IMPERFECTIONS OF MODERN HARMONY. 



513 



In this case the melody leaves the scale, but returns to it again, 

 as shown by the notes marked [/) which are raised. This method of 

 altering the melody to obtain correct harmony is almost impossible to 

 performers. It being understood that a note repeated or sustained is 

 to be repeated or sustained at the same pitch, that it may become a 

 pivot (ligature) for the harmonies to turn on, and form a standard 

 of measurement. The errors would therefore more often be as fol- 

 lows : 



5. "When the chords are true, the melody is permanently out of 

 proportion. 



Here the ratios of each chord are prefixed to the letters, representing 

 the musical notes, that the harmonies may be readily verified. At the 

 fifth chord the key-note is seen at once to be changed, and the melody 

 therefore to be untrue. Viewed vertically, all is correct ; viewed hori- 

 zontally, errors appear in all four lines. Such music can not be made 

 correct from both points of view. 



No idea is more firmly rooted in the minds of musicians than that 

 of a fixed key-note. AVhenever the pitch is changed the belief is 

 universal that the chords have been out of tune. Even Helmholtz and 

 other scientists are unaware of the fact that perfect harmony requires 

 a moving key-note. It will probably surprise them as much as it 

 would have surprised Ptolemy Philadelphus to learn that the sun is 

 moving in the direction of the constellation Hercules. 



For the solar system to be, as it were, in tune, the sun must move ; 

 for the harmonic system to be in tune, the key-note must move. In the 

 last illustration the pitch of the key-note (C) was depressed in the ratio 

 of 129f : 128. There would be three such depressions made in the first 

 half of the melody, and by the same chords. There is no method by 

 which the sum of the errors made in this direction may be atoned for 

 by errors in the opposite direction. If, on repeating this half, the 

 composer were to adopt the following harmonies, the key-note (C) 

 would rise in the ratio of 63 : 64. 



