ove.
By 1A[b], 1B[b] or 1B, tune 2E[b], fifth, fourth or major third above.
By 1B[b], 1B, 2C[#] or 2E[b], tune 1F[#], major third, fourth, fifth
or sixth below.

As each step is taken in this system, the tone tuned is tested with
any or all of the tones previously tuned.

You will notice that six tones are tuned by the first standard, F.
Therefore, if any error is left in any one of the intervals it exists
in this only and is not transmitted to other tones, if corrected
before such other tones are used to tune by.

The numerous tests possible, early in the system, and the small
compass used, one octave, may be said to be the chief advantages of
the system.

The intervals used are the minor and major third, perfect fourth and
fifth, and major sixth. The thirds and sixths beat from about 7 to
nearly 12 per second. The exact number of beats for each step in the
system may be calculated from the "Table of Vibration Numbers" in
Lesson XIII. For instance, take middle C (2C) at 256, and its major
third, 2E. The exact third, determined by multiplying 256 by 5/4, is
found to be 320. By reference to the table, we find the tempered third
vibrates 322.54. The difference then is 2.54 vibrations per second,
and, knowing that a difference of one vibration from the exact major
third produces 4 beats, we simply multiply 2.54 by 4 and we have
10.16, the number of beats we should hear per second when this third
is tempered correctly. Other intervals may be figured out in like
manner by reference to the various tables given.

It is very doubtful if a beginner could succeed with this system. He
should tune by an easier system until he can hear the beats very
distinctly and judge quite accurately the rapidity of them. Having
acquired this ability, he may try this system and follow it in
preference to others.

In any system used it is well to test your work in the following
manner:

Begin with your lowest major third and strike each third in
succession, ascending chromatically. Of course, each third should beat
slightly faster than the one below it. For instance, in our system of
two octaves, take 1C-E; this third should beat about 5 per second.
Next, take 1C[#]-F, which should beat about 5-1/2 per second. The
beats should increase each test nearly a half beat, or the amount of 5
beats in this octave; hence, 2C-E will beat about 10 per second; or,
using the exact figures, 10.16. After arriving at the last-named test,
2C-E, you m