384 
octave, twice the velocity of the fundamental ; the twelfth, which 
is three times; the fifteenth, or double octave, four times ; the 
seventeenth, five times, and so on, always an acceleration by 
uniform addition. In the examples taken from the compilation 
of Dr. Brewer, the echo-tones go beyond all law of harmonic 
progression, and must be accounted for as belonging to other 
classes of tones, if the data can be relied upon, seeing that some 
instances are questionable as to authority, and others are beyond 
proof. The Bedgebury Park instance may be taken as proved ; 
it is simple, and attested by living authority. Who will vouch 
for the other instances as evidence? The question is not put to 
cavil, but because of the dubiousness of the possession by the 
several recorders of the necessary qualification for an accurate 
estimate of the phenomena recorded. 
Musical people of any pretension to critical power in these 
matters are generally ‘‘ self-centered,” each individual considers 
himself competent to pronounce judgment on “ pitch,” yet the 
delusiveness of this belief would be testified to by none more 
readily than by men who are daily engaged in tuning and in 
estimating minute relations of the invisible geometry denomi- 
nated ‘‘ pitch.” Notwithstanding long experience and daily prac- 
tice, no sooner does any question arise out of ordinary routine 
than they hesitate to depend on judgment alone, but resort to 
comparison with some fixed pitch already ascertained, and by 
this means prove themselves to be frequently at fault when least 
expecting it. Harmonic sounds are difficult to judge of, they lie 
at wide intervals, are frequently sharp, and if pure and faint, the 
ear is as liable to be deceived by an apparent lowness as it is with 
pure ground-tones. Fineness of ear for perception of niceties of 
pitch is by no means a common endowment, and where it exists, 
does not certify a fine musical organisation. Pitch bears re- 
lation to musical tune and to quality of tone similar to that 
which geometry bears to figure drawing and to painting. In 
rare instances only are the faculties for each associated in fair 
proportion, and frequently the possession of one power seems to 
exclude or override the others. Some men are gifted in this 
respect, and will tell you the pitchnote of a button, or a pencil, 
or a pin, as accurately as they will the notes of a song; or will 
discriminate, without hesitation, every note in a series of com- 
plicated chords with a skill almost as sure as instinct. 
Professor Tyndall introduced the term ‘‘ over-tones” in con- 
nection with “harmonic ;” more recently, in Helmholtz’ Lec- 
tures, Mr. Ellis has substituted ‘‘ partial tones ;” and Mr. Sedley 
Taylor adopts the same. This is a pity, for there is something 
incongruous in the idea of ‘‘partial tones” which yet are com- 
plete whilst component, and Tyndall’s term “‘ over-tones”’ is far 
more expressive. 
The question of harmonic force, in which probably lies the 
explanation of the Bedgebury echo, came before me a few days 
since in experiments made to obviate, if possible, the wavy 
unsteadiness common to stopped pipes with high-cut mouths. 
Many variations were made without useful results. On with- 
drawing to some few yards’ distance from the pipe into a recessed 
doorway, it was observable that the fundamental tone com- 
pletely vanished, and the first harmonic, the twelfth, came 
into prominence instead of it, although you had only to step a 
yard forward to become again aware of the continued co-exist- 
ence of the fundamental. On comparing this segregated twelfth 
with a corresponding note in the scale of the standard pitch of 
the organ, it was found to be decidedly too sharp, and thus the 
real cause of the waviness of tone was discovered, thereby saving 
many experiments ina false direction. 
