162 



THE NATURE OF MUSIC 



phrases. In the following illustration the forms of 

 all the periods are dual. 



3 13 913 13 91313 515 13 



^ jfM-'Mf-^^-nf-htj; r iJ f I f Ji 



IV IV I IV VI 



In their relative order from shorter to longer the 

 above wave-lines indicate respectively beat-periods, 

 measure-periods (subrhythm), two-measure periods, 

 four-measure periods, lastly the whole or eight-meas- 

 ure period. Just as each shorter period is balanced 

 by another of the same length, just so the larger eight- 

 measure period requires another eight-measure period 

 in order to effect a balance. Thus the repetition of 

 the eight-measure period produces a still greater wave 

 or period of sixteen measures. The possibilities of 

 rhythmic expansion are alone limited by the percep- 

 tive and conceptive faculties. Although our example 

 presents the simplest form of rhythm it suffices to 

 illustrate the subrhythm and its expansion. On the 

 line of least resistance the repetition of an initial 

 subrhythm is spontaneous; however, it is an error to 

 speak of repetition as a principle of form, since it but 

 superficially describes the operation of the actual prin- 

 ciple, equilibrium. The regular alternations and repe- 

 titions of periods long and short are plainly due to the 

 cardinal shaping principle, equilibrium, which is the 

 vera causa of balanced motion and rhythmic unity. 



Appearing in the above example are the numbers 



