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ON HARMONICS. 595 



as well as the general theoryof practical music, is founded. Many prolrx treatises 

 Jiave been written on the subject, but they only contain particular illustra- 

 tions of the application of these principles, together with a few refinements 

 upon -them. The art of composition, however, depends much more on a 

 good taste, formed by habitual attention to the best models, and aided, 

 perhaps, by some little natural predisposition, than upon all the precepts of 

 science, which teach us only how to avoid what is faulty, without in- 

 structing us in the mode of attaining what is beautiful or sublime. 



It is impossible to assign any such proportions foi the twelve sounds thus 

 employed, that they may be perfectly appropriate to all the capacities in 

 which they are used; their number is, therefore, sometimes considerably 

 increased; and in some instruments they may be varied without limit, at the 

 performer's pleasure, as in the voice, in instruments with finger boards, and 

 in some wind instruments; but in many cases this is impracticable, nor 

 could any imaginable alteration make all the intervals perfect, unless 

 every note were varied, whenever we returned to it by steps different 

 from those by which we had left it. The simplest mode of arranging the 

 twelve sounds, is to divide the octave into twelve equal intervals, 

 all the notes being in the same proportion to those which immedi- 

 ately follow them: this is called the equal temperament, because the imper- 

 fection is equal in all keys. In this system of temperament, the fifths, which 

 consist of seven semitones, are a littfe too flat, that is, the interval is a little too 

 small; the minor thirds, consisting of three semitones, are also too flat,and the 

 ,major thirds too sharp. But it has generally been esteemed best to preserve 

 some keys rnore free from error; partly for variety, and partly because some 

 are more frequently used than others : this cannot, however, be done with- 

 out making some of the scales more imperfect than in the equal temperament. • 

 A good practical mode of performing it, is to make six perfect fifths, in de- 

 scending from the key note of the natural scale, and six ascending fifths 

 equally imperfect among themselves. We thus retain a slight imperfection 

 in the scales most commonly used, and make the keys which are most 

 remote from them considerably less perfect. Anoth*er method, which is 

 perhaps somewhat more easily executed, is to make the fifth and third of 

 the natural scale perfectly correct, to interpose between their octaves, the 

 second and sixth, so as to make three fifths equally tempered, and to de- 



