It’s T6 day

A year ago on Twitter, I started a musical T6 advent calendar : from December, 1st to December, 6th, i.e. Saint Nicholas’ day 🎅, I posted each day some examples of the transformation $T_6$ in music. Since today is December, 6th, I thought it would be nice to collect all these examples here. The text of this post is largely copied from my tweets.

The $T_6$ transformation is simply the transformation that takes a major (resp. minor) chord to its transposed by six semitones. Here’s what it looks like in graphical form for the two types of chords. You can see that it can be seen not only as a transposition but also as a center inversion. And this aspect is used meaningfully in the various examples below (some of which we have already seen in this blog).

It appears for example in the opera Rusalka by Dvořák at two points (36:33, and also 2:23:50 in the video below).

Rusalka is a mermaid living in the underwater world, and she wishes to live with a prince on earth. The first time, she asks a witch to help her. The point reflection of the $T_6$ transformation corresponds to these two upside-down worlds. The second time, it’s the prince who says to her that he will happily die with her. This time we are going from earth to the underwater world: $T_6$ again !

If we continue with opera, we can also look at Debussy’s “Pelleas et Mélisande” (see below at 1:03:00): a $T_6$ major tritone transposition occurs when Pelléas sings “Je ne vois plus le ciel à travers tes cheveux” (I can’t see the sky anymore through your hair) Here again, the point reflection inherent to the T6 transformation makes perfect sense since Mélisande is up in the tower and has unfolded her hair, whereas Pelléas is singing to her from the bottom of the tower. One world up, one world down, opposed as the tritone interval, and yet very close… Have you noticed that in a major $T_6$ transposition, two notes in the chords differ only by a semitone, yet the third one is diametrically opposed ? Pelléas and Mélisande are very close to each other, yet their love is thwarted by Golaud…

These two examples deal with major chords, but we can also look at the $T_6$ transformation between minor triads. It gives the harmonic progression a sense of darkness, that something malefic is going to happen. As an example, take the Ark theme in Indiana Jones – Raiders of the Lost Ark. The $T_6$ transformation is heard throughout the map room scene (in particular at 2:47 in the video below): that the ark is a dreadful object from a very different world is well rendered by the $T_6$ transposition, with its inherent tritone and point reflection.

Another truly malefic example: the Emperor’s theme in Star Wars – Return of the Jedi, below in the video at 2:37.

Yet another example, this one comes from Bela Bartók Bagatelles for Piano op.6, and more particularly Bagatelle n°13 (at 20:47 below). The whole left hand part is built around a T6 oscillation between Eb minor and A minor… and the piece is called “She is dead” :(

The opening of Strauss’ ‘Die Ägyptische Helena’ also features a $T_6$ transformation, which illustrates a shipwreck, and is highly reminiscent of the Ark theme we have seen above.

Let’s end this post on a more upbeat note, with major triads again… and the use of the $T_6$ transformation in science-fiction. The $T_6$ transposition between major chords is used in many sci-fi movies soundtracks. What other transformation can best represent the ideas of huge space distance (the tritone is the largest interval in $\mathbb{Z}_{12}$), and alien worlds (it is also a strange dissonant interval) ? As a first example, we find it in Star Wars – Episode IV: A New Hope. You can hear it below at 0:29, which corresponds to the moment when the pod escapes from the starship towards the planet.

Speaking of starships, here’s the second example from Starship Troopers. You can hear it below at 1:33, precisely when Ibanez shows us the cruiser she’s going to pilot later to go to the bug planets, which are on the other side of the galaxy.

And going further in space, what else but the Enterprise, to boldly go where no man has gone before ? Here’s a use of T6 in the Star Trek – Wrath of Khan soundtrack, at 1:01:43 below.

That’s it ! I hope you enjoyed it ! If you have other examples of the use of $T_6$ transformation, I’d be glad to hear about it. For those who would like to know more, here are some useful references:

• Scott Murphy, The Major Tritone Progression in Recent Hollywood Science-Fiction Films, Music Theory Online, available online.
• Frank Lehman, Hollywood Harmony, Oxford University Press