Hi my name is Roger Pell and I’d like to briefly share some insights I have gained when composing poly tempo music.  In the following three repertoires there is a progression of rhythmic developments.  The 1st repertoire explores one member from a dyadic family of polyrhythms, the 2nd introduces the relatives of each family and the 3rd modulates between families suggesting multi tempos.

Rhythm can be regarded as the inference of contrary vibrations. If we rub two sticks together in a certain way the friction will generate enough energy to produce fire, so we know it's a powerful emotive motivator.

Traditionally rhythm syncopates time at one tempo, it does this by the subdivision of its numerator, the denominator informs us of its natural accents, either odd or even. Our proposition asks, what happens when there’s more than one tempo ?

To help answer this question we acknowledge that when a polyrhythm forms a continuum of its self, a second non-identical tempo is established. The interference of these two tempos is what we call a Dyadic Tempo.

All dyadic polyrhythms contain a retrograde which is highlighted by the mirroring of the two shortest durations within the poly called, Ones. We can see this clearly in graphic form, by the example No1 of p7-4.

The top line maps seven fours and the second line four sevens and by drawing perpendiculars from each duration their interference produces a resultant that contains a retrograde which is mirrored by the Ones, b3 and 6d.

To identify this coincidence one tempo is named by letters and the other by numbers.  Listen for the Ones b3 & 6d as we interpret the code of p7-4 as, a2b34c56d7.

In example No2a, the p7-4 pattern is heard across 2 bars in example No2b the guitar from the tune Quarter Septa which is from the 1st repertoire of 5 Duets.