Export and import sound give different data

Question

If I export a sound object

and then I import the same sound

I have a different data array. The errors seem to have a certain regularity. They are all multiples of the same value:

Why does it happen? How can I get the same data?

First of all, thank you for the answers.

The raw data are here.

The code is as follows:

datiU2 = Import["https://pastebin.com/raw/sWmUzT9a", "List"];
datiU3 = SetPrecision[datiU2*2^-15, 16];
S1 = Sound[ListPlay[datiU3, SampleRate -> 44100, SampleDepth -> 16, 
    PlayRange -> {-1, 1}]];
dataS1 = List @@ S1[[1]];
dataS1[[1]][[1, 1 ;; 10]]
SetPrecision[
Export["OKDC.wav", S1, "AudioEncoding" -> "Integer16"], 16];
S11 = SetPrecision[Import["OKDC.wav"], 16];
dataS11 = SetPrecision[List @@ S11[[1]], 16];
dataS11[[1]][[1, 1 ;; 10]]

I added the SetPrecision commands after the first post to make a further attempt. I tried with AudioEncoding-> Integer24 and it does not change anything.

The problem is in the conversion that Mathematica does in command Export because if I read in Python the file "OKDC.wav" exported from Mathematica I see the raw values integer16 and they are different from those calculated in previous code by

dataS1[[1]][[1, 1 ;; 10]]*2^15

Answer 1

You specified that the data was to be saved at 16-bit resolution. This means the accuracy should be about 2^-16 overall. But since the audio is signed, you might expect half that. Observe that

2^-15//N 
0.0000305176

is just about the size mismatch you are encountering. You can decrease this by choosing to save at 24 or 32 bits, e.g., by specifying the option

"AudioEncoding" -> "Integer24"