Harmonic Series

In many musical instruments, a note does not vibrate at just one frequency. The lowest vibration rate is the fundamental frequency, and the higher modes of vibration occur at integer multiples of that rate, so the nth harmonic is given by f_n = n f_1. This comes from standing waves fitting into a fixed vibrating length, such as a string or an air column, where only certain wave patterns are allowed.

Use this formula when you want to find the frequencies of overtones in idealized strings, pipes, or resonant systems. It is especially useful in acoustics, instrument design, and identifying harmonic content in a sound spectrum.

• Using the harmonic number as the frequency instead of multiplying it by the fundamental
• Forgetting that the fundamental is the 1st harmonic, not the 0th
• Applying the formula to non-harmonic overtones in real instruments without checking whether the spectrum is approximately integer-multiple based