But If an audio recording is mixed and encoded in stereo, it has mono information and sides information.
In a good time intensity trading setup, which requires more or less constant directivity in a range of ...
Once it is stereo it isn't mono, right? The question was, if some kind of mono can be derived from stereo, but you just state it as a given. Sounds circular to me, or tautological, if you will. Then directivity again, the universal adhesive to make every argument stick.
The tech/ of mono downmixing is fundamental to the "directivity" paradigm, not the other way round. Here's how it goes.
Which measurable parameters of a loudspeaker are essential for good sound reproduction? To determine these, loudspeakers should be listened to and evaluated using industrially produced, commonly used stereo recordings. A preference ranking is established, and a set of parameters is derived from it. This constitutes the modeling of “good.”
However, it turned out that the distinguishability of loudspeakers is greater when they operate as single units, i.e., in mono. Therefore, there is a need for a downmix from stereo to mono. Think about that … let it sink in and never forget anymore.
Interjection: Directivity is a parameter of “good,” meaning it is a consequence of the evaluation after downmixing from stereo to mono, not a prerequisite.
The question, then, is whether the sound balance resulting from a downmix from stereo to mono is suitable for ranking loudspeakers for the actual purpose of stereo listening. I would say: absolutely not**, unless there are strong arguments supporting the necessary equivalence. To my knowledge, proponents of mono evaluation have not provided a chain of conclusions trageting that topic.
I give the whole approach the benefit of the doubt. Ultimately, the model mentioned above confirms general standards that have long been implicitly established (after a painstaking period of trial and error). Namely, a nicely linear response on-axis, smooth, with a tilt in the diffuse field that results from even, non-abrupt omnidirectional radiation.
To lend some weight to this method, which would be rather untenable by strict standards, one could simply have assigned a limited number of sound engineers to produce mono recordings of everyday sounds, musical instruments, and speech. Well then, that would have cost money and required a defined program. Apparently, this effort was spared—the result of the standardization was simply plausible: a standard can be whatever already exists.
Now you adhere closely to the standard, emphasizing 'directivity' a tiny bit obsessively, but that's engineering on standards, less science. ASR => AER, audio engineering review? But I acknowledge that science is, in American English, often taken as a synonym for engineering.
** illustrative caveat: a signal having inverted phase in the two stereo channels would be clearly audible in stereo, but vanishes in a summing mono downmix; many microphone techniques, M/S and what have you, do that