Your solution involves knowing what my "desired tonality" is! At this point, I can only listen to speakers and say "I like them" or "I don't like them". Occasionally, I might be able to pin down a few specific reasons.
Also, the things I am looking for often cannot be described in terms of tone, but only in subjective terms like "clarity" or "imaging"
Using my current speakers as examples:
The S30s have some of the most precise imaging I have heard. Soundstage is wide and deep, but lacks height. Vocals and acoustic instruments sound very lifelike, but electric guitar sounds a bit weak. Bass extension is limited, but what there is is exceptionally well-defined. Overall detail is extremely good, especially on complex percussion. Dynamics are good, but not great. As an added bonus, there is a tremendous "wow factor" in hearing so much sound from such tiny cabinets.
The Primuses have very deep, powerful bass, but it can be a tad muddy at times. Soundstage is reasonably deep and wide (though not as much so as the S30s), while height is much better than the S30s. Electric gutars have plenty of bite, and vocals and acoustic instruments are fairly natural, but sometimes exhibit a slightly boxy character. Overall detail is fairly good, but there are subleties I hear on the S30s that I miss on these. Dynamics are right up there with a live concert. No "wow factor" because one expects a big sound from cabinets this size.