144? -® r ' Young's Experiments and Inquiries 



the use of an impracticable instrument, leaves the whole subject 

 precisely where it found it. Kirnberger, Marpurg, and other 

 German writers, have disputed with great bitterness, almost 

 every one for a particular method of tuning. It is not with 

 any confidence of success, that one more attempt is made, 

 which rests its chief claim to preference, on the similarity of its 

 theory to the actual practice of the best instrument-makers. 

 However we estimate the degree of imperfection of two tem- 

 pered concords of the same nature, it will appear, that the 

 manner of dividing the temperament between them does not 

 materially alter its aggregate sum; for instance, the imperfection 

 of a comma in a major-third, occasions it to beat very nearly 

 twice as fast as that of half a comma. If indeed the imperfection 

 were great, it might affect an interval so materially as to destroy 

 its character; as, in some methods of temperament, a minor 

 third diminished by two commas approaches more nearly to the 

 ratio 6 : 7, than to 5 : 6 ; but, with this limitation, the sum of 

 harmony is nearly equal in all systems. Hence, if every one of 

 the twelve major and minor thirds occurred equally often in 

 the compositions which are to be performed on an instrument, 

 it would be of no great consequence, to the sum of the imper- 

 fections, among which of the thirds they were divided : and, 

 even in this case, the opinion of the best practical authors is, 

 that the difference of character produced by a difference of pro- 

 portions in various keys, would be of considerable advantage in 

 the general effect of modulation. But, when it is considered, that 

 upon an average of all the music ever composed, some parti- 

 cular keys occur at least twice as often as others, there seems 

 to be a very strong additional reason for making the harmony 

 the most perfect in those keys which are the most frequently 



