Hutton, Charles Mathematical and Philosophical Dictionary 1795

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277

Divide the given line into two equal parts at C; then subdivide the part CB equally in two at D, and again the part CD into two equal parts at E. Here AC to AB is an octave; AC to AD a fifth; AD to AB a fourth; AC to AE a greater third, and AE to AD a less third; AE to EB a greater sixth, and AE to AB a less sixth. Malcolm's Treatise of Music, ch. 6. sec. 3. See Monochord.

To find the number of Vibrations made by a Musical Chord or String in a given time; having given its weight, length, and tension. Let l be the length of the chord in feet, 1 its weight, or rather a small weight fixed to the middle and equal to that of the whole chord, and w the tension, or a weight by which the chord is stretched. Then shall the time of one vibration be expressed by 11/7√l/(32 1/6w), and consequently the number of vibrations per second is equal to 7/11√(32 1/6w./l)

For example, suppose w = 28800, or the tension equal to 28800 times the weight of the chord, and the length of it 3 feet; then the last theorem gives 354 nearly for the number of vibrations made in each second of time.

But if w were 14400, there would be made but 250 vibrations per second; and if w were only 288, there would be no more than 35 16/45 vibrations per second. See my Select Exerc. prob. 21. pag. 200.

, in Music, is used for the union of two or more sounds uttered at the same time, and forming together a complete harmony.

Chords are divided into perfect and imperfect. The perfect chord is composed of the fundamental sound below, of its third, its fifth, and its octave: they are likewise subdivided into major and minor, according as the thirds which enter into their composition are flat or sharp. Imperfect chords are those in which the sixth, instead of the fifth, prevails; and in general all those whose lowest are not their fundamental sounds.

Chords are again divided into consonances and dissonances. The consonances are the perfect chord, and its derivatives. Every other chord is a dissonance. A table of both, according to the system of M. Rameau, may be seen in Rousseau's Musical Dictionary, vol. 1, pa. 27.

, the art of delineating or describing some particular country or province.

This differs from geography as the description of a particular country differs from that of the whole earth: And from topography, as the description of a country differs from that of a town or a district.

, a species of music which proceeds by semitones and minor thirds. The word is derived from the Greek xrwma, which signifies colour, and perliaps the shade or intermediate shades of colour, which mingle and connect colours, like as the small intervals in this scale easily slide or run into each other.

Boethius and Zarlin ascribe the invention of the chromatic genus to Timotheus, a Milesian, in the time of Alexander the Great. The Spartans banished it their city on account of its softness. The character of this genus, according to Aristides Quintillianus, was sweetness and pathos.

, is that part of optics which explains the several properties of the colours of light, and of natural bodies.

Before the time of Sir I. Newton, the notions concerning colour were very vague and wild. The Pythagoreans called colour the superficies of bodies: Plato said that it was a flame issuing from them: According to Zeno, it is the first consiguration of matter: And Aristotle said it was that which made bodies actually transparent. Descartes accounted colour a modification of light, and he imagined that the difference of colour proceeds from the prevalence of the direct or rotatory motion of the particles of light. Grimaldi, Dechales, and many others, imagined that the differences of colour depended upon the quick or slow vibrations of a certain elastic medium with which the universe is silled. Rohault conceived, that the different colours were made by the rays of light entering the eye at different angles with respect to the optic axis. And Dr. Hooke imagined that colour is caused by the sensation of the oblique or uneven pulse of light; which being capable of no more than two varieties, he concluded there could be no more than two primary colours.

Sir I. Newton, in the year 1666, began to investigate this subject; when finding that the coloured image of the sun, formed by a glass prism, was of an oblong, and not of a circular form, as, according to the laws of equal refraction, it ought to be, he conjectured that light is not homogeneal; but that it consists of rays of different colours, and endued with divers degrees of refrangibility. And, from a farther prosecution of his experiments, he concluded that the different colours of bodies arise from their reflecting this or that kind of rays most copiously. This method of accounting for the different colours of bodies soon became generally adopted, and still continues to be the most prevailing opinion. It is hence agreed that the light of the sun, which to us seems white and perfectly homogeneal, is composed of no fewer than seven different colours, viz red, orange, yellow, green, blue, purple, and violet or indigo: that a body which appears of a red colour, has the property of reflecting the red rays more plentifully than the rest; and so of the other colours, the orange, yellow, green, &c: also that a body which appears black, instead of reflecting, absorbs all or the most part of the rays that fall upon it; while, on the contrary, a body which appears white, reflects the greatest part of all the rays indiscriminately, without separating them one from another.

The foundation of a rational theory of colours being thus laid, the next inquiry was, by what peculiar mechanism, in the structure of each particular body, it was fitted to reflect one kind of rays more than another; and this is attributed, by Sir I. Newton, to the density of these bodies. Dr. Hooke had remarked, that thin transparent substances, particularly soap-water blown into bubbles, exhibited various colours, according to their thinness; and yet, when they have a considerable degree of thickness, they appear colourless. And Sir Isaac himself had observed, that as he was compressing two prisms hard together, in order to make their sides (which happened to be a little convex) to touch one another, in the place of contact they were