Take 1F as a standard.
By 1F, tune 2C, fifth above.
By 1F, tune 1Bm, fourth above.
By 1F, tune 1A, major third above.
By 1F, tune 2D, sixth above.
By 1F, tune 1Am, minor third above.
By 1F, tune 2F, octave above.
By 2C or 2D, tune 1G, fourth or fifth below.
By 1G, 1A or 2C, tune 2E, sixth, fifth or third above.
By 1G or 2E, tune 1B, third above or fourth below.
By 1A or A♯, tune 2C♯, major or minor third above.
By 1A♭, 1B♭ or 1B, tune 2E♭, fifth, fourth or major third above.
By 1B♭, 1B, 2C♯ or 2E♭, 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: