A little exercise on syncopation, part 2

In this blog I will apply the same rhythm creation formula as in the previous one but I will take the syncopation below as my starting point.

Here are the three possible positions in a four-four time with rests filling the empty beats.

This is the decisive outline again: *dashed ties* showing the possible connections (the syncopation needs to remain untouched).

And here now is syncopation in position 1 with ties

on / on

on / off

off / on

off /off

Here is syncopation in position 2 in the middle of the measure.

And finally syncopation in position 3.

Clapping the rhythms will give you an idea but can't show the effect of the long notes so an instrument which can sustain notes is better suited (in my test I use big band brass sections but this is a matter of taste of course).

A little exercise on syncopation

Today I was musing: if I had a syncopation in four-four time how many variations are there given that the other notes are not less than a quarter note?
And by syncopation I meant simply an eighth note plus a dotted quarter note like this

If I surround the syncopation by rests one can see that there are 3 possible positions for the syncopation

In order to find out how to fill the remainder of the measure I replaced the rests by quarter notes.
Now comes the interesting bit: the quarter notes can be combined with itself and with parts of the syncopation (of course dependent of the position of the syncopation). Each possible combination has been denoted by a dashed tie in the image below.

Let's look at the first measure with the syncopation at the beginning. There are two possible ties, each tie can be there or not. Simple mathematics will tell you that there are four possibilities altogether how to construct a rhythm.
Here are the four variations in the order:

both ties are there (resulting in a long note and one would probably use a half note in the notation)

the first tie is there, the second is not

the first tie is not there, the second is though (again the last two quarter notes would be denoted properly by a half note)

none of the ties is there

The same can be done for the other two positions of the syncopation and here are the variations analogous to the above.

Since syncopations are used to break up an otherwise monotonous beat focused rhythm these variations show the bandwidth. Some of the rhythms (the ones without any ties where the quarter notes are the beginning or end) are still very beat centric whereas others show a - what I would call - pushing or pulling quality, exactly what the syncopation is trying to achieve.

To find out which one of these one likes best it is ideal to play them multiple times in a row, then the feeling develops.