466 

skill in physical and physiological research with the 
technical knowledge of a trained musician, he stands 
absolutely alone. It need therefore surprise no one that 
the volume before us, the first edition of which was 
published in 1862 as the fruit of eight years’ work, has 
practically revolutionised the subject with which it deals. 
He begins by completely clearing up the nature of the 
guality (timbre) of musical sounds. He fixes his reader’s 
attention on the Aarmonics which previous observers had 
recognised as accompanying a fundamental note. These, 
he shows, are no isolated phenomena, but invariable con- 
comitants of nearly all musical sounds. In fact, what 
appears to be a simple note of any assigned instrument, 
is really a composite sound consisting of a number of 
different tones, all, however, members of a series con- 
nected together by a simple law. The gvwadity of the 
sound depends on the relative intensities in which these 
partial-tones are present in the whole mass of sound 
(Kang) heard. Helmholtz illustrates his theory by deter- 
mining the relative intensities of the audible partial-tones 
produced by the principal kinds of musical instruments, 
and also those corresponding to the different vowel-sounds 
of the human voice. He has also invented an apparatus 
by which the most important members of the complete 
series of partial-tones corresponding to a fundamental 
tone can be sounded with any assigned relative 
intensities, and which is capable of producing a tolerably 
close imitation of many sounds differing widely from 
each other in quality. These investigations occupy the 
first part of the work. 
In the second part the nature of the difference between 
consonance and dissonance is explained, and thus a 
problem which has baffled natural philosophers since the 
time of Pythagoras finally solved. Here, again, the key 
to the solution is a perfectly well known phenomenon, the 
real significance and scope of which it was reserved for 
Helmholtz to recognise. Intermittent noises called dcats 
had been observed whenever two notes nearly, but not 
quite, in unison with each other, were sounded together. 
Helmholtz asks what becomes of these beats when they 
are so rapid that the ear can no longer distinguish them 
as separate sounds. It had been supposed since the time 
of Young that they coalesced into athird musical sound, 
and thus formed the combination ones discovered as 
early as 1740 by a German organist named Sorge, but 
more generally known as Zartinz’s tones. Helmholtz 
proves that Young’s view is erroneous. The beats never 
coalesce into a musical sound, but when they cease to be 
individually distinguishable, produce the sensation which 
we call discord. 
This fact, taken in connection with the composite charac- 
ter of musical sounds, leads at once to Helmholtz’s theory 
of consonance and dissonance. When two notes of dif- 
ferent pitch are sounded, we have two series of partial- 
tones co-existing. If no member of the one series pro- 
duces deats with any member of the other, the interval be- 
tween the fundamental tones of the two sounds is an abso- 
lute consonance. If, on the other hand, beats ave so 
produced, the consonance ceases to be absolute, and may 
be classed as a good or an imperfect consonance, or pass 
into a dissonance, according to the amcunt of discord in- 
volved in the combination. Helmholtz goes through the 
ordinary scale, and classifies the different intervals accord- 
NATURE 

[April 13, 1871 

. 
ing to the above theory, his results tallying perfectly with 
those of the best writers on harmony. For the case of 
the comparatively unimportant class of sounds which have 
no upper-tones, Helmholtz employs a different method, 
which need not be detailed here. It is interesting to ob- 
serve that his theory not only confirms some of the ordi- 
nary rules of musical composition, but is able to deduce 
principles which, though actually adopted by great masters, 
Mozart for instance, have never been explicitly stated by 
any theoretical writer. The third and last part of the 
work discusses the construction of musical scales, and the 
relation of each to its key-note. In this investigation zs- 
thetical considerations necessarily assume an importance 
which they could not claim in the two earlier purely scien- 
tific parts of the work. As, moreover, musical technicali- 
ties of much complexity abound throughout the inquiry, it 
is not possible to give a popular 7ésusé of the general re- 
sults obtained in the third part. 
The above is the most meagre outline of the subjects 
treated in the “ Tonempfindungen.” Indeed it is abso- 
lutely hopeless, within any reasonable limits, to try to 
convey an idea of the thoroughness, the laborious accu- 
racy, the wonderful many-sidedness which appear on 
every page of it. The author, though a great mathe- 
matician, is fortunately too great an experimentalist to 
allow the laws of nature to figure as mere examples of the 
integration of differential equations, or as but affording 
subject-matter for new mathematical conundrums. Each 
acoustical law is thoroughly explained in popular language, 
with the most attractive richness and variety of illustra- 
tion, a method of treatment infinitely refreshing to a 
student who has hitherto experienced only the husks of 
our arid examination-ridden manuals. All details of cal- 
culation are relegated to an appendix, and, though mathe- 
matics has its due honour given it, as a science absolutely 
indispensable for thorough independent mastery of any 
branch of physics, the most effective practical discourage- 
ment is given to the pedantic notion that no valuable 
knowledge can be gained without it. We may well doubt, 
indeed, whether the long exclusive domination of theory 
has made anything beyond mathematical symbuls really 
understood. Cambridge honour-men will know what we 
mean by saying that an average wrangler, if asked what a 
wave was, would probably unhesitatingly answer— 
a2 IK 
“asin zt ut—x),” 
and refuse to produce any further explanation. We desire 
for works like the “Tonempfindungen” a triumph in this 
country over English books “adapted for writing out in 
examinations” as decisive as the victory of the German 
armies on the soil of France. SEDLEY TAYLOR 


OUR BOOK SHELF 
A Monograph of the Alcdinide, or Family of King- 
Jishers. By R. B. Sharpe, F.L.S., &c. Librarian to the 
Zoological Society of London. 4to. (Published by the 
Author. 1868—1871.) 
THIS work reflects the highest credit upon its author, and 
will establish his reputation as an Ornithologist. Very 
few monographs published in England are so entirely 
satisfactory as this one, for not only have the several 
parts appeared regularly during the last three years, but 
the concluding double number just issued contains a 
copious and well-written introductory chapter on classifi- 
