Hi Theodore,

I don't really follow you at all, I'm afraid. Why would the ear care 
whether the waveform fit nicely into an arbitrary period of time at all? 
Even if the sound cut out exactly after one second, whether there's a 
little bit left at the end of the waveform makes no difference to the 
pitch of the rest of it! 415.3Hz is a slightly higher frequency than 
415Hz, no matter where we stop listening. The question is whether it's 
enough to matter, and if so, which of the two we should be using as our 
reference.

Another factor that I didn't mention in my initial post is that the 
pitch of harpsichords tends to wander - if it's a tiny bit under pitch 
to begin with, (because it was tuned to 415 instead of 415.3) and then 
drops a tiny bit more, what was insignificant could (more) quickly start 
causing real problems. Starting as close to an ideal pitch as possible 
would certainly be of benefit.

So again, the question - is the 'standard', such as it is, 415, or 
should it really be 415.3? Does anyone but me tune to 415.3?

Jonathan

On 07/02/16 01:34 PM, T. Diehl wrote:
> 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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-- 
Jonathan Addleman - http://www.redowl.ca

::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
Note:  opinions  expressed on HPSCHD-L are those of the  individual con-
tributors and not necessarily  those of the list owners  nor of the Uni-
versity of Iowa.  For a brief  summary of list  commands, send mail to
[log in to unmask]  saying  HELP .
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