, a right line connecting the two extremes of an arch; so called from its resemblance to the chord or string of a bow; as AB, which is common to the two parts or arches ADB, AEB that make up the whole circle. The chords have several properties:

1. The Chord is bisected by a perpendicular CF drawn to it from the centre.

2. Chords of equal arcs, in the same or equal circles, are themselves equal.

3. Unequal Chords have to one another a less ratio than that of their arcs.

4. The chord of an arc, is a mean proportional between the diameter and the versed sine of that arc.

Scale or Line of Chords. See Plane Scale.


, or Cord, in Music, denotes the string or line by whose vibrations the sensation of sound is excited; and by whose divisions the several degrees o tune are determined.

To divide a Chord AB in the most simple manner, so as to exhibit all the original concords. |

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.

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Entry taken from A Mathematical and Philosophical Dictionary, by Charles Hutton, 1796.

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CHEYNE (George)