What is this term 'analytical' ?

A boosted treble/high frequency response giving the impression of detail at the expense of timbre and tonal contrasts.

It’s an old trick that often succeeds in gaining the listener’s attention.

Hi-Fi journalism is littered with such anecdotes as the following, " I’ve heard this track countless times but I’ve never noticed X or Y before."

The only place you might need this elevated response is in monitoring where you want to put a spotlight on possible issues especially in the so called presence/brilliance bands up to 9 kHz.

It is generally agreed that the industry favourite Sony MDR 7506 headphones employ this frequency response for exactly that purpose.

In domestic audio its a sure fire way to discover the dreaded listener fatigue.

I would say equipment having all the detail up to fault presenting music not as a whole but somehow independently. I would not confine it into highs region only and is rather a subjective term commonly not expressed in a positive manner. Some people can call it detail, accuracy, neutrality but these are softer expressions leading to analytical if in excess.

A system that emphasizes the details of music loosing midrange emphasis as well as rhythm and pace (think musicality / the emotional connection). So the tick of a drumstick against the cymbal is highlighted but voices are typically subdued. Typically a trait of  older and less expensive solid state (not tubed) audio gear. 

High end audio for those that care to pursue it has a very large vocabulary. It takes a lot of exposure to music and to the nomenclature to learn and connect the two. If you are interested, I recommend Robert Harley’s book The Complete Guide to High end Audio. This is an excellent place to start and a reference to reread occasionally.

Good thoughtful answers. Seems like it means what I might think of as bright, or top heavy.

Now if someone would tell me what 'musical' means, and how it's different...

Who knows the brilliant Mingus (I think) quote?

All together now: 'talking about music is like...' 

Too sterile. also, boring with no character....you want/need some warmth to make it more enjoyable over the long term. Too bright can be characterized as fatiguing and full of sharp ssss’s... That’s just my opinion. Musical in my book is if your tapping your foot.