Virtual Fundamental

Hey folks, I've got a question for you. I'm having
trouble tracking down research on virtual
fundamentals; I'm trying to figure out 1) what/how
many partials can be missing before one ceases to hear
a virtual fundamental, and 2) whether the use of
harmonics to create a virtual fundamental can allow
one to hear a pitch lower than one's usual low
frequency limit. So, for example, if the lowest sine
wave I can hear is 20 Hz, can my brain imply a virtual
fundamental lower than 20 Hz when provided with upper
harmonics; if so, how much lower? Any bibliographic
tips? I know this has to more to do with
psychoacoustics than tuning, but I figured there might
be some crossover knowledge out there.

Thanks much,

JG

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--- In tuning@y..., Jeremy Grimshaw <jngrimshaw@y...> wrote:
> Hey folks, I've got a question for you. I'm having
> trouble tracking down research on virtual
> fundamentals;

There's plenty of research out there . . . some good starting
points include Hall's textbook _Musical Acoustics_ and Ernst
Terhardt's website.

> I'm trying to figure out 1) what/how
> many partials can be missing before one ceases to hear
> a virtual fundamental,

Virtual fundamentals can be evoked by just two partials -- an
extreme example even involved only one partial plus some
noise.

> and 2) whether the use of
> harmonics to create a virtual fundamental can allow
> one to hear a pitch lower than one's usual low
> frequency limit. So, for example, if the lowest sine
> wave I can hear is 20 Hz, can my brain imply a virtual
> fundamental lower than 20 Hz when provided with upper
> harmonics;

No -- but fundamentals heard in this range are more often than
not virtual fundamentals rather than actual frequency
components -- look up the "acoustic bass" of pipe organs, for
example.

> Any bibliographic
> tips?

I'll try to find more on this subject for you. I've read a ton on this,
spending hundreds of hours in libraries doing so, but
unfortunately I don't have these materials at my fingertips.