The spectrum of the sum of two periodic signals
the Fourier Series for a single periodic function, having period $P$, 

$$ x(t) = x(t+P) \qquad \forall \ -\infty &lt; t &lt; +\infty $$

is 

$$ x(t) = \sum\limits_{k=-\infty}^{\infty} c_k \, e^{j(2\pi k/P)t} $$

each harmonic $c_k$ is labelled with its harmonic number, $k$, in the above. the actual frequency of each harmonic, in Hz or units of 1/time, is $\frac{k}{P}$.  the fundamental frequency is the reciprocal $\frac{1}{P}$ of the period.  in angular frequency (radians per unit time), multiply both by $2\pi$.  but, in the harmonic number $k$ there lacks enough specific information to tell you what the actual frequency is of the harmonic.  e.g. the second harmonic of a periodic tone of 220 Hz is the same frequency as the fourth harmonic of a periodic tone of 110 Hz.

so the spectrum of $x(t)$ is about what actual frequencies the energy of a signal is.  it doesn't matter whether $x(t)$ is periodic or not (actually it does with the esoteric mathematics, but we won't go there).  and we use the Fourier Transform, not the Fourier Series to visualize it.

So each harmonic in the Fourier Series above is attached to a dirac delta function, $\delta(f)$.

$$\begin{align} X(f) &amp;\triangleq \mathscr{F} \Big\{ x(t) \Big\} \\
 &amp;= \int\limits_{-\infty}^{\infty} x(t) \, e^{-j2\pi f t} \, \mathrm{d}t \\
 &amp;= \mathscr{F} \Big\{ \sum\limits_{k=-\infty}^{\infty} c_k \, e^{j(2\pi k/P)t} \Big\} \\
 &amp;= \sum\limits_{k=-\infty}^{\infty} c_k \,\mathscr{F} \Big\{  e^{j(2\pi k/P)t} \Big\} \\
 &amp;= \sum\limits_{k=-\infty}^{\infty} c_k \, \delta(f-k\tfrac{1}{P}) \\
\end{align}$$

If you express the spectra of your periodic signals in this form, the spectra sum to a single spectrum.