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

📏 What that means for the LFT panels
1) Tweeter panel (narrow)
Implication:
Off-axis, you still get a lot of tweeter energy.
2) Midrange panel (much wider)
Implication:
Off-axis, the midrange falls off faster than the tweeter.
🎯 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)
But now:
👉 This can actually improve integration, because:
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)
2) Changing relative dispersion
🟢 Why crossing in front works (this is the key insight)
When you toe-in so axes cross in front of you:
Geometry effect:
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)
👉 Sound:
Too much toe-in (axes far in front)
👉 Sound:
-
Bright / etched
-
Narrow stage
🧠 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
🧾 Final mental model
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).
👉 At ~10 kHz:
🧩 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:
-
Amplitude balance via dispersion
-
Which lobe you sit in (phase pattern)
👉 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
Dispersion
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
👉 On-axis maximizes information and the audibility of the interference pattern.
A2) Axes cross behind you (reduced toe-in)
Geometry
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
👉 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:
🟢 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:
👉 This intentionally counteracts the natural dispersion mismatch.
Combined effect
1) Amplitude matching
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
Therefore you must use angle to:
-
Match amplitudes (dispersion)
-
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:
👉 Constraining to at/behind:
👉 Allowing in-front crossing:
→ That’s why it often sounds clearly “right” when you hit it.