Several works now give elaborate analyses of harmonic 
tones; Mr. Sedley Taylor's “Sound and Music” is the 
last most useful addition, and supplies much previously want- 
ing. In no work, however, do we meet with any defi- 
nite statement as to the causation of harmonic tones; yet 
it seems necessary for the full understanding of their nature 
and of the relation they bear to the instruments producing 
them that the mode of their origination should not be left 
unheeded. The conclusion derived from my own investigations 
is that the harmonics of musical instruments have their origin 
solely in the surplus energy of the generating force over and 
above that necessary to produce the fundamental tone ; this 
superabundant vigour finds its outlet in accessory vibrations, 
and the harmonics are the escape valves for securing to the fun- 
damental tone freedom from fluctuations to which otherwise it 
would succumb, When the vibrating force is inadequate to 
waken the ground-tone of an organ pipe it settles down into the 
harmonic nearest related to its power ; the tone may be consi- 
NATURE 
[Sepd, 11, 1873, 
dered as surplus energy, since it is disproportionate'to its work, 
and only becomes harmonic because it falls short of the funda- 
mental after which it is striving. Except in this relation we 
should regard it as ground-tone. When a pipe is overblown, 
the harmonics maintain themselves through the excess of energy 
to the complete exclusion of the fundamental, and they are sharp 
to the regulated pitch of the pipe. Harmonic tones when thus 
produced independently have considerably more intensity than 
the normal tones of pipes of corresponding pitch. In all the- 
orchestral wind'instruments it is the higher notes that require 
greatest wind-force for their production ; the clarionet alone dif- 
fers as respects a certain range of its high notes, where the reverse 
is the case, the force being considerably-less than for the lower 
range, but the structural conditions of the instrument sufficiently 
account for the peculiarity. 
The experiment with the stopped pipe previously described 
clearly shows the penetrating power of accessory tones, and that 
whilst the fundamental occupies the ear by its volume, the 
harmonic has the strongest vitality even in its associated con- 
dition. In view of these facts we may reasonably infer that the 
“octave echo” in Bedgebury Park is the reflected harmonic 
heard alone ; still it would be well to prove it in the manner 
suggested. That the voice was returned from a plantation 
“* across a valley,” gives intimation of a distance favourable to 
the loss of the fundamental tone in the depths of the valley ; and 
that ‘‘ the original sound required to be loud and rather high” 
is an additional assurance of the presence of harmonic vigour in 
the vocal tone. 
A remarkable instance of echo freaks within my own experi- 
ence is well timed to be spoken of here. At the bottom of my 
garden there is a meadow, then a double row of houses with a 
high railway embankment at the end, and a wall rising beyond 
that. About two months ago, whilst looking over the meadow 
at the clouds of sunset, the sound of a band in the distance came 
upon me, and, immediately following, the sound of another and 
more demonstrative band from an opposite direction, giving pre- 
diction of horrible discord. Strange to say, although the two 
bands were playing most noticeably different melodic phrases, 
there was no conflict ; one band seemed to be the symphonic 
accompaniment of the other, and there was a peculiar charm in 
the effect, causing regret that the music should come to a natural 
end. Knowing that the first band was echo-music, there was at 
once a singularity to attract attention, how to account for the 
precedence of that which shouid be secondary? but the greater 
puzzle was to understand how it came to pass that the music was 
different, so that whilst listening the illusion of a distinct band 
was difficult to dispel, doubts arose about Echo having any voice 
in it at all, only that from time to time the pauses between the 
phrases showed the /o//owing of the form upon the shadow. Re- 
flection upon the matter afterwards furnished the probable ex- 
planation. The distance of the place of echo was approximately 
between six and seven hundred feet from the source of the sounds, 
my standing place being at about one-fourth of the distance ; 
between me and the band three houses intervened, over which 
the music came to me, whilst the terrace on which the band was 
stationed opened freely on to the meadow ; thus Echo received the 
music earliest by reason of the unobstructed passage, and her ren- 
dering was that of natural selection, the most vigorous tones, 
and the penetrating harmonics, whatever had most living power, 
infused by the players and sustained by the characteristics of the 
instruments, all these reached her and rose again in perfect 
accord with the original harmony, whilst all the other notes, 
those of low vibrating power and of inferior stamina, were lost 
by the way. It should also be noted that observation afterwards 
of the angle of incidence and positions of the band and of the 
listener showed that the course of the sound waves on their 
way to Echo was in front of a detached line of cottage buildings, 
then passing into the enclosed space between the double row of 
houses up to the embankment, the recourse being by the Jack of 
the cottage buildings, across gardens and the meadow to the 
listener. Doubtless the singular vividness of the phenomena 
was due in great measure to the state of the atmosphere, which 
at the time was peculiar, the western sky heavy with gorgeous 
clouds, and the air silent and sultry. The relation which the 
organ-pipe experiment first detailed has to the theoretical solu- 
tion here offered will be readily perceived; and but for the 
support afforded by it one could hardly have ventured on the 
statement and the explanation, which else would have appeared 
to be, the one unreal, and the other fanciful. 
August 25 HERMANN SMITH 
