The Harmonic Model of Tones

  We define a tone to be a sound that is perceived to have a single frequency. This is sometimes called a pitched sound, or a sound that has a pitch, but we will scrupulously observe the following distinction between pitch and frequency. A pitch is a discrete element of a musical theory or system (like `A4'). A frequency, on the other hand, is a continuous physical quantity indicating the rate of a periodic phenomenon such as a tone.

Tones are herein modeled as being composed of a sum of harmonically related sinusoids. The amplitude and phase of these sinusoids may vary slowly over time. Tones are assumed to be perceived as having a frequency equal to the fundamental, the lowest of these sinusoids. For example, a sound composed of sinusoids at 100, 200, and 300 Hz would be identified as having a frequency of 100 Hz. Phenomenon such as missing fundamentals are therefore not accommodated by this model. In addition, this model does not accommodate frequency fluctuations such as vibrato.