NRT – Cyclic Transformations

In some passages of music, the same pattern of chord transformations will occur over and over again; they repeat in cycles of transformations.

Common cycles are PR, PL, RL, and PLR:

The cycles may not last long and they may change to another cycle.

Let’s look at an example in a piece of music.

Look at and listen to the following excerpt from the fourth movement of Schubert’s Sonata in Bb Major for piano, D 960.

A chordal reduction of this excerpt give us the following chords and analysis:

Now let’s determine the transformations used.  Since the Tonnetz includes only major and minor triads, we will ignore any 7ths of chords.

The last few chords (ms. 128-130) will be compound transformations.

The transformations are shown below:

We see in this example a cycle (repetition) of the pattern RLR in measures 122-123 and then another cycle of RLRLRLR from measures 124-128.

If we ignore the 7^th of the C7, we also get a cycle of RL-LR-RL at the end (V7-I-V7-I).

Listen again to the chords and see if you hear these transformations.