DDF
Addicted to Fun and Learning
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The significant frequency response drop outside the axial frequency response, for frequencies above 5kHz, leads to a drop in the sound power frequency response and must therefore be compensated by increasing the axial frequency response.
The direct response dominates timbre at high frequencies, much more than the "room". Toole's and Olive's studies reflect this by their recommendation to eq the room response in the bass, more so the on axis at higher frequencies. MLSSA's perceptual FFT window follows this logic as well.
I've designed many speakers since the 90s, and find that some on-off axis amplitude trading is necessary even around tweeter crossover (most DIY speakers miss this). IME and based on the research, trying this >5 kHz never really sounds neutral. I'd expect this to be bright on axis.
However, if the speaker is toed in so on axis is flat again, this sort of EQ can sound really good. I've done this on a few speakers and it helps get rid of that dead sound that highly directional tweeters may have.
Simultaneously bright and dead sounds like a contradiction, but its not.