The persistence of these simple equivalences appears also in the treatment of syncopated measures and of supplementary or displaced accents.  Of the form | >q. q >q. | one reactor says, and his description may stand for all, “This deliberate introduction of a third accent on the last beat is almost impossible for me to keep.  The single group is easy enough and rather agreeable, but in a succession of groups the secondarily accented third beat comes against the first of the next group with a very disagreeable effect.”  This is the case where no pause intervenes between the groups, in which case the rhythm is destroyed by the suppression, in each alternate simple group, of the unaccented phase; thus, | >q. q >q. | alone is pleasant, because it becomes | .q. q; >q % |, but in combination with preceding and succeeding groups it is disagreeable, because it becomes in reality | >q. q; .q % |, etc.  A long pause between the groups destroys this disagreeableness, since the lacking phase of the second subgroup is then restored and the rhythm follows its normal course.

The amphibrachic form, | >q q. q |, is more difficult to maintain than either the dactylic or the trochaic, and in a continuous series tends to pass over into one of these, usually the former.  ’With sufficient pause,’ the reactors report, ‘to allow the attitude to die away,’ it is easily got.  The same inability to maintain this form in consciousness appears when a continuous series of clicks is given, every third of which is louder than the rest.  Even when the beginning of the series is made coincident with the initial phase of the amphibrachic group the rhythmic type slips over into the dactylic, in spite of effort.  In this, as in the preceding type of reaction, if the interval separating adjacent groups be lengthened, the rhythm is maintained without trouble.  The ‘dying away’ of the attitude lies really in such an arrangement of the intervals as will formally complete a phrase made up of simple two-beat units.

The positive evidence which this investigation affords, points to the existence of factors of composition in all rhythms of more than three beats; and a variety of peculiarities which the results present can be explained—­and in my estimation explained only—­on the basis of such an assumption.  I conclude, therefore, that strictly stated the numerical limit of simple rhythm groups is very soon reached; that only two rhythmical units exist, of two and three beats respectively; that in all longer series a resolution into factors of one of these types takes place; and, finally, that the subordination of higher rhythmical quantities of every grade involves these simple relations, of which, as the scope of the synthesis increases, the opposition of simple alternate phases tends more and more to predominate over triplicated structures.