The pitch of a sound depends wholly upon the number of vibrations per
second that produce it; and if one of two sounds consists of twice as
many vibrations per second as the other one, they differ in pitch by the
interval called in music an octave, this latter term merely signifying
the number of intervals into which the larger interval is divided for
the ordinary musical scale. The difference between a high and a low
sound is simply in the number of vibrations of the air reaching the ear
in a given time. The smaller intervals into which the octave is divided
stand in mathematical relations to each other when they are properly
produced, and are represented by the following fractions:--
C D E F G A B C
1 9/8 5/4 4/3 3/2 5/3 15/8 2
[Illustration]
These numbers are to be interpreted thus: Suppose that we have a
tuning-fork giving 256 vibrations per second: the sound will be that of
the standard or concert pitch for the C on the added line as shown on
the staff. Now, D when properly tuned will make 9 vibrations while C
makes but 8; but, as C in this case makes 256, D must 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.