I owned a blue and gold macaw that passed away and I own one now (her name is Gabby). Gabby is a femaie B&G macaw and the other macaw was a male. I can tell you Gabby does not scream throughout the day. She may scream once every couple of weeks if she really, really wants attention and I don't give it to her, but only for about 2 seconds. My macaw that passed away did not scream either. They both screamed when I first brought them home, but with training and a lot of patience they became extremely quiet birds.
When Gabby wants attention, she climbs onto the door of the cage and says "hello" a couple of times. If I don't respond immediately then she moves on to "pickaboo", "hi", "i love you" or "beshito" (spanish for "kissy"). If I don't respond to any of that, she usually goes back to playing with her toys. She always has toys in her cage. She is never without toys. Once in a blue moon, if she's calling for me and I leave the room she screams for maybe 2 seconds and then stays quiet for a little bit. Then she starts saying "hello" again.
I really do believe that all birds can be trained to be quiet. My main focus when I get a new bird is to train it to be quiet. You have to be consistent with your training and it never ends. You can't just train it for two months and then think she will be quiet for the rest of her life. You have to set the rules and stick with them. The bird needs to know that if she screams, she will not get any attention from you.
I posted a comment on another thread how I trained them. You can find this all over the internet:
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