fundamental rhythm and seem to play with the hearers by making them feel that one rhythm is superimposed on another. Even in actual modern dance tunes of the best kind the impulse to add something independent to the fundamental rhythm is found in such devices as tying over the last note of a group of three in a valse to the strong beat of the succeeding rhythmic group, while the essential rhythm is maintained by the bass or other instruments of the accompaniment, and composers have even successfully devised such attractive ingenuities as the effect of three long beats being superimposed on two groups of the three lesser beats of the established rhythm. The well-known combination in Mozart’s _Don Giovanni_ of a minuet and a valse each in triple time and a country dance in 4/4 time is one of the most ingenious illustrations of such combined rhythms. The essential basis of all such devices is the sophistication of the obvious, which is the natural impulse of every true composer. Such sophistication is, however, ultimately dependent on the development of harmony into its latest polyphonic phases, which represent the furthest progress of intellectual perception in the races which make use of it. The use of harmonies systematized on the basis of tonalities is the highest development in respect of expression that has been attained in art and it has become a means of widening the possibilities of organization which seems to be unlimited. It is said of a famous English philosopher, whose range of intellectual power was abnormal, that he wept because he thought that the range of melodic variety was exhaustible. He was possibly one of the many whose musical sense is not sufficiently developed to understand progressions of harmony. For, if he had known that every note of every melody is capable of being accompanied by an immense number of different harmonies, probably several dozens apiece, and that each different harmony is capable of altering altogether the expressive character of the melodic note in relation to other notes of the melody, and that the changes in expression not only apply to notes which are contiguous but to notes that are several steps removed, he need not have been distressed at the limitations of the musical scale as developed by European peoples. But this does not by any means exhaust the possibilities of expressive effect, because the same harmony will have a different effect if it is in close order or in open order; if it is in close order in a high part of the scale or a low part of the scale; and the melodic significance is also variable with the rhythmic treatment to which it is subjected. The full force of harmonies to minister to expression was dependent on the systematization of chords on a tonal basis. This had been in the air for a long time before composers definitely grappled with the problem, as may be observed in the splendid use J. S. Bach made of the expressive resources of harmony.