Harmonics

A harmonic is a frequency component of a sound that is an integer multiple of a fundamental frequency. If the fundamental is 100 Hz, its harmonics are at 200 Hz, 300 Hz, 400 Hz, and so on. The full set of these multiples is the harmonic series.

Why Harmonics Exist

Most pitched sound sources — vocal folds, vibrating strings, columns of air in a wind instrument — do not vibrate at one frequency only. They vibrate at all integer multiples of a base frequency simultaneously. Each of those frequencies adds its own component to the radiated sound; the relative strengths of those components are what give an instrument or voice its characteristic timbre. Two trumpets playing the same A4 sound similar because both produce harmonics at 440 Hz, 880 Hz, 1320 Hz, … but they sound recognisably like trumpets because the relative loudness of those harmonics follows a pattern that is typical of trumpets.

In the human voice, the source of harmonics is the regular opening and closing of the vocal folds. The shape of the resulting waveform — sharp closure, smoother opening — determines how much energy ends up in the higher harmonics. The vocal tract then filters this source by amplifying frequencies near its resonances and attenuating others. The harmonics carry the source’s energy through the vocal tract; the resonances shape which harmonics come out loudest.

Harmonics and Overtones

The two terms refer to almost the same set of frequencies, with a small difference in counting:

  • The first harmonic is the fundamental itself. The second harmonic is one octave above the fundamental, the third is an octave plus a fifth above it, and so on.

  • The first overtone is whatever sits above the fundamental — i.e., the second harmonic. The "first overtone" and the "second harmonic" are the same frequency.

In VoceVista the harmonic numbering is used.

Reading Harmonics in the Display

In the Spectrum, harmonics appear as a series of peaks at evenly spaced frequencies. In the Spectrogram, they appear as parallel horizontal lines: evenly spaced when the frequency axis is linear, progressively closer together when the axis is logarithmic.

In VoceVista

A Note Slider can be drawn out to show the position of each harmonic of a chosen fundamental, which makes it easy to verify whether a peak in the Spectrogram is a harmonic of a given note and to read off harmonic numbers. See Note Sliders for how to place and configure sliders.