Rhythm.     Initial Interval.   Final Interval
Five-Beat,       1.000             1.386
Six    "         1.000             0.919
Seven  "         1.000             1.422
Eight  "         1.000             1.000
Nine   "         1.000             1.732
Ten    "         1.000             1.014

The alternate rhythms of this series fall into two distinct groups in virtue of the sharply contrasted values of their final intervals or group pauses.  The increased length of this interval in the odd-numbered rhythms is unquestionably due to a subdivision of the so-called unit into two parts, the first of which is formally complete, while the latter is syncopated.  In the case of five-beat rhythms, this subdivision is into threes, the first three of the five beats which compose the so-called unit forming the primary subgroup, while the final two beats, together with a pause functionally equivalent to an additional beat and interval, make up the second, the system being such as is expressed in the following notation:  | .q. q q; >q. q % |.  The pause at the close of the group is indispensable, because on its presence depends the maintenance of equivalence between the successive three-groups.  On the other hand, the introduction of a similar pause at the close of a six-beat group is inadmissible, because the subdivision is into three-beat groups, each of which is complete, so that the addition of a final pause would utterly unbalance the first and second members of the composite group, which would then be represented by the following notation:  | >q. q q; .q. q q % |; that is, a three-group would alternate with a four-group, the elements of which present the same simple time relations, and the rhythm, in consequence, would be destroyed.  The same conditions require or prevent the introduction of a final pause in the case of the remaining rhythm forms.

The progressive increase in the value of the final interval, which will be observed in both the odd-and even-numbered rhythms, is probably to be attributed to a gradual decline in the integration of the successive groups into a well-defined rhythmical sequence.

This subdivision of material into two simple phases penetrates all rhythmical structuring.  The fundamental fact in the constitution of the rhythmical unit is the antithesis of two phases which we call the accented and the unaccented.  In the three-beat group as in the two-beat, and in all more complex grouping, the primary analysis of material is into these two phases.  The number of discriminable elements which enter each phase depends on the whole constitution of the group, for this duality of aspect is carried onward from its point of origin in the primary rhythm group throughout the most complex combination of elements, in which the accented phase may comprise an indefinitely great number of simple elements, thus: