Having tuned 2E, you can now make your first trial:  the chord of C. If you have tempered your fifths correctly, this chord will come out in pleasing harmony, and yet the E will be somewhat sharper than a perfect major third to C. Now, just for experiment, lower 2E until all waves disappear when sounded with 2C.  You now have a perfect major third.  Upon sounding the chord, you will find it more pleasing than before; but you cannot leave your thirds perfect.  Draw it up again to its proper temperament with A, and you will notice it has very pronounced beats when sounded with C. Proceed with the next step, which is that of tuning 1B, fifth to 1E.  When tuned, try it as a major third in the chord of G. At each step from this on, try the note just tuned as a major third in its proper chord.  Remember, the third always sounds better if lower than you dare to leave it; but, on the other hand, it must not be left so sharp as to be at all unpleasant when heard in the chord.  As to the position of the chord for these trials, the second position, that is, with the third the highest, is the most favorable, as in this position you can more easily discern excessive sharpness of the third, which is the most common occurrence.  When you have gone through the entire system and arrived at the last fifth, 1F-2C, you should find it nearly as perfect as the rest, but you will hardly be able to do so in your first efforts.  Even old tuners frequently have to go over their work a second or third time before all fifths are properly tempered.  By this system, however, you cannot go far wrong if you test each step as directed, and your first chord comes up right.  If the first test, G-C-E, proves that there is a false member in the chord, do not proceed with the system, but go over the first seven steps until you find the offending members and rectify.  Do not be discouraged on account of failures.  No one ever set a correct temperament at the first attempt.

QUESTIONS ON LESSON IX.

    1.  Define the terms, “International Pitch,” and “Concert Pitch.”

    2.  How would you arrive at the most favorable pitch at which to
    tune a piano, if the owner did not suggest any certain pitch?

    3.  What is the advantage in using the continuous mute?

    4.  Tell what is necessary in the tuning of a string to insure it
    to stand well?

    5.  What would result in the major third C-E, if all the fifths, up
    to E, were tuned perfect?

LESSON X.

THEORY OF THE TEMPERAMENT.

The instructions given in Lessons VIII and IX cover the subject of temperament pretty thoroughly in a way, and by them alone, the student might learn to set a temperament satisfactorily; but the student who is ambitious and enthusiastic is not content with a mere knowledge of how to do a thing; he wants to know why he does it; why certain causes produce certain effects; why this and that is necessary, etc.  In the following lessons we set forth a comprehensive demonstration of the theory of Temperament, requirements of the correct scale and the essentials of its mathematics.