Cat, that's a great question. Notation tries to take one medium, sound, and represent it for a different sense - sight. It's like trying to draw a heartbreak or taste a rose's perfume. So it can only have meaning for you if you already know the medium it's trying to capture... I mean, how can you accurately describe "red" to someone who's always been blind?
I often compare standard notation to theatrical scripts. Two different actors can say the exact same lines with completely different effect. The words are identical, but we get different emphasis, and we pick up other cues at the same time - our minds add meaning to the words based on gestures or facial expressions.
Music's got the same kind of stuff going on. Sound essentially has four elements: pitch, intensity, duration, and timbre. We can write pitch and duration pretty accurately (by the placement of notes on the staff and the types of notes used), but intensity is sort of like an actor's delivery - we can't really write it. We can try, by putting an instruction to the actor in a script (like "sarcastically" or "quizzically"), but we can't dictate the exact performance. The best we can do is relative terms, like forte or mezzopiano. Some modern composers have tried more precise representations of intensity, but all have failed so far.
Timbre is even more elusive, so it's kind of like those added facial expressions. We can use a technical instruction like "ponticello" (play it near the bridge) or an expressive one like "giocoso" (merry), but no two people will interpret it exactly the same way, and no one person will deliver it exactly the same in two successive performances.
As far as conducting goes, up until Berloz and Wagner, they pretty much beat time and left the interpretation to the musicians. Maybe they'd yell at them for playing an mf passage too loud, or slowing too much on a ritardando. Modern conducting, which is only about 150 years old, worries about balance too... a composer studies a score, imagines the performance, and then tries to get it out of the orchestra - getting the oboes to play a hair softer here, the third french horn to play a little sharper attack there, etc.
Here too they have problems. You're trying to tell somebody what's in your head. They'll never hear it in their head exactly like you do. (From experience, I can tell you that some of the sounds I hear in my head simply can't be done! As a student, I wrote a flute part that sounded gorgeous in my mind - and when I gave it to a flautist I learned it was impossible to play.)
Many of the best conductors recognize that problem, and use non-verbal communication. Last year a friend with the CSO told me about a rehearsal with Muti, their new conductor - he wasn't getting the sound he wanted, and simply said "no - watch me". He changed the motion of his wrist, and got a completely different tone from the orchestra as a result.
Oh yeah - one more point: what we call "phrasing" in music actually has nothing to do with sound, at least in my opinion. It's an effect of memory. Staccato notes and legato ones can have exactly the same wave shape - we experience staccato because we remember the brief silence that just happened; take away the silence and we experience legato. The same is true of ALL phrasing effects - a bend on a guitar is only heard as a bend because that pitch was something else a moment ago. As a result, I believe that developing a sense of "musicality" requires developing the memory required to keep an entire phrase in mind, and organize the momentary things we do to fit the image we have in our mind's ear.
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