Subharmonics

Mathematically, the subharmonics of a fundamental are the inverse of its harmonics: harmonics multiply the fundamental, subharmonics divide it. Drawn on a logarithmic frequency scale, the harmonic series spreads upward and the subharmonic series mirrors it downward. VoceVista can show both at once on a Note Slider.

Unlike harmonics, subharmonics do not arise spontaneously from most ordinary vibrating systems. A plucked string, a column of air, or a freely vibrating vocal fold radiates harmonics, not subharmonics. Subharmonics show up only when something more complicated is going on.

In the human voice, a subharmonic at half the fundamental frequency typically signals period doubling: the vocal folds are vibrating in alternating cycles instead of in a single repeating cycle. Two consecutive cycles differ slightly — for example in amplitude, in closing pattern, or in duration — and the result is an extra component at half the fundamental frequency, an octave below the apparent pitch.

The most common occurrence is vocal fry (also called creaky voice), at the lower end of the modal range. Period doubling can also appear as a transient feature in stressed singing, in some forms of overtone singing, or in pathological voices. Subharmonics at one third of the fundamental, from period tripling, are rarer but follow the same mechanism.

On the Spectrogram a subharmonic appears as a horizontal line between the harmonics of the apparent fundamental — at the half-way position for period doubling, the third-way position for period tripling.

A Note Slider can be drawn to show subharmonics (undertones) below its fundamental, mirroring the harmonics above it. See Note Sliders for how to set this up.