conductor turns into a windmill...one second flute or third trombone for example tries to keep up with him while the rest of the orchestra will pick up the pace by following the leaders reaction to these gestures. The result is a disaster.
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Music is about sound ...
I think that your last statement, music is about sound, is by far the most important when dealing with these very awkward moments.
Seeing the conductor panic should ideally not make the orchestra do likewise - he goes into windmill mode, ok, he's giving the signal to pick up the tempo. he's probably not wanting the tempo to suddenly jump to catch up with him, like a scratched cd, so it's up to the musicians to- very quickly- decide what to do, and somehow do it as a unit. these very difficult moments are where every musician in the orchestra is tested, and i find it really interesting to discuss.
It all happens in a few seconds but here's how i think about it in super slow-motion.
Seems as how the conductor's gestures in these first few moments really only indicate 'play faster, i'm panicking, help!', for me, the players must in the first place go with what is being played around them - putting their notes into the correct place as they (and the audience) hear/feel them. Otherwise the danger of random early entries is even further increased. At the same time they must remain very flexible and highly aware of signals coming from the within the orchestra (section leaders)
It is up to the leaders to start the forward motion, and bring their individual sections (hopefully) along. If the orchestra know the score enough, they'll know which section's entry are most important for setting the tempo, and the whole job becomes easier. (see how i brought that right back on topic? nice)
so yes, i think knowing the score is vital for the orchestra. This way a good orchestra will still sound like a good orchestra, even with a terrible conductor.
Also, as a general point, not knowing the full score of a piece you are playing as a soloist is terrible, but i think you really have to know whats going on in the orchestra too. if you just look at the bass part it's like looking at a painting but removing everything except shades of brown (or whatever other colour you like!)