Partial Tones Those simple sounds which in combination form an ordinary sound and cause its special quality of tone. [Stainer, John; Barrett, W.A.; A Dictionary of Musical Terms; Novello, Ewer and Co., London, pre-1900]
After vibrations the next thing is musical notes, the sounds produced by the vibrations falling into the ear. Sounds arise in association. There are no bare simple sounds in music; it is a thing full of the play of sympathy. Such a thing as a simple solitary sound would be felt as a strange thing in our ears, accustomed as we are to hear affiliated sounds only. These affiliated sounds, called "harmonics," or "partials" as they have also been called, because they are the parts of which the sound is made up, are like perspective in vision. In perspective the objects lying in the line of sight, seem smaller and smaller, and more dim and indefinite as they stretch away into the distance; while nearer objects and those in the foreground are apparently larger, and are more clearly seen. This is the way of a musical sound; one of its component elements, the fundamental partial, being, as it were, in the foreground to the ear, is large and pronounced; while the other elements are less distinctly heard, and are fainter and fainter as they recede into the musical distance in the perspective of the ear. Few have any idea of the number of these weaker partials of a musical sound. Tyndal's illustrations in his very instructive work on Sound show a string spontaneously divided into twenty segments, all vibrating separately, being divided by still nodes along its length; and a vibrating string will keep thus [Scientific Basis and Build of Music, page 58]
dividing itself by 2 or 3 or 5, etc., up through the whole geometrical series of numbers, not keeping fixed at one thing; but while the whole length is vibrating the fundamental partial, it keeps shifting the still nodes along its length, and sometimes longer and sometimes shorter segments are sounding the other partials which clothe the chief sound. It has been commonly said that "a musical sound is composed of three sounds," for every ear is capable of hearing these three, and with a little attention a few more than these; but many will be startled when told that there are twenty-five sounds in that sound. Eighteen of them are simply the octaves of the other seven, all of these seven except one having one or more octaves in the sound. Four of the seven also are very feeble, the one which has no octave being the feeblest of all. Two of the other three are so distinctly audible along with the chief partial that they gave rise to the saying we have quoted about a musical sound being composed of three sounds.1 If the three most pronounced partials were equally developed in one sound, it could not be called one sound - it would decidedly be a chord; and when in the system they do become developed, they form a chord; but in the one sound they, the partials, having fewer and fewer octaves to strengthen them, fade away in the perspective of sound. The sharp seventh, which in the developed system has only one place, not coming into existence until the sixth octave of the genesis, is by far the feeblest of all the partials, and Nature did well to appoint it so. These harmonics are also sometimes called "overtones," because they are higher than the fundamental one, which is the sound among the sounds, as the Bible is the book among books. [Scientific Basis and Build of Music, page 59]
Speaking of acute harmonics Pole says - "The first six are the only ones usually considered to be of any practical importance, and it is rarely possible to distinguish more than 10 or 12."
Mercenne (French, 1636) says - "Every string produces 5 or more sounds at the same instant, the strongest of which is called the natural sound of the string, and alone is accustomed to be taken notice of; for the others are so feeble that they are only perceptible to delicate ears . . . not only the octave and fifteenth, but also the twelfth and major seventeenth are always heard; and over and above these I have perceived the twenty-third and ninth partial tones in the dying away of the natural sound."[Scientific Basis and Build of Music, page 59]
Helmholtz falls into a mistake when he says- "The system of scales and modes, and all the network of harmony founded on them, do not seem to rest on any immutable laws of Nature, but are due to the aesthetical principle which is constantly subject to change, according to the progressive development of taste." It is true, indeed, that the ear is the last judge; but the ear is to judge something which it does not create, but simply judges. Nature is the maker of music in its scales and modes. The styles of composition may vary with successive generations, and in the different nations of men; but the scientific basis of music is another thing. It is a thing, belonging to the aesthetic element of our being and our environment; it is under the idea of the beautiful, rather than the idea of the useful or the just; but all these various aspects of our relation to creation have their laws which underlie whatever changes may be fashionable at any period in our practice. If the clang-farbe of a musical tone, that is, its quality or timbre, depends on the number and comparative strength of the partial tones or harmonics of which it is composed, and this is considered to be the great discovery of Helmholtz, it cannot be that the scales and modes are at the caprice of the fickle and varied taste of times and individuals, for these partials are under Nature's mathematical usages, and quite beyond any taste for man's to change. It is these very partials or harmonics brought fully into view as a system, and they lead us back and back till they have brought us to the great all-prevading law of gravitation; it is these very partials, which clothe as an audible halo every musical sound, which constitute the musical system of sounds. [Scientific Basis and Build of Music, page 78]