Acoustic oscillators such as a string or a column of air vibrate at numerous modes simultaneously. Waves travel in both directions along it, reinforcing and cancelling each other to form standing waves, that produce audible sound in surrounding air. The longest allowed wavelength of an oscillator is twice it’s the length. Wavelengths that are 1/2, 1/3, 1/4, 1/5 1/6, 1/7, etc. times that of the fundamental are members of it’s harmonic series. They form an arithmetic series (1×f, 2×f, 3×f, …) of frequencies with constant difference equal to the fundamental.