98 



NA TURE 



[Nov. 29, 



The octave is 



"the expression for the notion of identity, unity, or 

 equality with self" 



The fifth 

 "contains acoustically the determination that something 

 is divided within itself, and thereby the notion of duality 

 and inner opposition {stch selbst Entgegengesetsies)." 



The third contains 

 "the notion of identification of opposites ; of duahty as 

 unity." 



Of the scheme of a major key, as derived from triad 

 construction, it is said : — 



" The organic property of amembered whole can never 

 be represented exhaustively, either by symbols and numbers 

 or by words ; it can only be spiritually indicated to intel- 

 lectual feeling, i.e. reason, that meets it half-way 



Now, because this notion has to unite both union and 

 separation, it can only be fulfilled in endlessly continued 

 passage into contrary and comprehension of all oppo- 

 sites. Thus it must be conceived as an infinite process, 

 and consequently as the notion of eternal becoming, living 

 or being real. This is Nature, who, produced as duality 

 from the prime unity {Ufei?theit a/s Zweiheit hervorge- 

 gangen), and busied continually in making her opposites 

 be absorbed into one another, is live being itself and 

 reality." 



This is the sort of way in which harmony is treated ; 

 and the same system is adopted in the latter part of the 

 book in regard to metre and rhythm. Most elaborate 

 explanations, illustrated with tables and diagrams, are 

 given of all varieties of time, rhythm, and accent, and 

 they are all etherealized in the same transcendental style. 

 For example, in regard to four-timed metre, we are told 

 that— 



" It is this inner reconcilement of separation in unity 

 and unity in separation, the completed negation of every 

 negativing excluding element, that speaks to us here in 

 metrical determination as the essence of the triad, but in 

 combinations of notes as the perfection of harmony ; and 

 generally in any guise of phenomenon as the perfected 

 notion of determinate reality." 



But we must, in justice to the book, explain that it is 

 not entirely given up to Hegel. The translator properly 

 remarks that, independently of the theory involved, it 

 contains an account, written by a skilful musician and 

 experienced teacher, of harmony and metre, in which the 

 received rules are explained on general principles, while 

 upon particular points new and unexpected light is 

 frequently cast. This is true, for, though Hauptmann 

 loved Hegel well, he loved music more, and nothing 

 could repress his desire to amplify his explanations upon 

 it. It is quite delightful to find him now and then throw- 

 ing the metaphysics overboard, and breaking out into 

 intelligible common-sense language on the facts and rules 

 of harmony. One can only regret that this sort of thing 

 is not general instead of exceptional. 



We have good precedent for this regret. Hauptmann's 

 book was well known to Helmholtz. He studied it care- 

 fully, made himself master of all its intricacies, and com- 

 mented on many of his predecessor's statements and 

 opinions with much respect. Yet what judgment did he 

 pass upon Hauptmann's work as a whole ? We will give 

 the passage in the original, as it is really a most true and 

 effective criticism. He says (original edition, p. 427) : — 



" Ich kann mich nur dem Bedauern anschliessen, 

 welches C. E. Naumann ausgedriickt hat, dass so viele 

 feine musikalische Anschauungen, welche dieses Werk 

 enthalt, unnothiger Weise hinter der abstrusen Termino- 

 logie der Hegel'schen Dialectik versteckt und deshalb 

 einem grosseren Leserkreise ganz unzuganglich sind," 



It is, indeed, a great pity that so much excellent musical 

 matter, so many " refined musical views," as this work 

 contains, should be hidden in such an atmosphere of 

 impenetrable transcendental fog, and thus rendered 

 inappreciable by any large circle of readers. 



There is another reason which adds seriously to the 

 difficulty of understanding these portions— that is, the 

 use of a complicated system of alphabetical letters in 

 varied types to express musical notes, chords, and 

 passages, instead of the ordinary musical notation. The 

 latter conveys its idea at a single glance ; the former 

 requires mental labour which is most wearisome. It is 

 true the author explains that he wants in some cases 

 greater accuracy than the ordinary notation will give ; 

 but this is obtained at a fearful sacrifice of clearness and 

 intelligibility, and surely the object might have been 

 accomplished in some less repulsive manner. 



It seems odd that the translator, in his elaborate explana- 

 tory introduction, never mentions or notices Helmholtz in 

 any way. One would hardly have expected that in the 

 present day, when the science of music has come to be 

 based chiefly on Helmholtz's investigations, a philo- 

 sophical essay on the subject could have been penned 

 without some allusion to them. There are many passages 

 where the comparison seems invited ; for example, Mr. 

 Heathcote says : " The science of music is concerned 

 more with the form than the materials." This is directly 

 at variance with the work of Helmholtz, who bases all his 

 science on the nature of the materials of music— namely, 

 musical sounds — leaving the form to develop itself there- 

 from. Again, in explaining to us how we are to pro- 

 ceed to learn and follow out the Hegelian system, the 

 translator says : — 



" Therefore, when musical sound is said to be unity, we 

 are not to think of it as existing as it does now, and 

 capable of being distinguished into chords, notes, and 



scales Musical pitch, tone, or quality of sound, 



wh'ch depend upon the triad, must not be thought of as 

 existing before the triad exists, and still less as contributing 

 to the formation of the triad." 



How different this is from the philosophy of Helmholtz, 

 who demonstrates to us that the triad is a product 

 directly springing out of the physical nature of musical 

 sound ! 



To sum up, the book is a very remarkable one, the pro- 

 duct of a great mind, and of a great authority on the sub- 

 ject it treats of. But we should fear that its interest to 

 English readers will be very limited. The Hegelian por- 

 tion of it, although, as the translator remarks, it may 

 serve the metaphysician as an application of this peculiar 

 philosophy to a concrete subject, can be of little use to 

 the musician as an explanation of the principles of his 

 art. And as to the technical musical matter, which is 

 really very valuable, the way to render its value ap- 

 preciable by the public would be to translate it, not 

 merely into English, but into a kind of language with 

 which musicians are familiar, and which ordinary minds 

 would be able to comprehend. W. Pole. 



