10 On Musical Temperament, 



when a greater number of flats or sharps is introduced, the 

 music can be executed only by striking, in the former case, 

 the sharp of the note next below ; and, in the latter, the flat 

 of the note next above. But as the diatonic semitone is more 

 than half the major, and much more than half the minor tone, 

 if the additional sounds in the common artificial scale be made 

 perfect for one of the above employments, they must be ex- 

 tremely harsh for the other. Hence arises the necessity of 

 adjusting the position of these five inserted sounds so that they 

 may make tolerable harmony, whichever way employed. A 

 change in these will require corresponding changes in the po- 

 sition of the several degrees of the natural scale ; so that it is 

 highly probable that the best scheme of temperament will 

 leave no concord, either of the natural or artificial scale, ab- 

 solutely perfect. 



In adjusting the imperfections of the scale, the three follow- 

 ing considerations have been usually taken into view. 



I. One object to be aimed at is, to make the sum of the tem- 

 peraments of all the concords the least possible. Since expe- 

 rience teaches us that the harshness of a given concord in- 

 creases with its temperament, it is obvious that of two sj'^stems 

 which agree in other respects, the best is that in which the 

 sum of the temperaments is least. 



II. When other things are equal, the best adjustment of the 

 imperfections of the scale is that which diminishes the har- 

 moniousness of all the different concords proportionally. The 

 succession of a worse to a better harmony, is justly regarded 

 by several of the best writers on this subject, as one of the 

 principal causes of offence to the ear, in instruments imper- 

 fectly tuned. 



III. When different chords of the same kind are of unequal, 

 ly frequent occurrence, there is an advantage, cceteris paribus, 

 in giving the greatest temperament to that which occurs most 

 seldom. This important consideration has indeed been ne- 

 glected by Dr. Smith, in the systems which he recommends, 

 both for his changeable and the common fixed scale ; as it is, 

 also, by the numerous advocates of the system of equal semi- 

 tones. But many authors on temperament, and most instru- 

 ment-makers, pay a vague regard to it. Their aim has been, 



