@nogaps 

What  an inspirational series of posts, mind boggling!!!

I will be experimenting for sure, but are the dimensions to my speakers, in metric if you don’t mind: distance between speakers : 260 cm; distance to listener : 300 cm. 
 

I crunched numbers for a living, once upon a time. I've worked in most unit and coordinate systems out there, at one time or another. Metric is fine. I'll figure it out in the morning and get back to you. 

@ledoux1238 

Here you go.  I'll make two posts with different results as you say your between speaker distance is 260cm. I would think the calculation will be the most accurate if the between speaker distance was on-center on the panel face.  I'm guessing(?) your 260cm refers to the distance between the inside edges of the speaker. With the speakers(including trim) being about 13 inches (33cm) wide, the second post I'll make adds 33cm to your 260cm  to arrive at what I think may be your on-center distance between speakers. 

OK..this response is for 260cm on-center between speakers. 

ChatGPT question on listening triangle of 260cm x 300cm:

ok, i have a different room where I need toe-in angles. The distance between the speakers is 260cm (on center). The distance from the speaker face to the listener is 300cm. Please give the result in the same format as your last response above. Also please give the resulting toe-in angles in degrees and radians. 

Answer:

Perfect—same method, new room. Let’s run it cleanly.

---

🧠 Your new geometry

• Speaker spacing = 260 cm

• Listening distance = 300 cm

• Half-spacing = 130 cm

---

📐 1. Toe-in for axes crossing at your head (on-axis)

---

🎯 RESULT

👉 23.4° (0.408 rad) toe-in = speakers aimed directly at your head

This is your reference point.

---

🧠 Context (same physics as before)

• Your spacing vs distance is wider relative to listening distance than your previous room

• So:

  • Toe-in angle is smaller

  • But lobe sensitivity (~7° at 10 kHz) still applies

---

🔵 2. Axes crossing behind your head

Reduce toe-in slightly:

Practical range:

👉 20°–22°
👉 0.35–0.38 rad

---

What happens here

• Slightly off-axis to midrange

• Tweeter dominates a bit more

Result:

• smoother

• less comb filtering

• but:

  • softer center image

  • reduced vocal density

---

🟢 3. Axes crossing in front of your head

Increase toe-in beyond 23.4°:

Optimal range:

👉 25°–28°
👉 0.44–0.49 rad

---

Why this works

• Moves you out of 10 kHz null zones (~±7° spacing)

• Better aligns:

  • midrange beam

  • interference main lobe

---

🎯 Your exact “target zone”

👉 Best starting point: ~26° toe-in
👉 ≈ 0.45 rad

---

🎧 Fine-tuning window

• Adjust in ~1° increments

• Sweet spot likely:

👉 25°–27°
👉 0.44–0.47 rad

---

🧠 What you’ll hear when it’s right

• Dense, locked center image

• Smooth but present treble

• No “hole” in upper mids

• Speaker disappears

---

📊 Summary

 

---

🧾 Final answer

👉 Calculated toe-in (on-axis): 23.4° (0.408 rad)
👉 Optimal real-world toe-in: ~26° (≈0.45 rad)

---

 

OK..this is for 293cm between speakers on-center

ChatGPT question on 293 x 300 listener triangle:

ok, one more room where I need toe-in angles. The distance between the speakers is 293cm (on center). The distance from the speaker face to the listener is 300cm. Please give the result in the same format as your last response above. Also please give the resulting toe-in angles in degrees and radians. 

Answer:

Perfect—same process again, now with your wider spacing.

---

🧠 Your new geometry

• Speaker spacing = 293 cm

• Listening distance = 300 cm

• Half-spacing = 146.5 cm

---

📐 1. Toe-in for axes crossing at your head (on-axis)

---

🎯 RESULT

👉 26.0° (0.454 rad) toe-in = speakers aimed directly at your head

This is your reference point.

---

🧠 Context (important subtle shift)

Compared to your previous room:

• Speakers are wider relative to distance

• So:

  • Slightly more toe-in required

  • Greater sensitivity to small angle changes

👉 You’re getting closer to a wide triangle, which makes lobe alignment more critical.

---

🔵 2. Axes crossing behind your head

Reduce toe-in slightly:

Practical range:

👉 23°–25°
👉 0.40–0.44 rad

---

What happens here

• You move off the midrange beam

• Tweeter dominates slightly

Result:

• smoother

• less comb filtering

• but:

  • softer imaging

  • reduced presence energy

---

🟢 3. Axes crossing in front of your head

Increase toe-in beyond 26.0°:

Optimal range:

👉 27.5°–31°
👉 0.48–0.54 rad

---

Why this works

• Your wider spacing increases lobe steering sensitivity

• Extra toe-in:

  • pushes nulls outward

  • aligns main summation lobe with your ears

---

🎯 Your exact “target zone”

👉 Best starting point: ~28.5° toe-in
👉 ≈ 0.50 rad

---

🎧 Fine-tuning window

• Adjust in ~1° increments

👉 Likely sweet spot:

• 27.5°–29.5°

• 0.48–0.52 rad

---

🧠 What you’ll hear when it’s right

• Center image becomes very dense and stable

• Treble integrates cleanly (no edge, no dip)

• Strong sense of depth

• Speaker disappears

---

📊 Summary

 

---

🧾 Final answer

👉 Calculated toe-in (on-axis): 26.0° (0.454 rad)
👉 Optimal real-world toe-in: ~28.5° (≈0.50 rad)

---

 

...and for an update on my setup/toe-in tuning:

A few days ago, after swapping the left for right and right for left speakers to get the midrange panels on the inside, I played with toe-in and arrived at 21 degrees of toe-in as "good".  This was based on ears & listening alone. Sounded pretty good and was an improvement over the toe in I 'd set previously, which, guessing only, was probably in the 15ish degrees area. 

As a side-note..GPT states the speakers "disappear" when you have things set up right..well..I've had 9 months of "setting them up wrong" and they've always disappeared and sounded great, though some seat-of-the-pants setups were better than others. 

After the ChatGPT adventure yesterday and GPT suggesting my optimal toe-in for an axis crossover slightly behind my head was 24-26 degrees, I increased the toe in from 21 to 23 degrees.  It was an improvement, though things are getting pretty marginal with trying to distinguish improvements. 

Being a little anal..and that 24-26 degree "optimum" hanging out there like a big matzah ball..I made a further toe in adjustment to 24.5 degrees. I think I'm done & GPT may have gotten it right.  This is the best setup I've heard..and I've heard at least 6-8 with these speakers..and honestly, they all sounded great (except for direct axis on head..that was a little intense).