Here each triplet fills the time of one-third of a beat; that is, three-sixteenths equal one-eighth, according to the sublime precision of the old notation! But then no such thing as a twenty-fourth note is in use: three twenty-fourths would just do it! This is a part of a vocal exercise. The learner would have to divide each beat into three parts each, unless very familiar with such exercises; and one of these divisions would fall on a rest, another in a prolongation, another in the middle of an eighth note. In the new method see how the crooked places are straightened: --------------- --------------- ----- ----- ----- ----- 1 0 2 3 4 3 2 1 . 2 3 . 4 5 It "sings itself" the moment you look at it, after a little study of this rational notation. Note also that there is no mathematical absurdity here: the division is logical, and yet the air is perfectly expressed in every particular. The mastery of time in music is at best an arduous task, yet teachers of music, as a rule, expect their pupils to learn it incidentally while studying intonation. They give no special drill in pure time at every lesson; and the result is that army of mediocre singers and players who never become able to execute any but the very simplest music at sight. They may know the theory of time, may be able to explain to you clearly the divisions of every measure, but this is not sufficient for the musician: he must decipher his measures with great readiness, precision and rapidity, or he never rises above the mediocre. The ambition to excel without hard labor is the bane of students of the piano especially. It leads them to muddle over music too difficult for them; finally, to learn it after a fashion, so that they may be able to "rattle and bang" through it to the delight of fond relatives and the amazement and pity of severe culture. Not that we should have consideration for all that passes for severe culture and exquisite sensitiveness among musical dilettanti. In no field of art is there so much affectation, assumption and charlatanry as in music. Some years ago a musician in New York of considerable reputation refused to play on a friend's piano because, as he said, it was a little out of tune and his ear was excruciated by the slightest discord. The lady wondered that the instrument should be out of tune, as it was new and of a celebrated manufacturer. She sent to the establishment where it was made, however, and a tuner promptly appeared. He tried the A string with his tuning-fork, ran his fingers over the keyboard, declared the piano in perfect tune, and left. That evening the musician called, and was informed that a tuner had "been exercising his skill" upon the instrument. Thereupon he graciously condescended to play for his hostess, and the sensitiveness of his ear was no longer shocked. She never dared to undeceive him, but mentioned the fact to another musician, a violinist, who exclaimed, greatly