How Science Got Sound Wrong

Thank you David. I will have to think about that.

As for the Nyquist-Shannon theorem, yes, I am familiar with it, and am not convinced that it says what some engineers think it does. For one thing, it involves a limit in terms of an infinite series (or integration over infinite time), and infinite time is available for relatively few signals.

My reference, A Handbook of Fourier Theorems by Champeney (Cambridge University Press), is a little too dense for casual reading, but I’ll persevere for a time.

Thanks again for the discussion, and also for re-igniting an interest in that branch of mathematics.

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.