The Wonderful Lulu Chord

The Lulu Chord is what I call a chord formed by playing a perfect fifth with a perfect fourth nestled inside it: for example, C-C#-F#-G. The outer notes, C-G are the fifth and the inner ones, C#-F#, are the fourth. This chord is non-diatonic and, as far as I know, unknown in tonal music. But it was very popular with the Second Viennese School and is a good thing to get a handle on if you're looking for some modernist vocabulary.

The Lulu chord has the following remarkable property: if you stack three of them separated by whole tones, you get all twelve notes with no repetitions. It's very like stacking diminished chords, except with those you have to use semitones instead. Apart from chromatic clusters, no other chords have this property.

I'll write CLu for C Lulu (C-C#-F#-G). You can play it in a closed voicing and it's very crunchy, but spread out it has a kind of solid seriousness about it. Two ways I do this on piano: either with the fourth in one hand and the fifth in the other, or with a tritone in both hands (i.e. C-F# in one hand, C#-G in the other). These are very easy to find with only a tiny bit of visualization.

CLu + DLu + ELu is the total chromatic. But even better, it's a symmetrical structure that repeats at the tritone, so CLu = F#Lu, which means we can rewrite this as CLu + ELu + AbLu, which is just Lulu chords built on the notes of an augmented arpeggio, like the Coltrane cycle of major sevenths. Any two of these form a structure I called the Double Chromatic in my scales book.

Stacking two Lulu chords a semitone apart creates another symmetrical structure. CLu + DbLu is C-Db-D-F#-G-Ab, Messiaen's Fifth Mode of limited transposition (called Tritone Chromatic in the scale book). Of course, this is another structure you can combine with itself to cover all 12 notes without overlap; in this case, just shift it by a major third. This is much more obvious on an instrument than in words.

Finally, stacking two Lulu chords a minor third apart yields the octatonic diminished scale. For example, CLu + EbLu is C-Db-Eb-E-F#-G-Bb-B, which is C half-whole diminished. And you can continue to stack them on all the notes of a diminished chord all the way round the cycle of minor thirds.

So the Lulu chord has lots of nice symmetry. And these are the only things you can make by combining them: Double Chromatic, Messiaen's Fifth Mode, diminished. Looking through the other end of the telescope, you can see C Lu as a superposition of Csusb2 and Csus#4, two very dissonant triads that are very typical of serialist language.

Another thing I've been experimenting with is stacking a second fourth on top of or below the one that's already present. That is, if I'm playing it as a fifth in one hand (say, C-G) and a fourth in the other (Db-Gb), the fourth becomes expanded to three fourths (Db-Gb-Cb or Ab-Db-Gb). This produces the pc set 5-7, which I don't really know anything about. If you play Lulu in closed form instead (C-Db-Gb-G) you can get the same sonority by adding an extra note on the outside or inside of the chord: in this case, you can choose B or Ab (expanding the chord outwards) or D or F (expanding inwards). If you play it as two tritones, just add an extra note to either of the tritones, inside or outside, as long as it doesn't overlap with one of the existing notes.