IMPERFECTIONS OF MODERN HARMONY. 511 



lin. The Parthenon and Theseum were to be contemplated as wholes, 

 and therefore all apparently straight lines and plane surfaces were 

 made respectively curved and convex, that the effect might be smoother 

 — less hard and dry. There are, however, these notable differences in 

 the two cases : It was possible for the architectural purist to make 

 line meet line, but for the musician it would prove impossible. For 

 he, working in a tonal system that is a slowly ascending infinite spiral, 

 can not make his lines return into themselves without making delicate 

 modifications. 



Whichever way he proceeds he is led out into infinity ; * but, with- 

 out passing the fourth step, he is 

 compelled to make modifications 

 to reconcile melody with harmony. 

 And whereas the Greek architects 

 made slight variations from ab- 

 stract truth that the effect on the 

 beholder might be heightened, 

 knowing well the peculiarities of I |A27 



the human eye, the musician trusts 



in the inability of the ear to detect 



the modifications he is bound to \ yE8l 



make, and which he hides with 



subtile devices. &c"\^^ ^^^?,'iLH3 



Five modes of proceeding are 

 now to be exemplified to prove that 

 it is imjjossible to observe just proportions, and that the course taken 

 by musicians is the best known : 



1. The errors may be acknowledged and defined, by the employ- 

 ment of some one fixed " temperament," to determine the nature and 

 extent of the deviations. Whether this be Pythagorean or Helmholt- 

 zian, cyclic or non-cyclic, skhismo-cyclic or mesotonic, equal or un- 

 equal, it will have as a matter of course its own peculiar inherent im- 

 perfections. The "equal" temperament is the one universally em- 

 ployed now for piano-fortes and organs. 



2. The errors may be unacknowledged and undefined. In such cases 

 all is left to chance or vague feeling, and the performance may be an 

 ignorant floundering in an open sea of tone, rather than the mathemati- 

 cally accurate rendering as supposed by Helmholtz in the quotation 

 given above. It is true that performers who have practiced long to- 

 gether, who sympathize with one another and with the aims of the 

 composer, and who are deej^ly imbued with the spirit of his work, give 

 artistically good renderings. The soul-state recorded by the composer 

 is impressed upon the auditors. This is the purport of the music, and 

 nothing more seems desired. It transcends all formal, cold measure- 



* See article on " The Modern Piano- forte " in " Popular Science Monthly " for Oc- 

 tober, ISVY, p. 701. 



