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
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Speaker spacing = 260 cm
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Listening distance = 300 cm
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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)
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Your spacing vs distance is wider relative to listening distance than your previous room
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So:
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Toe-in angle is smaller
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But lobe sensitivity (~7° at 10 kHz) still applies
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🔵 2. Axes crossing behind your head
Reduce toe-in slightly:
Practical range:
👉 20°–22°
👉 0.35–0.38 rad
What happens here
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Slightly off-axis to midrange
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Tweeter dominates a bit more
Result:
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smoother
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less comb filtering
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but:
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softer center image
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reduced vocal density
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🟢 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
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Moves you out of 10 kHz null zones (~±7° spacing)
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Better aligns:
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midrange beam
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interference main lobe
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🎯 Your exact “target zone”
👉 Best starting point: ~26° toe-in
👉 ≈ 0.45 rad
🎧 Fine-tuning window
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Adjust in ~1° increments
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Sweet spot likely:
👉 25°–27°
👉 0.44–0.47 rad
🧠 What you’ll hear when it’s right
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Dense, locked center image
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Smooth but present treble
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No “hole” in upper mids
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Speaker disappears
📊 Summary

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



