Partial, harmonic, fundamental, inharmonicity, and overtone
Any complex tone "can be described as a combination of many simple periodic waves (i.e., sine waves) or partials, each with its own frequency of vibration, amplitude, and phase."[1] (Fourier analysis)
A partial is any of the sine waves by which a complex tone is described.
A harmonic (or a harmonic partial) is any of a set of partials that are whole number multiples of a common fundamental frequency.[2] This set includes the fundamental, which is a whole number multiple of itself (1 times itself).
Inharmonicity is a measure of the deviation of a partial from the closest ideal harmonic, typically measured in cents for each partial.[3]
Typical pitched instruments are designed to have partials that are close to being harmonics, with very low inharmonicity; therefore, in music theory, and in instrument tuning, it is convenient to speak of the partials in those instruments' sounds as harmonics, even if they have some inharmonicity. Other pitched instruments, especially certain percussion instruments, such as marimba, vibraphone, tubular bells, and timpani, contain non-harmonic partials, yet give the ear a good sense of pitch. Non-pitched, or indefinite-pitched instruments, such as cymbals, gongs, or tam-tams make sounds rich in inharmonic partials.
An overtone is any partial except the lowest. Overtone does not imply harmonicity or inharmonicity and has no other special meaning other than to exclude the fundamental. This can lead to numbering confusion when comparing overtones to partials; the first overtone is the second partial.
Some electronic instruments, such as theremins and synthesizers, can play a pure frequency with no overtones, although synthesizers can also combine frequencies into more complex tones, for example to simulate other instruments. Certain flutes and ocarinas are very nearly without overtones.
