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of the meafures of Mr. Derham and M. Caflini is 34 French, ■ or 36 Englifh feet in a fecond. According to this laft mea- fure, the velocity of founds when the wind is ftill, is fettled at the rate of a mile, or 5280 Englifh feet, in 4 T y^".
UNDULATION, or Beat, in mufic, is ufed for that rat- tling, or jarring of founds, which is obferved, chiefly, when difcordant notes are founded together. The phenomenon is more fully defcribed thus, by Dr. Smith ■ : In tuning mufical inftruments, efpecially organs, it is a known thing, that while a confonance is imperfect, it is not fmooth and uniform, as when perfect, but interrupted with very fenfible undulations or beats \ which, while the two founds continue at the fame pitch, fucceed one another in equal times, and in longer and longer times, while either of the founds approaches gradually to a perfect confonance with the other, till at laft the undulations vanifh, and leave a fmooth, uniform confonance. — [ s Harmonics, p. IG7.J This learned author obferves farther, that quicker undula- tions are beats, and are remarkably difagreeable in a concert of ftrong, treble voices, when fome of them are out of tune ; or in a ring of bells ill tuned, the hearer being near the fteeple; or in a full organ badly tuned. Nor can the beft tuning wholly prevent that difagreeable battering of the cars with a conftant rattling noife of beats, quite different
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from all mufical founds, and deftrefliive of them, and chieflv caufed by the compound flops called the cornet and fefqui- alter, and by all other loud flops of a high pitch, when mixed with the reft. But if we be content with compofiti- ons of unifons and odlaves to the diapafon, whatever be the quality of their founds, the beft manner of tuning will ren- der the noife of their teats inoffenfive, if not imperceptible. The Doctor has with great ingenuity deduced the theory of thefe undulations from his principles, and has applied his doctrine to the tuning of inftruments ; by which he has (hewn, that a perfon of no ear at all for mufic may foon learn to tune an organ, according to any propofed tempera- ment of the fcale, and to any defired degree of exaftnefs, far beyond what the fined ear, unaffifted by theory, can poffibly attain to. This may be done by counting the num- ber of undulations in a certain time, fuch as 15 feconds. See the treatife before cited, Prop. xx. p. 215. and the ta- ble, p. 244. Plate 20.
From this ingenious theory the learned author has demon- ftrated feveral errors in what Monfieur Sauveur has delivered concerning thefe undulations or beats. See Harmonics, Scho- lium 2. p. 115.
In the fame treatife we find fome curious obfervations re- lating to the analogy of audible and vifible undulations. See p. 128, 273.
FINIS.
