Text: A Simple Tone is one that cannot be analysed into two or more sounds of different pitch. A Compound Tone or Clang is a tone which is made up of two or more Simple Tones of different pitch. Almost all sounds employed in modern music are compound. The Simple Tones that form part of a Compound Tone are termed Partials or Partial Tones. The lowest Partial of a Compound Tone is termed the First Partial; the next above, the Second; the next, the Third; and so on. The first partial of a compound tone is also called the fundamental tone, and the others, overtones; thus the second partial is termed the first overtone; the third partial, the second overtone, and so on. In almost all the compound tones used in modern music, the vibration numbers of the partial tones, starting with the fundamental, are in the ratios of 1:2:3:4:5:6:7:etc. Any one or more of these partials, however, may be absent in any particular tone. Thus, for example, the even numbered partials are absent in the tones of cylindrical stopped pipes. The relative intensities of the partials of compound tones vary almost infinitely. As a general, but by no means universal rule, the higher the order of the partial, the less is its intensity; that is to say, the first partial is generally louder than the second; the second louder than the third, and so on. Approximately simple tones may be obtained from carefully bowed tuning forks mounted on suitable resonance boxes; or from flutes and wide stopped organ pipes, gently blown. If two pure musical tones are of the same pitch and of equal intensities, all those respects in which they yet differ, are included under the term quality or timbre. The quality of a compound musical tone depends upon the number, order, and relative intensities of its constituent partials. Helmholtz has demonstrated this proposition by the analysis and synthesis of compound tones. Just as pitch depends on wave length, and intensity on amplitude; so the quality of a tone (that is, the number, order, and relative intensity of its partials) depends on wave form. A simple tone is the result of pendular sound waves or pendular vibrations, that is, of vibrations similar to those of a simple pendulum. A compound tone is due to the combination of two or more pendular vibrations, or waves. Every compound tone may be resolved into a certain number of simple tones, whose relative pitch follows the law of the partial series. Similarly, every compound wave may be resolved into a certain number of simple pendular waves, whose lengths are in the ratios of 1:1/2:1/3:1/4:1/5:etc. The form of the sound wave, therefore, determines the number, order, and relative intensities of the partials, that is, the quality of the resultant sound. On the other hand, given the quality, it is not possible to determine the corresponding wave form, since for any one such quality, there is an infinity of wave forms, due to the infinite number of relative positions or phases in which the constituent pendular waves may start. The ear does not perceive a compound tone as such, but analyses it into its constituent pendular waves, each of these latter producing the sensation of a simple tone at its own particular pitch and intensity. (Hand Book of Acoustics, 5th edition; Harris, T.F.; J. Curwen & Sons, London, 1903?)

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