Tuning typically follows a little ritual, where (1) the concertmaster stands to indicate that tuning should begin, (2) the oboe gives the 440 Hz A tone, which by the way, they normally have an electronic tuner these days to help them nail that pitch, (3) the brass and winds tune off the oboe, (4) the concertmaster tunes her violin off the oboe, (5) the concertmaster plays the A for the strings, who tune their open A string off that note, (6) the strings tune their other three strings to their A, usually by ear.
Source: Me, playing in amateur orchestras for twenty-plus years.
Sidenote: I find the sound of an orchestra tuning to be a deep joy! All those instruments sliding into place is just delightful
As a regular orquestral concert goer (I would say I average a concert a week per year at least) reading your description of the tuning process gave me goosebumps.
It really is one of the best sounds on the world! The tension! The anticipation! And then seeing and hearing a well rehearsed group of people move from casual conversation mode into serious business mode in a few seconds. And from chaos comes order. And then the silence, only broken by the applause when the maestro and soloist(s) arrive.
I don't know if this is true - might just be a joke - but I've heard stories of people unfamiliar with Western classical music going to concerts and telling the people who brought them that they liked the "first part" of the music, their hosts thinking they meant the first movement or the piece that was played first, but they actually meant the tuning. See e.g. https://silpayamanant.wordpress.com/2013/11/06/if-you-apprec....
It seems like the story is usually told about an "Indian musician" and something similar happened in reverse at a Ravi Shankar concert, where the Western audience applauded after he tuned.
This is the best description of orchestra tuning I've ever read. I've always wondered what gives it that specific sound of everything coming into place with relative consistency across orchestras, but didn't really know the mechanics of it. Thank you.
Addendum: some orchestras tune to a slightly different A (442 Hz is common I think), and the oboe player often gives a B-flat as well for those instruments where that's more natural.
Source: Me, playing in amateur orchestras for twenty-plus years.
Sidenote: I find the sound of an orchestra tuning to be a deep joy! All those instruments sliding into place is just delightful