In http://plus.maths.org/content/music-primes DuSatoy describes the relation between the prime number staircase and harmonics from music. So in the article he uses music as an analogy. But I wonder if anyone has tried to produce a sound recording from those frequencies? Or even an image?
Tao also describes a prime sound wave in his presentation, called the "von Mangoldt function" which is noisy at prime number times, and quiet at other times.
chrome-extension://bpmcpldpdmajfigpchkicefoigmkfalc/views/app.html
Even when one plays around with the zeta functions we see:
$\sum_{1}^{\infty}\frac{1}{n^{a+ib}}=0\Rightarrow $
$\sum_{1}^{\infty}\frac{cos(ln(n)b)}{n^{a}}=0$ and $\sum_{1}^{\infty}\frac{sin(ln(n)b)}{n^{a}}=0$.
Musically, when an instrument plays a note, the basic note can be represented by A.cos Lt + B.sin Lt. The number L has to do with how high the note is (pitch), and A and B have to do with how loud it is; t is time.
So from here there are many routes:
1)for $a=\frac{1}{2}$ and $b=14.135$ (non-trivial zero), we could create notes as follows
$\frac{cos(ln(2)14)}{2^{1/2}}+\frac{sin(ln(2)14)}{2^{1/2}}$
$\frac{cos(ln(3)14)}{3^{1/2}}+\frac{sin(ln(3)14)}{3^{1/2}}$
$\cdots$
2)for $a=\frac{1}{2}$ and $b=14.135, 21.022, 25.011...$ (non-trivial zeros), we could create notes as follows for fixed n=2
$\frac{cos(ln(2)14)}{2^{1/2}}+\frac{sin(ln(2)14)}{2^{1/2}}$
$\frac{cos(ln(2)21)}{2^{1/2}}+\frac{sin(ln(2)21)}{21^{1/2}}$
$\frac{cos(ln(2)25)}{2^{1/2}}+\frac{sin(ln(2)25)}{21^{1/2}}$
$\cdots$
Maybe smn can use the above to make a sound recording.
Regards
PS
Here are some links
https://www.youtube.com/watch?v=i1FqnfrcWA4 (logarithm of primes)
https://www.youtube.com/watch?v=EIpmvTAsaMI (modular arithmetic)
https://www.youtube.com/watch?v=BkCZvhvJdy4 (difference of primes)
I dont really understand the question you are asking here, but a while ago I made this video while working on something else that created something vaguely melodic in a simple way from the prime factorisation of the integers if that is relevant:
http://m.youtube.com/watch?v=l_KEzLb6Cd4