is as great, and perhaps even greater gift to budget audiophiles than Magnepan or Vandersteen. I have owned all 3 brands through the years. 

I listened to the Maggie 2.7i at the Florida Audio Show in Feb, and the 1.7x at Axpona.  Neither speaker was anywhere close to the quality of sound from my LFT-8b's  The 2.7i sounded very clean, but very thin. I couldn't believe it so I visited the roon twice with about 2 hrs in between. Sounded the same. The 1.7x..meh. I hung around long enough to hear a couple tracks..nope, not even close to the LFTs. 

FWIW#2

When I had the LFTs on axis to the listening position..it was pretty intense. The center was focused, but overall it was just too much as compared to listening off-axis. As @ledoux1238 will probably attest, significantly off axis listening still sounds really, really good, but there's always tweaks that can improve on things. 

..and to continue the deep dive (while I noticed one inconsistent statement in GPT's presentation, it didn't veer off course.  I think it's doing ok)

It seems the constructive and destructive frequency interference lobes are located 7 degrees apart. I'm not sure I understand the rotating lobes discussion on having the axis cross in front..

ChatGPT question to expand on transducer lobing: 

Generate a true polar plot with actual curved radiation patterns and summed response

answer:

Here’s a true polar plot showing:

• Midrange (narrow beam)

• Tweeter (wide beam)

• Combined response with interference lobes

for your Eminent Technology LFT-8b geometry at ~10 kHz.

---

🧠 How to read this plot

• 0° (right side) = straight ahead / on-axis

• Angles sweep outward left/right from that

• Radius = relative output level

---

🎯 What the plot is telling you

1. Midrange (blue curve)

• Tight, focused lobe

• Falls off quickly with angle
  👉 Confirms strong beaming

---

2. Tweeter (orange curve)

• Much wider radiation

• Stays strong far off-axis
  👉 Confirms broad dispersion

---

3. Combined response (green curve) — THIS is the key

You can clearly see:

🔹 Multiple lobes (peaks)

• Where mid + tweeter sum constructively

🔹 Deep nulls (dips)

• Where they cancel (comb filtering)

---

🔥 Critical observation

Look how:

• The main lobe is very narrow

• Side lobes appear just a few degrees away

👉 That matches the earlier math:

~7° spacing between peak and null

---

🎧 Now connect this to toe-in

🔴 On-axis (0°)

• You are sitting right in the central lobe structure

• Also near rapid lobe/null transitions

👉 Result:

• maximum detail

• but unstable / etched sound

---

🔵 Behind-axis (a few degrees off)

• You move into:

  • a smaller lobe

  • or between lobes

👉 Result:

• smoother

• but reduced energy / weaker mid

---

🟢 In-front crossing (ideal case)

What you’re doing:

👉 Rotating this entire green lobe pattern

So that:

• one clean main lobe is aimed at your ears

• the deep nulls shift off to the sides

---

🧠 The real insight (this is the “aha” moment)

This graph shows:

You are NOT aligning drivers
You are choosing which lobe your head sits in

---

🎯 Why crossing in front works

Because it:

• Keeps you inside a strong, smooth lobe

• Moves:

  • sharp nulls

  • rapid fluctuations

…away from your listening position

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🧾 Final takeaway

• Your speaker behaves like a multi-lobed radiator at the crossover

• Toe-in = steering this lobe pattern

Best sound happens when:

• Your ears sit inside a single dominant lobe

• Not on a slope or near a null

---

If you want, I can extend this to:

• 8 kHz and 6 kHz plots (you’ll see the lobes widen)

• OR simulate your exact listening distance + toe-in angle to predict the sweet spot numerically