702 THE POPULAR SCIENCE MONTHLY. 



note, say " D " on the piano-forte, which has to do duty for all the 

 various kinds of " D," as well as those of " C double-sharp " and " E 

 double-flat," must be so attuned as to form a happy mean between 

 them. 



If, then, in the extremely simple case given above, drawn from 

 the triune system of scales and chords, exemplified in the most insig- 

 nificant compositions, one may be led to doubt and difticulty, it is easy 

 to understand that violinists and others prefer to follow blind rules, 

 leading them to make, for instance, all notes with sharps, higher than 

 their enharmonic equivalents in flats, and vice versa, in elaborate com- 

 positions, that would involve calculations of extreme complexity ; or, 

 in such cases, to follow their own subjective feelings rather than seek 

 justification by mathematical proofs, especially when performing 

 alone their own parts, and thus not called upon to act in conformity 

 with others. In such cases, notes depressed, and having a downward 

 tendency, are more depressed ; and notes raised, which are aspiring, 

 are made more elevated. The interval C : G flat would therefore be 

 contracted, and that of C : F sharp enlarged in the following (fre- 

 quently-heard) expressions : 



G-flat F. F-sharp G. 



C D-flat and C B. 



The " C " in the first progression is also virtually a raised note, and 

 the " C " in the second a depressed note, as may be seen by reference 

 to the scales indicated by the terminating chords. The laws which 

 musicians obey, consciously or unconsciously, in the ordinary routine 

 of composition and performance, are very fascinating, and will ere long 

 be systematized. 



The three scales given above prove that the chord of A-minor, 

 formed with two notes from the chord of C, differs in altitude from 

 the chord of A-minor formed from the chord of the parallel A-major, 

 by depressing the third ; and also that the minor-third from the sec- 

 ond to the fourth note of a scale is smaller than the remaining minor- 

 thirds. These facts seem to have escaped the attention of all writers 

 on harmony, who bewilder students with elaborate arguments respect- 

 ino- the so-called " chord of the added sixth," that undermine their 



own theories. 



Having now drawn attention to the use of the piano-forte, its evo- 

 lution, longevity, ailments, etc., and compared it with the violin with 

 reference to its vitality; having also shown some of the singular facts 

 that are the common experience of piano-forte makers and tuners 

 respecting the human ear, and the system of temperament, which has 

 not been a hinderance to the course of modern art let us now con- 

 sider that remarkable phenomenon, the " peculiarity of the key," which 

 remains, or is acknowledged to remain, by most candid persons, even 

 now that equal temperament is universal, and that the pitch has been 

 gradually raised. 



