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THE
MUSIC TRADE
REVIEW
13
OuTTECHNICAL DEPARTMENT
FUNDAMENTAL TONES OF SOLID BODIES.
Mr. A. Shiel, of Burlington, Mo., sends me
the following interesting letter, which I shall try
to answer adequately, though briefly:
"Editor Technical Dept., Dear Sir:—I am a sub-
scriber of the Music Trade Review and take note
of your department. If it is permissible, I should
like to ask a question. I observed an article
which I have cut out of the Review on the key-
note or dominant note of buildings. For instance,
the dominant note of the Metropolitan Life Build-
ing is C; the vibrations of which is claimed would
disintegrate the building within two weeks, and
the article says further the dominant note of the
Trinity Building is E, the Terminal Building is
F sharp, and so on. I think this an interesting
question on the power of vibratory force and
would like a further explanation and to know
how the dominant or key note is found?"
Any solid body is subjected to the influence of
external forces acting upon it. So far as we are
aware, the forces which may act upon any solid
body tend to assume a vibratory motion, frequently
of regular periodicity. Thus the various transfor-
mations of energy which manifest themselves as
light, heat, electricity, sound, etc., are all due to
periodical motions of the universal ether, at vary-
ing frequencies. Now, it is plain, by well known
physical laws, that an accumulation of small
shocks will equal in effect a single shock, or ap-
plication of energy, equivalent to the sum of the
series of small shocks. Further, since all bodies
which are in a state of compression or tension are
particularly susceptible to the impress of external
forces, and since, further, all such bodies may, and
in fact must, partake of some periodic vibratory
motion, due to their state of compression or ten-
sion, it is plain that in every such solid body there
will be some particular frequency of periodic vi-
bration proper to it; such frequency depending
upon the factors of mass, density and compression
or tension. Hence, the action of external forces
upon such bodies must ever tend to produce vibra-
tory motions proper in their frequency to the
fundamental frequency imposed by the conditions
aforementioned. And since an accumulation of
small forces so acting will in time, by the con-
tinual accretion of their shocks, produce a cumu-
lative effect of any imaginable magnitude, it is
plain that, if the fundamental vibration period of
any solid body be determined, and if an aerial agi-
tation of identical frequency be permited to act
thereupon—as by the continuous playing of a
musical tone corresponding in frequency—the
cumulative effect of the transmission of the per-
iodic aerial motions to the solid body of similar
frequency will induce a continually greater and
greater response so that, in course of time, the
vibration will communicate itself so powerfully to
every portion of the solid body as to wreck it
entirely; a condition which would probably super-
vene in the case of a building, for instance, long
before actual molecular disintegration could set in.
Could the body be maintained in shape for a suf-
ficiently great length of time, the molecular in-
ternal vibration, continually increasing in ampli-
tude, would, theoretically at least, induce a mole-
cular disintegration.
With regard to the matter of determining the
fundamental pitch of a structure, it will be ob-
served that the continual action of any force, no
matter whether this have a similar, or indeed any,
periodicity, will tend to induce a response to the
accumulation of shocks, the nature of which will
be determined by the periodicity of the structure.
Hence the continual action of wind on a building,
though it will not wreck or disintegrate the struc-
ture, will set it into its proper fundamental vibra-
tion. A steel-frame building, which is in one piece
practically from top to bottom, will naturally re-
spond very rapidly and intensely. Now, if one
carefully notes the pitch of the sound which is in-
duced by the vibration of a steel structure, as by
listening near a steel pillar in the basement, or in
the steel framing at the very top, one may de-
termine, with some approach to accuracy, the vibra-
tory frequency of the structure, and hence its
fundamental tone. It should, however, be noted
that there will always be a vast series of partial
tones coincident with the fundamental, and in-
duced by the simultaneous vibration of segments
of the structure. The fundamental will, of course,
be the lowest tone. My personal impression,
founded on observation, is that the fundamental
tone of the Metropolitan Tower in New York is
Al, two octaves below the middle A. When one
stands on the observation gallery of the Metropoli-
tan Tower, and listens to the roar and hum of
noises ascending at mid-day from Madison Square,
there arises, after a time, an unmistakable funda-
mental, obviously a complex of all the vibratory
motions going on below. In connection with the
low but distinct hum of the sound due to the vibra-
tion of the tower, one hears the sound of A 2,
the hum of the building seeming to provide a sub-
octave to this. I have made no observations as
yet on the Trinity or Terminal buildings.
THE TEMPERAMENT METHOD.
I had intended this week to make a general
reply to the position so ably assumed and defended
by Mr. Hale of Boston, in the article from his pen
published in this department of August 19th and
August 26th. Before beginning to write this, how-
ever, I received the following communication from
Los Angeles. The writer, Fred Very, takes a posi-
tion similar to that, assumed by Mr. Hale. I shall
print his remarks and then add some comments
which may tend to clear up my own position in
the matter. Mr. Very says:
"Being so far from the scene of action, some
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one may already have demolished the position
taken in your article in The Review of July 29th,
with reference to the best method of setting equal
temperament. I read the first seven paragraphs
of your article with much satisfaction. The re-
marks therein on equal temperament would seem
to be so obvious as to make them unnecessary as
a matter of argument or information. However,
we all known well enough that the latter is not
the case, as there seems to be an indifference and
lack of information on the subject which is well
nigh incredible.
"In view of the lucid statements in the first
seven paragraphs of your article, the statement in
the eighth paragraph comes as a surprise. The
only real question for discussion is on the practical
and accurate method of setting a temperament as
absolutely equal as the human ear can achieve.
It seems to me to be an obvious statement that
this cannot be done by fourths and fifths alone.
The thirds, major and minor, and the major
sixths, must be scientifically accurate before the
temperament is equal. The order in which the
tuner goes about it depends, of course, upon his
training, preference and habit. It makes no dif-
ference which he takes first, the fifths or the
thirds, so long as he gets them all correctly tuned.
"However, I will call attention to the fact that
the thirds are particularly useful if the tempera-
ment is set in the octave from C in the bass to
middle C. Their rate of wave interference is there
sufficiently slow to be plainly audible and easily
compared, and fast enough accurately to indicate
the slightest change in sharping or flatting. In
the latter respect, the thirds test is much more
sensitive than that of fifths, since the latter are
tuned so nearly perfect that the wave interference
is very slow. Hence the fifths do not show a
change of disturbance so quickly as the thirds,
which are tuned further from perfect, and so beat
more rapidly.
"I have found, as a matter of fact, that if the
lowest thirds (C-E) in the octave above men-
tioned is tuned so as to beat five times per second,
and each ascending third is tuned with a perfectly
graduated increase of speed to the highest third,
so as exactly to take up the 'wolf (as it was
originally called), the fourths and fifths will test
correctly.
"I will take no more space at present to amplify
the subject, but think that the foregoing is enough
to indicate a solid foundation for an argument that
there cannot be two methods in theory, for laying
an equal temperament. An equal temperament re-
quires every interval, major and minor third,
fourth, fifth and major sixth, to be accurately
tuned according to a system which makes one in-
terval as good as another. And if there is a flaw
at any point in the system, the temperament is not
equal. There must not be a little portion more
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