Initialization of Xronomorph Well-Formed Rhythms

Our book did not make it clear how Xronomorph creates the initial polygon for a well-formed rhythm. The papers at the XronoMorph website indicate that the initial polygon for a well-formed rhythm is defined by applying the Euclidean algorithm method to a specified number of long sides of length L and short sides of length s, together with their ratio r  =  L / s. For example, suppose we want 3 long sides of length L and 2 short sides of length s. Then the Euclidean algorithm would go as follows:

L L L , s s   (5 = 3 + 2)

L s L s , L   (3 = 2 + 1)

L s L L s     (this step is not required for Euclidean rhythms, but Xronomorph uses it)

As the following image shows, Xronomorph will set up a well-formed rhythm polygon with sides in the form L s L L s (starting from the top, marked by the green arrow):

 

The red box shows where you can adjust the number of long and short sides. The red arrow at the bottom right shows where you can adjust r. In each case, you click on the number you want to modify, type in the new number and press Enter if needed. The red arrow points to where 2.75 has just been entered for the value of r. The picture shows that the sides of the polygon follow the pattern L s L L s. In one of the papers at the XronoMorph website, there is a discussion of the relationship between well-formed and perfectly balanced rhythms. The discussion shows that perfectly balanced rhythms and well-formed rhythms are not clearly related, in the sense that some perfectly balanced rhythms are well-formed but some are not. Likewise, some well-formed rhythms are perfectly balanced but some are not.