Overtone ( $n = 1, 2, \dots$ )

An overtone is an oscillatory mode above the fundamental mode in the same mode family. Waveguide branches are compared at fixed horizontal wavenumber. Their frequencies need not be integer multiples of the fundamental frequency. In a scalar layered guide, additional vertical nodes distinguish successive overtones.

The first overtone is the lowest oscillatory normal mode above the fundamental mode. It is an ordering by frequency, not a claim that its frequency is an exact integer multiple of the fundamental. If the fundamental is labeled

n = 0

n = 1

; another common convention labels them one and two.

For a string fixed at both ends, the frequencies are

f_{n} = n c / (2 L)

with

n \geq 1

, so the first overtone is the second harmonic at twice the fundamental. For an ideal pipe closed at one end, the next allowed mode is at three times the fundamental. Geometry and boundary conditions determine the relation.

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Overtone can refer to different concepts depending on the context in which it is used. Here are a few common interpretations: 1. **Music**: In music, an overtone is a frequency that is higher than the fundamental frequency of a sound. When an instrument or voice produces a note, it vibrates at a fundamental frequency, but it also generates additional frequencies that are multiples of the fundamental (harmonics). These overtones contribute to the richness and timbre of the sound.