My friend may work on that, I'll check with him.
You two would probably have fun talking shop. I've never seen someone who invests so much time with audio. It's his day job and it's also his hobby.
I wonder if it is beneficial to adjust directivity based around human ability to localize different frequency wavelengths and our preferences for reflections.
In this research paper on sound source localization they say,
At the same time, in Loudspeakers and Rooms for Sound Reproduction—A Scientific Review Floyd Toole said,
If someone likes increasing DI it might be because they want wide directivity in the range of hearing where sound source localization is in the 'gray zone' (derive the benefits Toole notes without sacrificing imaging) and they want narrow at higher frequencies where humans are able to sharply localize again.
However, I don't know if sheetrock walls absorb those high frequencies, meaning wide directivity at higher frequencies wouldn't matter very much anyway. Maybe in a normal room narrowing the high frequencies doesn't help because they don't reflect anyway. That's something I'm still trying to figure out.
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When talking about "early reflections" it is important to be clear on the timing. Greater than about 10 ms. and they are all good, but below that they degrade imaging. Toole and other acousticians usually mean > 10 ms. since in most larger spaces this is always the case. But in a home situation the VER (Very Early Reflections < 10 ms.) are an issue. This is precisely where Floyd and I disagreed, but he seems to have softened his position somewhat.
Early reflections like > 10 ms. do not degrade imaging (much.) But <10 ms. will. How this is determined is a long story told somewhere here at DIY. It has to do with looking at the impulse responses of gammatone filters - which emulate hearing. These get shorter and shorter with frequency so, say at 1 kHz the gammatone impulse response might be, say, 10 ms. long (guessing at the number right now) hence a reflection > 10 ms will not interfere with the direct sound. But everything below 1 kHz will and this will degrade our hearings ability to separate the direct from reflected sound. At > 20 ms it would be 500 Hz and 5 ms. would be 2 kHz. You get the idea.
I also have to say that the plot that is being shown is confusing to me because according to Blauert the mid frequency range has a high capability of resolving localization because the ears have both ITD and ILD cues at their disposal. The cues are not conflicting but enhance one another. Moore has stated 2 kHz as the point where our hearing is most acute.
Here's the link to the paper I got that image from. It's from 2018 so I thought it captured earlier work but maybe it didn't or -- far more likely -- maybe I misunderstood the paper.
Sound source localization - ScienceDirect
With consideration of Blauert's findings, I was thinking a loudspeaker with narrow directivity below 1,000Hz, wide directivity 1,000-3,000Hz, and then narrow again above 3,000Hz might resolve ok because we use broadband cues to localize. By controlling above and below the "inaccuracy area" (if that 2018 paper is right, and if I interpreted the paper correctly) you would control directivity in the frequency ranges that helped you resolve localization using the combination of ITD and ILD cues in a broadband signal.
Why not control the entire spectrum, including the "inaccuracy area"? I don't know, maybe that is the best way. The reason I started thinking about widening the "inaccuracy area" is that it appeared Toole -- if I understood him correctly, too -- said reflections improve clarity, specifically in the 2,000Hz interaural crosstalk cancellation dip he described in chapter 7.1.1 Problems With The Stereo Phantom Image. He said the reflections fill in what we miss and reduce the perception of the dip.
In the scope of this thread, that would make me lean toward waveguides designed to operate as you approach 3,000Hz. Or another option, a waveguide that works from 1,000Hz with the addition of >10ms delayed side channels that operate in the "inaccuracy area." But only if my understanding of Toole and the 2018 paper is accurate. And my understanding is the big weak link here.
Thanks, I see where that comes from now. I can also see that this is a dip that stems from the same issue that Floyd talks about for mono signals - a weak inter-aural-cross-correlation at about 2 kHz. I would guess this pretty narrow and it's hard for me to see if what you suggest would be better or worse. Remember those studies were not about loudspeaker imaging in a room, but were quite specific to single sources in open spaces.
But thanks, it was an interesting review of the latest thinking.
But thanks, it was an interesting review of the latest thinking.
Is this quote the reason you liked that paper?
I thought this might be a useful quote as well, it appears to be consistent with what I've read the loudspeaker directivity chapter of Floyd Toole's book in the sense that different types of music styles or program material benefit from different and possibly conflicting design choices.
Thanks for reviewing it and interpreting it for me in the context of loudspeaker imaging in rooms. Your response leads me to think it might be beneficial to take a modular approach to speakers based on what you said here:
https://www.diyaudio.com/forums/multi-way/103872-geddes-waveguides.html#post1237595
I mean a literal modular approach. Multi-subs, Low-mid section 200Hz to 1,000Hz, then a separate mid-high section above 1,000Hz. The mid-high section could be swapped out based on listening material.
There is one correct answer to room modes, pretty much one correct answer to low-mid and it's forgiving anyway, but the 1,000Hz up section has more than one answer and is least forgiving.
I wouldn't overstate 'forgiving', in the 200-1k region. It is relative, and the magnitude of what you can get away with has to be in perspective with the expectations of the system.
Therefore it is one thing to say I'll let a crossover fall within this region.. and another to abuse it. It is not without challenge to get good results here given the nature of the modes and various practical issues.
Therefore it is one thing to say I'll let a crossover fall within this region.. and another to abuse it. It is not without challenge to get good results here given the nature of the modes and various practical issues.