Thanks for the response.
Timbre
Timbre is harmonics (overtones), this is easily seen by inputting a signal and seeing what the FFT/distortion graph looks like. I personally believe that no gear should have timbre, it should only be transparent and accurately reproduce the timbre of the instruments in the recording. Of course most speakers have timbre, but any expensive solid-state amp, DAC, or preamp that is competent will not have audible distortion/timbre.
Texture of the sound
Not sure what this actually means, so no answer.
the presence or absence of easily heard vs buried microdynamics in a passage
This is how “quick” the gear is. This would be the impulse response and the spectral decay/energy-time curve.
imaging
For speakers, it’s how the off-axis frequency response is in relation to the on-axis. If you look at the Lateral response graph done by Stereophile, the Vivid Audio Giya G3 for instance have amazing imaging, even at 90° it’s almost identical (the soundstage is super wide too though, so room treatment would be recommended). For amps, DACs, and preamps, this is the channel separation (crosstalk), channel amplitude mismatch, and channel phase mismatch.
whether the music sounds natural
I’d say the more transparent the more natural, unless you are implying the recording themselves don’t sound natural. As I’ve said though, blind-studies have shown we pretty much all like the same things, but the factor of how much bass and treble we like is a tad different, the amount of bass an audio engineer likes (pretty much no boost) is much lower than the amount of bass the average joe off the street likes, which is about 6dB more. However, the preferences of a smooth frequency response with the best imaging, with low distortion/resonances, etc. can be treated as identical.
rhythmic
I’d say this is the same as microdynamics, unless your defitnion is different than mine.
engages one emotionally or is presented in a mechanical and metronomic fashion
Come on dude, what does this even mean? I bet playing Sinatra’s ‘My Way’ on my car’s setup to my NY Italian relatives would be more emotionally engaging than any demo song played on a pair of Revel Ultima Salon2’s being powered by MarkLevinson gear.
The one thing I can tell you, which is a fact, is that even if you picked one speaker as a winner in a double-blind listening test, no one can tell you if you will like it sighted, as the brand, looks, and price all are factors, even if we try to disregard them. One of the tests Toole did was compare some nice looking tower speakers to a bookshelf+sub system that was much cheaper and plastic, and once the reviewers could see the product, they actually rated the sound quality as being worse.
Since no one listens blind, this is why I always suggest in-home demos/trials, and too look for companies that allow you to do so without charging insane return/restocking fees. Doesn’t matter if it’s the “best” speaker in the world, if it’s from a no-name brand, is not expensive as you thought, and is ugly, you likely won’t buy it.