Ordinary musical tones, the notes of the voice, the violin, and the piano, for example, simple as they sound, are, like ordinary white light, rather complex compounds of many simple elements. There are in them seven or eight constituent or «partial» tones, quite distinctly audible to the trained ear or to the untrained ear armed with suitable instruments; and these partial tones, produced by vibrations in the sound-emitting body whose rates are regularly related, bear a certain fixed relation to each other, like the spectrum-colors that compose white light. Not only this, but each partial tone arouses its own proper sensation in the ear by stimulating there one of the minute filaments called the cords of Corti, each of which vibrates sympathetically to a tone of given pitch and to no other. Now we are to imagine that when an ordinary musical tone is sounded, seven or eight of these little cords immediately start a-tremble, and send to the brain their messages, which combine there into the composite impression we name «a tone.» If now another tone is sounded, one which starts into motion another set of filaments, and if furthermore there is one filament now set in motion that was also excited by the first compound tone--if, in other words, the two tones happen to have a partial tone in common, which in both instances excites the same filament in the ear, then we shall have a sense of close relationship between them; they will make together a harmonic group or form. This, as a matter of fact, is what happens with any two tones that form what is called a consonant interval with each other, an «octave,» a «fifth,» or a «fourth.» If tones X and Y, for instance, are an octave apart, the second partial tone of X will be identical with the first of Y; if they are a fifth apart, the third partial tone of X will be identical with the second of Y; if they are a fourth apart, the fourth partial tone of X will correspond with the third of Y. It is obvious, then, that all these intervals will give us the sense of harmonic form; for they provide all the necessary conditions of a form, having enough in common to be associated by our minds, and enough not in common (their dissimilar partial tones) to be distinguished. When the partial tone in common is so high, and therefore so weak, that it impresses us but slightly, we shall have little or no sense of their being related; such is the case in the so-called imperfect consonances and the dissonances. When, on the other hand, all the most prominent partial tones of one exist in the other, they will fuse into one impression in our minds, losing the characteristic of form entirely, as is the case to some extent with the octave and entirely with the unison. But when, as in the case of fifths and fourths, there are both a distinctly audible partial tone in common and others not in common, then we shall have true harmonic forms.