My daughter did more of a roller coaster whiney noise that went from loud to quiet over and over and over for a long time. The thing that was most irritating about it is that she'd do a few dragged out quiet moans and then kick it into high gear for shock effect. Very grating on the nerves; it made me jump every time. On her first day of daycare they brought her to me and said..."You need to eliminate the roller coaster cry."
If you feel punished by the screetch...she is probably doing it on purpose to punish you. My daughter was an only child until she was 11, and thing with the whining, crying, moaning, and high pitch screaming didn't really effect anyone around her. Like, she wasn't told, "You can't do that right now... baby sister is sleeping." She had no reason to have consideration for other people.
I ignored it a lot so she'd drag it out, on and on, on and on. We spent a lot of our days with her crying through everything. I learned to not let the punishment effect me, but I did get concerned when she was hurting other peoples ears. It was just mean. And she had to learn consideration for others and just to put a stop to her selfish fits.
There came a time to address it directly and show some sort of response to it. She needed to learn how to "stuff it" and just get on with the day moving on to happier times. She needed to learn the self control to not unleash the noise. She needed to learn respect for other peoples ears and the pain they experienced. I had to respond. But, it became a habit.
Each time she did it, as a baby, I would close my eyes, turn her body away from me, and put her on the floor belly down. She'd continue. As she got older, I would tell her to go in her room and scream it into a pillow. In public, I would actually hold my hand over her mouth, head up against my chest, and speak sturnly into her ear, "You are not going to hurt these people's ears with your scream." She could breathe. We'd do that till she was done. Consider it a body hold to calm the child down. As a pre-teen, she would walk herself to her room, slam the door, and moan (like a cow) so loud as if to try and tell me how upset she was. Again, I'd say..."You stay in there. I will not allow you to hurt my ears." It's not about emotions, it's about control...and the pain hurts just as much as them slapping you. It's on purpose.
So, throughout the years, I've kept the focus on that purpose so as to not feed into it, ask questions, and drag it out any further. I just hold her accountable for what she's trying to do. Hurt me because she's hurting.
Now, as a more mature teen (sophmore and a very good girl)those episodes are few and far between. She's learned to just be grouchy, snippy, and crabby most of the time -expressing herself more consistantly and in more of a "normal" way. It's much more tolerable to live with a little venom leaking out all the time, than getting the big bites.
So, I don't know: ignoring vs. responding to it in an intense way... you never know what works. But, as long as you are a mom who is trying, she'll grow up & out of it just fine.