282 



Notices respecting New Books. 



Since the harmonic numbers decrease with the pitch, the author 

 terms this series " falling harmony." 



Thus the major and minor scales appear in a new and interesting 

 light as, so to speak, the inverse or the reciprocal of one another. 



The close connexion between the scales of C major and A minor 

 is familiar, and is emphasized by the fact that the combination of 

 the two gives the chromatic scale. The author discusses the usual 

 method of developing this scale, namely, by means of successive 

 tempered fifths. 



Either the rising or the falling harmony may be employed for 

 the analysis of music : but Protessor Goldschmidt finds it more 

 convenient to adhere to one, the rising harmony, even for pieces 

 composed in a minor key. He analyses and discusses in detail 

 seven examples selected from the works of classical composers. 

 To illustrate the method, we will give his analysis or Haydn's 

 familiar hvmn. 



4 1 



j^^j^ agsr 



J U 





SS 



■ar - £ ■ ' ' ' 7" f I ' . 1 p 



Gott er - hal - te Franz den Kai - ser un - sern gu • ten Kai - ser Franz. 



Pi A A 1— ! 1 1 J 1 - 





-imi 



Gott er- 



-hal 



-te 



Franz 



den 



Kai — ser 



unsern guten 



Kai -ser Franz 



9 a 



b 



a 



c 



b 



a ftTg 



e d c b 



a b g d 



b d 



9 



ft 



a 



9 



c c b 



c b ft g 



e e e a 



9 • 







d 



d 



ft a g 



..ah 



■ 9 9 ft 



9 ■ 







ft 



9 



d d g 



■ • d g 



c c% c% d 



0* 01 



0* 



*1 



0*13 



0*1 



0|13 0*13 0* 



0**10*180* 



0*2 0*12 . 0* 



9 d 



9 



d 



d 



9 



d d g 



c 9 



c 9 9 d 





"V". " 



q d 

 1 







9 

 



c d 

 I 1 



No single cipher occurs which exceeds those included in the third 

 normal row. The importance of the note Q?=3) in this selection 

 may be noticed. 



The next section deals with the physiological and psychological 

 grounds for the harmony of tones. Our knowledge of this inter- 

 esting subject has been enormously advanced by the classical 

 researches of Helmholtz, whose great work Lehre von den Tonemp- 

 fndungen marks an epoch. It is still, however, uncertain how the 

 sensation is conveyed to the brain, or by what means an educated 

 ear is able to distinguish almost minute differences of pitch. 

 Helmholtz considered that the fibres of Corti's organ correspond 

 in a manner to the wires of a pianoforte : others, among them 



