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Specifically discussing Omnidirectional speakers:
"The dominant sound energy and perceptions are attributable to the direct sound and the first reflections from walls, floor and ceiling (horizontal and vertical planes) - all other reflections travel much farther and encounter multiple reflecting surfaces. So, it is not necessary to have "true" omnidirectIonality, a point source, even though it is a popular theoretical, academic, concept. The question is "how close to the direct sound must the off-axis sounds be?"
"A truly omnidirectional speaker radiating a flat direct sound would exhibit flat sound power and a "flattish" room curve. There would inevitably be a small downward tilt because of air absorption, absorption at room boundaries and furnishings that tend to be a higher frequencies."
"Harman sells monitor loudspeakers to music and movie studios, and to consumers ... you will see that in order to minimize the influence of the "circle of confusion" and thereby have any hope of delivering the "art" as it was created, one needs similar loudspeakers everywhere. I know of no recording facility that uses multidirectional loudspeakers."
"They exist in homes, I believe, mainly in an attempt to improve on the spatial limitations of stereo. They are contraindicated for multichannel installations."
"However, I long ago decided that multichannel upmixing was a more rewarding way to embellish stereo. It is adjustable, and it can be turned off. A permanent form of embellishment, as in a loudspeaker design, cannot work for all recordings."
My interpretation of the above (and other Toole writings on loudspeaker directivity) is that he believes that omnidirectional loudspeakers are an excellent choice for two-speaker stereo reproduction (as they enhance perceived spaciousness) but a poor choice for multichannel reproduction (as the spatial cues already contained in multichannel recordings are actually diminished by too many/too strong reflections).