THE ANALOGY OF MUSICAL SOUNDS. CHAPTER IV. HARMONICS. 167 1083. By the term HARMONICS, we here denote the science of the relations of sound, silence, and note, which science is otherwise called Music, Acoustics, or Phonics, the third and last of the purely Esthetical Sciences, and dependent upon the sense of hearing, as the sister-science of Chromatics is upon vision, and that of Plastics upon touch. 1084. The principles of sound and silence are in Harmonics, or acoustic science, what those of light and shade are in Chromatics, and also what position and magnitude are in Plastics, they are the agent and patient, or cause, of all the effects and phenomena of hearing: from the coaction or concurrence of which principles arise all the variety of note and sound. 1085. Sound and silence, and also their parallel relations, the acute and grave, or the treble and bass, are correlative extremes in music, as light and shade are in colours, and position and mag nitude are in figures; so that, in fact, as declining light is an approach towards darkness, so is the declension of sound, to the grave and bass, an approach toward silence, or the absence or negation of musical sound or note. In Harmonics, therefore, we may either deduce the treble, &c., from the bass, or the bass from the treble, indifferently. 1086. As the generator of figure and colour is in each a punctum, or point, so is that of note, or tone, a pulse or point of sound; and every pulsation of sound, like the plastic and chromatic points, generates and resolves into three others, bearing the relations of the common chord, or chord major of the musician, by the various combinations of which every musical interval may be determined. 1087. This triunity of sound has been demonstrated in a variety of ways, to the satisfaction of the cultivated ear of the musician, by Mersennus, Wallis, Rammau, Tartini, and others; and it follows that these three tones of every tone are resolvable into other like tones, even to the extremest limits of sensation indefinitely, and in a manner perfectly analogous to the like analysis of colours, by which every hue and shade resolves into like triads of primaries to infinity, -every one three, and every three one, in indivisible triunity to infinity, or bounded only by sense. 1088. The first of these facts is shewn in the well-known experiments of the monochord, trumpet-marine, &c.; and of the other we have instances in the succession of chords observed issuing from certain sounds generated beneath domes, arches, or in caverns, and in the sympathetic sounds and cadences of the Eolian lyre, &c. 1089. The mechanical theory of the sounds of a musical string, or monochord, &c., explains them by the variety of their vibrations or pulsations, and by shewing that different vibrations, which may be sustained separately, may be also sustained simultaneously; and thus accounts mathematically, or through measure, for the variety of the harmonic notes which accompany, or, as we say, constitute, every musical sound, though more apparent to sense in the low or bass, than in the high or treble, tones of instruments. 1090. The simplest of such vibrations takes place when the string, H K of the following figure, assumes the regular harmonic curve, HIK, and pulsates or sounds the full or fundamental note of the string. Fig. 48. H I K 1091. Next in simplicity is that in which a double vibration in opposite directions takes place, dividing the string at the half of its length L, which point, called the Node, is quiescent, and |