How Science Got Sound Wrong

terry9,

Excellent catch on infinite series, but also easily addressed. As we are dealing with audio, there is effectively no information below 10Hz, and some would argue 20, but let’s say 10Hz. For that reason, any real single data set, i.e. a song file, can be modelled as an infinite series as there is a maximum rise time and minimum fall time at beginning and end, hence you can "set" all data outside to 0 (whatever your 0 is) for all points when applying the theorem. Any "errors" in bit level would be in the silence at the beginning and end of the track. In some ways, this is like a natural windowing function.

There are lots of papers, proofs, course books, material, etc. that goes into detail, including size of error when you don’t have an infinite series, which in a practical audio case, would be much smaller than other error sources.

If you want to play with "math", GNU Octave is a free-ware version of Mathcad (not as graphical) and would let you simulate any of these concepts.

My proofing the digital vs analog thing, was to put the imaginary speakers 8 feet apart...

Is that imaging or imaginary? If the speakers are imaginary, how do the listeners hear the sound?

and put the listener 8 feet back, at the tip of an equilateral triangle, kinda thing.

then fire a signal off both speakers at the same time, a sharp tick or ping sound.

then vary the timing of the signal released off one speaker, vs the other

Humans can generally hear a ’one inch’ shift of the position of the phantom between the speakers ’ping’ sound.

This equates to a perfected zero jitter timing change of 1/100,000th of a second.

Sound travels about 13,500in/s or 74µs/in. Delaying the signal 10µs is ≈0.143in. 

So if the sound is delayed, but constant level, this will contribute phase shift alone, which is not exactly how humans hear.

atdavid: Great explanations. It's incredible these issues are still poorly understood nearly a century on.

Thanks David. Will have to think some more. Haven't use Octave - Maple is my poison.

I had Mathcad on the brain as I use it pretty regularly. GNU Octave is a freeware version of Matlab, not Mathcad.

David, you posted something earlier that resonated (no pun) with me.  You said...

So how does the brain measure this timing? By the latest research, it appears to have 2 mechanisms, one, that works on higher frequencies, higher than the wavelength of the head’s size, that is based on group delay / correlation, i.e. the brain can match the same signal arriving to both ears and time the difference and another mechanism for lower frequencies, that can detect phase, likely by a simple comparator and timing mechanism. The two overlap.
  
Phase hmmm.  If a point source of sound has a given freq range and originates as all freq at zero phase AND, air is dispersive as is all mediums, more phase change at different freq could be interpreted as farther.  Ok.  Well I was curious and looked at the phase plots of my speakers.  Phase varies fairly smoothly from about -40 deg at 50 hz to about +34 deg at about 500 hz and is flat after that for about 2 more octaves.  30deg is considered alot and over the most "important" freq to humans, this is twice that.  Point is, IF phase is used by our brains/ears to judge distance (rather than just delays for orientation),  especillay at low freq, with speakers doing that how is "depth" and what we call staging not affected negatively?  In my field, as I suspect audio is, phase is usually ignored as it's a nearly intractable problem for the most part.  I wonder if sampling/digitization etc and its issues could end up being a red herring as they pertain to this topic of natural (organic) sound.  

This doesnt address the source (CD or vinyl) question and their imaging differences but maybe someone can interject the phase aspects of the two to possibly add to the discussion.