Harmonics, Waveforms, and the Overtone Series / by Anne Lanzilotti

This week in our Extended Techniques for Strings class, the subject of different types of waveforms and timbre as harmonic spectrum came up. Posting these diagrams here for ease of reference (scroll down for a summary of basic terms):

Overtone Series on C, Partials 1–16 (Arrows indicate sixth tone or quarter tone alterations which occur naturally in the harmonic series). Yes, that's an alto clef. Diagram by Lanzilotti

Overtone Series on C, Partials 1–16 (Arrows indicate sixth tone or quarter tone alterations which occur naturally in the harmonic series). Yes, that's an alto clef. Diagram by Lanzilotti

The Natural Harmonic Series and Fractions of the String. Diagram by Lanzilotti.

The Natural Harmonic Series and Fractions of the String. Diagram by Lanzilotti.

Sine waves contain only the fundamental. Square waves (a form of pulse waves) and triangle waves contain only odd harmonics (with distinct amplitudes), giving them their individual sounds. Sawtooth waves have all partials present, but they decrease exponentially in relation to the ratio of the partial to the fundamental.

Harmonic spectra shown using musical notation. Diagram from Holmes's Electronic and Experimental Music

Harmonic spectra shown using musical notation. Diagram from Holmes's Electronic and Experimental Music

Some other terms that came up were:

  • frequency: pitch, measured in hertz (Hz) or cycles per second
  • amplitude: volume/loudness
  • timbre: tone color, determined by the set of harmonics or overtones in the sound
  • duration: how long the sound lasts (is audible)
  • envelope: overall shape of the amplitude of the sound over time including the attack, sustain, and decay of the sound