300 LECTURE XXXIII. 



augmentations of their force, they have the same effect as another impulse? 

 which recur in regular succession, and produce a musical note^-w^zh has 



been denominated a grave harmonic. Thus, two sounds in the proportion 

 of 4 to 5, produce, when they are both very low or grave, an audible suc- 

 cession of beats ; but when they are higher or more acute, a grave harmonic, 

 which may be separately distinguished as a third sound by an attentive ear. 

 Those combinations of sounds which produce beats distinctly audible, have 

 in general a harsh and coarse effect, and are called discords ; but those of 

 which the vibrations are so related, as to have a common period after a few 

 alternations, and which may be observed to produce a third sound, consti- 

 tute concords, which are in themselves the more perfect as the common 

 periods are shorter. (Plate XXV. Fig. 353.) 



The natural association of the secondary sounds, which generally ac- 

 company almost all musical notes, serves, in some measure, as a foundation 

 for the science of harmonics, the same sounds as are thus frequently con- 

 nected in nature, being found to be agreeable when united by art. But it 

 appears to depend still more immediately on a love of order, and a predi- 

 lection for a regular recurrence of sensations, primitively implanted in the 

 human mind. Hence, when two sounds are heard together, those propor- 

 tions are the most satisfactory to the ear which exhibit a recurrence of a 

 more or less perfect coincidence at the shortest intervals, expressed by the 

 smallest numbers of the separate vibrations ; for though we cannot im- 

 mediately estimate the magnitude of the vibrations, yet the general effect of 

 a regular or irregular succession necessarily produces the impression of 

 sweetness or harshness. The same sounds as form the best accompaniment 

 for each other, are also in general the most agreeable for melodies, consist- 

 ing of a succession of single notes ; their intervals are, however, too large 

 to be sufficient for the purposes of music, and they require to be mixed with 

 other sounds which are related to them in a manner nearly similar. 



The same constitution of the human mind which fits it for the perception 

 of harmony, appears also to be the cause of the love of rhythm, or of a re- 

 gular succession of any impressions whatever, at equal intervals of time. 

 Even the attachment to the persons and places to which we are accustomed, 

 and to habits of every kind, bears a considerable resemblance to the same 

 principle. The most barbarous nations have a pleasure in dancing ; and 

 in this case, a great part of the amusement, as far as sentiment and grace 

 are not concerned, is derived from the recurrence of sensations and actions 

 at regular periods of time. Hence not only the elementary parts of music, 

 or the single notes, are more pleasing than any irregular noise, but the 

 whole of a composition is governed by a rhythm, or a recurrence of periods 

 of greater or less extent, generally distinguished by bars, which are also the 

 constituent parts of larger periods, and are themselves subdivided into 

 smaller. An interruption of the rhythm is indeed occasionally introduced, 

 but merely for the sake of contrast ; nearly in the same manner as, in all 

 modern pieces of music, discords are occasionally mixed with concords, in 

 order to obtain an agreeable variety of expression. 



In a simple composition, all the intervals are referred to a single funda- 

 mental or key note. Thus, any air which can be played on a trumpet or 



