"Theoretical" relation between directivity and FR?

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Is there a "theoretical" relation between directivity and FR?

What FR (drop) to tune for in listening position, given that "HiFi" is desired, when the speaker directivity is given - say, for a 3 meter listening triangle?

How do room properties influence this?

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Oh, long debate... and I usualy don't visit this side of the forum

But here you go...

You may want to start with reading these 2 papers, easily found

"Directivity in Loudspeaker Systems" (white paper by Dr. Earl Geddes, GedLee LLC)

"Setup of Controlled-Directivity Waveguide Speakers" (Oct. 2012)

Have fun

Claude
 
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As of me, I have a pair of quite directive Klipsch in my secondary system, and given wall reflexions, FR at listening position, and personal preference at listening position I angle them the way... I like them best.

It is funny to see that the Klipsch, following one of the papers I refered you to, sound IMHO best angled at the listener (classic monitor positioning), in my case they even "cross" say 50cm in front of me as explained in the last paper and it works great, so are quite angled and that's the way we positioned them aswell at friend's... whereas my Infinity Renaissance speakers in my main system definitively don't like "toe in" and are nearly positioned parallel (OK, just a vey few degrees inwards to avoid unnecessary additional sidewall bouncing).

And in both cases, despite manufacturer's recommendation, I have quite more listening distance than distance between the speakers, and that despite 3m ish between them...

Short answer to your post: there is no ideal theoretical position (unless you have tons of measures and even then)... too many factors... and at the end eventhough you would have the equipment to measure your perfect HIFI FR it is very unlikely it would be the most enjoyable one to you. Refer to Toole and others re perfect response as perceived by listeners... we hear as much with our ears as with our brain and have quite an ability to hear, so despite being an engineer I have learned to take measurements for just what they are...

Just my 2ps

I am out... have fun experimenting!

Claude