Musical screaming is a type of singing, so the same methods you'd use to sound like Mariah Carey can also be used to sound like Oli Sykes.
Think of your respiratory tract as a whoopie cushion. Your lungs are large bags of air that when acted upon by an outside force push air through a tube. The larger this force is, the more air comes out, increasing volume. On a normal bag, this would be a hissing sound, but on a whoopie cushion there's a flap at the end vibrates, making a farting sound. That's the scream.
You can probably sing, but if you want the power behind your voice for screaming you need to learn how to use your diaphragm:
When singing you should be pushing the air out using only this muscle. Your abs should remain loose. This muscle at the base of your lungs will be doing all the work of pushing and pulling the air through your body. Add in vibration from your vocal chords and you have singing.
Now here's where the screaming comes in: the scratching noises need to come from the top of your throat, NOT your vocal chords. If your throat hurts, you're doing it wrong. Try impersonating Marge Simpson's sisters Patty and Selma: if you can match their raspy voices, you're using the right part of your throat. Add more power using your diaphragm, and you have a scream.
Posted 4233 day ago