COMPOSITIONAL TEXTS

an iterative rhythm environment

In this article, I would like to delve into a rhythmic concept that deals with iterations of a fixed numerical ratio.

 1/2       

 1/4        

 1/8

Specifically, this post focuses on non-binary rhythmic ratios. Initially, only three layers of a specific rhyhtmic ratio are presented. The quarter notes are used for the middle staff - simply to avoid a more complex notation in these examples.

In the following the sub-ratio is 1:2, which, in terms of an interval, corresponds to an octave. This connection between rhythm and pitch is meant as an orientation, as one can generally imagine an intervallic tension structure more easily. The idea is derived from the essay "wie die Zeit vergeht" (how time passes) by K.H. Stockhausen, where he explores the connection between rhythm and pitch.

Ex.: 2 : 3 - „fifth“   

3/8       (2/8)                

              (3/3)        2/3    

Ex.: 3 : 4 - „fourth“    

4/3        (3/3)                

               (4/4)        3/4    

Ex.: 3 : 5 – „major sixth“   

5/3        (3/3)                 

              (5/5)        3/5

Of course further interations are possible. Along with a bit more complex notation and creating a longer timeperiod before all rythmpatterns allign again on the same beat. 

Ex.: 2 : 3 - „fifth“

27/32        18/32

                      9/16        6/16

                                        3/8        (2/8)

                                                       (3/3)        2/3

                                                                                          2/3        4/9

In this example, it takes 108 quarter notes for the pattern to reapet itself.

Ex.: 3 : 5 - „major sixth“  

25/9       15/9                    

                   5/3       (3/3)                                      

                                 (5/5)       3/5                                                                       

                                                                   3/5       9/25    

A rule that can be derived is that a "slower" level is achieved by multiplying the existing level with the reciprocal of the proportional factor. 

On the other hand, a "faster" level is achieved by multiplying the existing level by the proportional factor. 

Here's a brief suggestion for further ratios that cannot be summarized in binary: 1/5, 2/5, 4/5, 1/6, 5/6, 1/7, 2/7, 3/7, 4/7, 5/7, 6/7 ...etc.    

Ryan Fontane – Nov 2020

211212: The reader will find me using this technique on the prelude of the track "Entwined" written for my ensemble Kylon