As far as I know, the first signs of a pre-recorded announcement system on the subway started onboard the R44s with the door closing chime? Then for all subsequent models, they had that chime until NTTs with proper recorded announcements. Just curious, is that chime played from a piano? It really sounds like it is. I tried to replicate it on an actual piano but I just can't seem to find the correct note to get the pitches right, though I could get the general tune of it. Then what about those screwed up chimes in some of the cars? Are they another recording altogether or its speaker problem? They sound very funny when I watched those videos on Youtube. 
So to play such a chime, does the conductor press the door close button which activates it at the same time? He would have two door close buttons to press right? One for the cars on his left and the other for cars on his right. Which is the button to press to only open one leaf of the door? Why would they only open one side?
For your NTTs, do conductors still press buttons to activate 'Stand Clear of the Closing Doors please'? I guess for NTTs there're 3 buttons to press at every station: 1 for that announcement, 1 to close first half of train and 1 to close second half of train? When the train's at the station, can the computer automatically play the 'This is a Manhattan bound 
train' route info announcement automatically once they detect the doors have been opened? How about 'This is the last stop on this train' or other general announcements like the 'Keep your belongings safe...'?
For other announcements especially for the arrivals, is there some unit in the cab that can manage the triggering of the announcements? Do you have special equipment laid trackside such that when the wheel goes over it or passes it the equipment will send a signal to the unit to play the arrival announcement in the cars? Or is it thru distance by wheel revolution?
Well back in Singapore we don't have announcement related equipment on the tracks. For our 2 oldest lines(only lines with a driver at front), we have a unit in the cab called the Automatic Train Information System (ATIS) that plays announcements and updates our strip maps based on how many revolutions the train wheels make. From there, the ATIS will constantly update the distance from the previous station and when it passes a certain distance, the next station announcement plays. Throughout the journey, the ATIS will always update itself on the train's distance from stations so once the train passes a certain distance from the next station, the arrival announcement plays. To play any delay announcements, the driver can manually scroll through the various recordings on the ATIS to play the announcement of his choice. The downside to this is that when it rains and rails are slippery, the wheels can lose traction so the turning of the wheels cant be tracked properly leading to early or late announcement playing. I'm not sure how the system can be re-calibrated but its usually done when the train's dwelling at a station. For Doors Closing announcement, there is a button in the cab to press to play it. Then the driver presses the Door Close button.
ATIS is really like an in-train music player. Whatever announcement you want to play, you can scroll through the list to play it. ATIS even has 'playlists' too. They're called routes. These routes are basically the playlist of announcements that are going to be played for the entire route once ATIS is triggered to do so. At the terminus, the driver will always preset the route to prepare for his return journey back to the other end. Thus for 1 line, there's a minimum of 2 routes. One per direction. There can be more routes within one line with additional announcements in the extra playlists for the peak hours only. These routes are all pre-imported into the system and will be updated by the depot staff when needed to.
If I link this back to the NTTs, my question would be something like whether the driver will preset the computer to play the playlist containing all the announcements a 
Bronx bound train would make then once it reaches Woodlawn, the driver will preset again to play the playlist a train would make for the return journey to Brooklyn. At the same time, I guess your ATIS will set the strip maps or FIND to show the correct information and update it at the same time right?