While it is true that there is no set volume for the verbal chant of the spell, both the definition and the real world common usage of chanting mean that it is typically shouted or sung. Just look at protests, religious ceremonies, etc. where chanting is done. It ain't quiet. Sometimes chanting is done atypically in a normal tone of voice, but that's rare. What chanting isn't ever, is in a low voice or whisper.
So DM's can vary the volume, but if they are going by what chanting means, it would be fairly easily heard.