HARMONICS, the accessory or collateral sounds accompanying the primary, fundamental or predominant note of any string, pipe or other sonorous body, and constituting in varying grees what in English is known as '9uality,° in French as °timbre° and in German as farbe.D No purely simple sound — one whose tions are all in the same period — is producible. When a sound is pro- duced by the vibration of an open string, the whole string vibrates as a unity, giving rise to a tone called the fundamental. The string, ever, further divided into various sections, which vibrate separately and more rapidly and produce sounds — the harmonics — differing from the fundamental, but bearing certain fixed proportions to it. By whatever vibrating body a musical sound is evoked harmonics also are produced; and although some of the harmonics are suppressed by modifying cir cumstances, some are always present. There is a regular succession of intervals in which the harmonics naturally accompany a fundamental sound, which is represented in the following scale of vibrations : 1, 2, 3, 4, 5, 6, 7, etc. These also are the intervals which produce the succes sive chords in harmony, although the natural harmonics when produced further go beyond the range of harmony which human ears can recognize or musical instruments produce at the will of the performer. (See illustration). 1 is the interval of the octave; 2 is the fifth; 3 is the fourth; 4 is the major third; 5 the minor third; from 6 to 7 is already beyond the range of production on a keyed instrument, but is recognized by musicians as the complement of a four-part simple chord, and is represented approximately on the pianoforte, by E flat, for example, for the key of F.
A musical tone, then, is always complex, but the harmony which attends it is not always the same. The different structure of different in struments suppresses now some, now others, of the succession of harmonics, and a different body of tone is thus produced, distinguishing a note in one instrument from the same note in another. Hence the distinctive construction of the pianoforte in which dissonant harmonics are suppressed, and on the other hand, the use in the organ of mutation and mixture stops the thirteenths and fifteenths — whereby the consonant harmonics of a given tone are much emphasized. Again, many of the higher har monics are strongly dissonant both with the fundamental tone and with each other, whence arises the discordant quality of such instru ments for instance as the cymbals. Harmonics are also called °overtones,* and all the primary and secondary tones constituting an actual tone are frequently termed °partials" or °partial tones,' the fundamental tone being the first partial, and the harmonics, the upper partials. See HARMONY.