make 256x9/8=288.
In like manner G is produced by 256x3/2=384, and C above by 256x2=512,
and so on for any of the others. If other sounds are used in the octave
above or below this one, the number of vibrations of any given note may
be found by either doubling or halving the number for the corresponding
note in the given octave. Thus G below will consist of 384/2=192, and G
above of 384x2=768.

During the past century there has been a quite steady rise in the
standard pitch, and this has been brought about in a very curious and
unsuspected way. The tuning-fork has been the instrument to preserve the
pitch, as it is the best available instrument for such a purpose, it
being convenient to use, and does not vary as most other musical
instruments do. But a tuning-fork is brought to its pitch with a file,
which warms it somewhat, so that at the moment when it is in tune with
the standard that is being duplicated it is above its normal
temperature; and when it cools its tone rises. When another is made of
like pitch with this one, the same thing is repeated; and so it has
continued until the standard pitch has risen nearly a tone higher than
it was in Haendel's time.

The common A and C tuning-forks to be had in music stores, often vary a
great deal from the accepted concert pitch. Such as the writer has
measured have been generally too high; sometimes being ten or more
vibrations per second beyond the proper number. The tuning-forks made by
M. Koeenig of Paris are accurate within the tenth of one vibration, the C
making 256 vibrations in one second.

LIMITS OF AUDIBILITY.

Numerous experiments have been made to determine the limits of audible
sounds; and here it is found that there is a very great difference in
individuals in their ability to perceive sounds. Helmholtz states that
about 23 vibrations per second is the fewest in number that can be heard
as continuous sound; if they are fewer in number than that, the
vibrations are heard as separate distinct noises, as when one knocks
upon a door four or five times a second. If one could knock evenly 23
times per second, he would be making a continuous musical sound of a
very low pitch. But this limit of 23 is not the limit for all: some can
hear a continuous sound with as few as 16 or 18 vibrations per second,
while others are as far above the medium as this is below it. The
limits of sound in musical instruments are about all included in the
range of a 7-octave pianof