Hello David,
This topic, amongst others was in one of the textbooks we used in a course
at conservatory, Fundamentals of Musical Acoustics or such... The section
on how the ear works when 'tuning' was amazingly informative and
fascinating.

Anyway, let me try to explain in a simplified way, leaving out decibels and
other aspects:
Any tone or pitch, is the product of vibrations taking place within a unit
of time (for Hz: 1 second)

So let's imagine a simple sinusoid, a plain tone like those from a tone
generator and put it in a graph.Here is one we can use:
http://www.featurepics.com/online/simple-red-sound-wave-973855.aspx

If this wave you see on the link is taking place exactly within one second,
we could then say it is a picture of a sinusoid tone of 1 Hz. That is to
say both the 'humps' above AND below comprise the 1 Hz example.

It travels to your ear. (I leave out the inner workings further!)
The upper 'hump' compresses the typanum inwards;
The lower 'hump' allows the tympanum to release outwards;
If this COMPLETE CYCLE inwards/outwards cycle takes place in one second you
will hear a tone of one Hz. 2x of these cycles, 2Hz - etc. etc. etc.

In reality, the sinus is incredibly complex, with overtones and all kinds
of spikes.
And human hearing does not go dwon to 1Hz  ;@-)
Nonetheless, this inward/outward motion in a second is how we are able to
define pitch as Hz.
Even microphones work in this exact same manner.

So, then what about the 0.3 Hz question?
Adding 0.3 Hz to this example means that the sinus would start another new,
partial journey upwards in the picture. Your ear cannot percive it as pitch
because, simply put, it needs the whole cycle of in/out as a measurement -
pitch is for the ear a very 'mechanical' process. Depending on the decibel
level and your distance to the sound, that 0.3 will dissapper into a
perception of color or be ignored by your brain

Hope this helps?
Cheers
Theodore

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