If you have followed this blog from the beginning, and especially the series of post about transformational music theory, you are now familiar with the fact that we are more interested in the transformations between musical objects, rather than the nature of these objects.

In particular, in my first post, I took the example of two melodies, the second one being transposed a semi-tone higher: both can be identified with each other as the transformations between the notes remain the same. Of course, transposition is a natural process and you could wonder whether the same thing would happen with other transformations, like for example the P, L, or R transformations we have seen in neo-Riemannian theory.

We have seen some answers to this question in this post. Among other things, we have seen how the PL transformation appears in Wagner’s Rheingold and in the Imperial March of Star Wars. We have also seen an example of the RPRP transformation, which is in fact nothing else than the T_6 transformation (the transposition by six semi-tones), which describes the harmonic relation in the Ark theme in “Indiana Jones: Raiders of the Lost Ark”. Recall that the Ark theme opens with two chords, C minor and F# minor, which can represented as such:



and which are positionned as seen below in the Tonnetz.




If you need to refresh your memory with the music, here it is.



The examples I had given in that previous post mainly dealt with the transformation of minor triads. What happens if we apply the same transformations to major triads ? Do we have any musical examples ?

Until last Friday, I had in fact no answer to this last question. It so happens that I went to the Opéra Bastille in Paris for a representation of Pélléas et Mélisande by Debussy (in the beautiful direction of Bob Wilson on stage). And right in the middle of the scene where Mélisande let her hair fall down from the tower and Pélléas takes it in his hands, I was struck by a very small passage. Here it is, right when Pélléas says “Je ne vois plus le ciel à travers tes cheveux” (“I can’t see the sky anymore through your hair”) (It begins at 1:14:22, and you get to see Bob Wilson’s staging).



This looked like a typical neo-Riemannian transformation to me, but I couldn’t really take out my phone and look for the score during the representation to check this ! But once home, I saw that the two alternating chords on “ciel” and “tes” (and then again on “cheveux”) are C major and F# major. Here is the representation of these chords:



and their position in the Tonnetz



They are related by the same RPRP (or T_6) transformation which appears in the Ark theme, but which is now applied on major chords.

And then, by some unprobable coincidence, I was listening to the soundtrack of “Star Trek II: the Wrath of Khan”. And here what happens at 1:01:40:



We now have a D major chord, evolving into a G# major chord before returning again to D major. And in the Tonnetz, this looks like this:




In other words, the same RPRP/T_6 transformation again ! It is interesting to see that it somehow has that distinct flavor which makes it recognizable in all sorts of contexts. I would also be interested to see some musical examples where the PL transformation we have seen in Wagner’s music had been applied on major chords, though I haven’t looked in details for such examples.


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