A sound wave of well-defined pitch is by definition a periodic function of time $t$ with a corresponding spectrum $\{\alpha_n\,:\,n=1,2,\dots\}$ based on a fundamental frequency $\omega$:
$$\phi_\omega(t)\,=\,\alpha_0+\sum_{n=1,2,\dots}\alpha_n\cos\bigl(2\pi n\omega (t-\tau_n)\bigr)~.$$
The set of frequencies which appear in this formula is called the harmonic series: frequencies ${\omega, 2\omega, 3\omega, 4\omega, \dots}$ are respectively called the fundamental ($n=1$), first harmonic ($n=2$), second harmonic ($n=3$), etc. We can think of each component of the wave as an additional note above the fundamental as in Figure 1.

The frequency $\omega$ gives its name to the resulting wave, for example any wave with fundamental frequency $\omega=440$ [Hz] is an A irrespective of which other coefficients appear in the series. When fundamentals of two notes are in a ratio of $2$ ($\omega_2=2\cdot\omega_1$) , they form an octave and share the same name. Therefore notes with $\omega = 110, 220, 440, 880$ [Hz] are all called A. Notice that the harmonic series of A$=880$ [Hz] is entirely contained within the harmonic series of A$=440$ [Hz] and similarly for any harmonic of any other note in the series (for example harmonics of E$=1320$ [Hz] or C♯$=2200$ [Hz] are all harmonics of A$=440$ [Hz]). These notes would however be considered “out of tune” in a perfectly equal temperament (which imposes E$=1318.51$ [Hz] and C♯$=2217.46$ [Hz]).