Your vocal cords can engage in a wide variety of behaviors, far beyond just modulating pitch and volume. Most people speak in their modal voice, but some singers employ a falsetto voice, either full time or intermittently, for artistic effect (e.g. Bruce Springsteen in “I’m On Fire”). There’s even a whistle register, (think Mariah Carey at the top of her range) although from the description there it sounds like not everyone can hit that range.
There’s also the vocal fry register, which seems to be getting a lot of mention recently.
So the phenomenon I’m thinking of us a kind of growlling, rumbling sound at normal speaking or singing pitches. The two most prominent examples are Bobcat Goldthwait (during the 80’s) and Joe Cocker. For comedic effect, Goldthwait alternated between a timid/nervous voice and a manic, almost angry voice; it’s the latter sound I’m thinking of here. Joe Cocker goes in and out of that mode too. Here’s an example; listen to the sound of his voice from 0:57 to about 1:10. It’s intermittent, but seems to happen when he hits a concert G, the highest note in the chorus.
Actually, there’s a third example: Louis Armstrong exhibits it quite a bit in What a Wonderful World.
So…is there a name for that?