A001097  Twin primes:

There is a clear audio difference between this and the primes (A000040); this sound is lower and much more 'crackly'.

For terms of the sequence less than 10^6, the number
that fall into each residue class modulo m are as follows:

2   [0, 16337]
3   [1, 8168, 8168]
4   [0, 8168, 0, 8169]
5   [1, 5433, 2735, 2737, 5431]
6   [0, 8168, 0, 1, 0, 8168]
7   [1, 3271, 1629, 3305, 3268, 1629, 3234]
8   [0, 4095, 0, 4100, 0, 4073, 0, 4069]
9   [0, 2729, 2651, 1, 2651, 2788, 0, 2788, 2729]
10   [0, 5433, 0, 2737, 0, 1, 0, 2735, 0, 5431]
11   [1, 1825, 901, 1830, 1785, 1820, 1820, 1819, 1828, 909, 1799]
12   [0, 4122, 0, 1, 0, 4046, 0, 4046, 0, 0, 0, 4122]
13   [1, 1473, 735, 1473, 1465, 1491, 1502, 1500, 1509, 1497, 1469, 743, 1479]
14   [0, 3271, 0, 3305, 0, 1629, 0, 1, 0, 1629, 0, 3268, 0, 3234]

There are only 16377 twin primes less than 10^6, compared to 78498 primes less than 10^6.

The residue counts are similar to what we see with the primes, with non-zero/non-one values
for all residue classes that are relatively prime to the moduli.  However, unlike the
primes, the distribution is not uniform.  Starting with modulo 5, we see that residue
classes 1 and 4 have twice as many as classes 2 and 3.  The reason for this is that
for n and n+2 to be prime, neither can be a multiple of 5.  So the only way a twin prime p
can be congruent to 2 (mod 5) is if it and p+2 are prime; that is, this can only happen
if p is the smaller of the twin primes.  Compare this to, for example twin primes congruent
to 1 (mod 5): they can arise as either the smaller or the larger of a pair of twin primes since
3 and 4 are both relatively prime to 5.
 
There is also a stark difference between this and the primes in the spectrogram. 
In the spectrum there is a symmetric drop at 11025 (44100/4) Hz which visually 
resembles a canyon (the frequencies before and after 11025 Hz taper down to that point). 
This is represented in the spectrogram as a very bold spectral line.  

Besides that point, this has very similar spectral lines to the primes at 
17640 (44100/2.5) Hz, 14700 (44100/3) Hz, 7350 (44100/6) Hz, and 4410 (44100/10) Hz. 
The main frequencies that arise are 4410 Hz and 7350 Hz, with multiples of them 
at 14700 (7350 x 2) Hz, and 17640 (4410 x 4) Hz. 

-Kai vanNood