Pulsating Static and Marching Soldiers?

Can pulsatile tinnitus come and go? Can it sound like pulsating static noise?

I normally have a mild tonal tinnitus, in either one or both ears, but I sometimes get this sensation of pulsating static. It sounds a bit like shushing someone, like this quite "shshsh... shshsh... shshsh..." and it's usually in only one ear. Each shush sound lasts about 2 seconds, then it fades to silence for 1 second, and then there's another shush. It can go on like that for a few minutes, then it goes away, only to be replaced by a quite tonal ringing in the same or the opposite ear. Anyone had this experience?

I have also had a stumping kind of sound in my right ear. It's a bit soft or muffled, but has a sharp rise and decay, and is a oscillating faster than the shush sounds. It's like a number of soldiers marching on gravel. The shush sound seems to appear mostly in my left ear, which is my bad ear. The marching appears exclusively in my right ear, and I usually hear it at night when I put my head down on the pillow. It lasts for about 5 minutes and then goes away. Unlike that other sound, this one appears to be in sync with my heart beat.

How do you explain these sounds? If the second one is caused by my heart beat, what's the first one caused by? Why would I hear my own heart beat and only for a short time when I put my head down on a pillow?

Could these be related to my tonal tinnitus? I guess it's my pulsatile tinnitus telling my tonal tinnitus to shut up for once! They are fighting each other for my attention. I wish I had the power to tell them both to shut up, and keep it that way!