Sometimes you want to portray a situation or a person that is completely off the beaten path, something or somebody that doesn't really fall into any usual standards. That could certainly be a situation that an eccentric voice could come in very handy.
Although eccentric is used to describe a person, situation or a piece of art that is strange and/or unusual, it does not essentially have a negative connotation. It has to be something so specific, that it really stands out from the crowd. Very, often, the connotations of eccentric can be even humorous. Still the spectrum in which an eccentric voice could range from something just something unusual to weird or even abnormal.
The audience for an eccentric voice is very often tied to the one that has artistic connections or is inclined towards art and artistic expression. It is also often used in a humorous context, stand-up shows, TV programs and movies. Yet another use of an eccentric voice can be found in suspens films, particularly those with elements of horror.
The behaviour of an eccentric person is said to reflect their genius in a fearless manner. To that effect, an eccentric voice is always colored, and always with very specific tonalities. Their range can be from very high to very low, can be cranky, throaty, or even studdering. At any point, there is an element or elements that make such a voice really stand out. An eccentric voice always includes elements that express creativity in thinking, positive or negative.