Future redshifting and effect on the 'pitch' of CMB radiation
The wavelength of the CMB increases linearly with the scale factor $a$, which is defined as 1 today, so the "sound" of the CMB has dropped an octave when the Universe has doubled in size (in all three directions), i.e. when $a = 2$, which will happen when it is roughly 25 billion years old (see e.g. Fig 1 of Davis &amp; Lineweaver 2004).

The magnitude of the dipole of the CMB is $3.4\,\mathrm{mK}$ (Kogut et al. 1993), i.e. $\sim10^{-3}$ of the peak value. The primordial fluctuations are even lower, roughly a factor $10^{-5}$ of the peak value. The dipole is partly due to our motion round the Milky Way, and so will fluctuate somewhat with the period of a Galactic year, which is 225 million years.

The figure shows how the peak frequency evolved in the past. Its current value is 160.4 Ghz. To calculate how a human would perceive the sound at a given time, I suppose you'll have to multiply the spectrum with the frequency-dependent transmission function of the human ear, but that's physiology which I know nothing about.



The figure was produced by calculating the frequency at a given time as
$$
\nu(t) = \frac{160.4\,\mathrm{GHz}}{a},
$$
where $a$ runs from $1/1100$ to $4$,
and calculating the age by integrating the Friedmann equation, assuming a Planck 2015 cosmology.