Zappa & Ligeti Simile

What is it about Zappa's G-Spot Tornado that reminds me of Ligeti's Allegro Grazioso from the Six Bagatelles For Woodwind, let's have a look shall we:

In the example below, we can see a very similar note configuration of G-Spot Tornado and that of Allegro Grazioso albeit with differentiated key centres and rhythmic presentation. Ligeti's does not change throughout the piece and is constant with the bassoon and clarinet alternating the septuplet figure with a lyrical melody in the flute. Zappa's develops the opening figure throughout the piece which becomes defragmented later on with a recapitulation of the opening figure towards the end.

The outset of G-Spot Tornado contains the complete note collection of B minor pentatonic whereas Allegro Grazioso contains the complete collection from C minor pentatonic. GST pentatonic scale relates to the root of B, and in AG the C minor pentatonic relates to F dominant. Since the B minor pentatonic relates to the root of B the natural D inherent in the scale is the only non-related note to AG where the C minor pentatonic has the natural G in order for the scale to relate to the F dominant.

Besides those differences, and the fact that GST is in 2/2 time and AG in 3/4, the note configuration produces a rhythmic simile in the sense that in GST the quaver groups in the first and third bars consist of 7 corresponding to AG's septuplet figures which in some way make the similarity slightly more prevelant.

I am not sure how acquainted with Ligeti's music Zappa was or if indeed the former had any influence on the latter, but there is a resemblance here.

Rollo Interior & Quartal Harmony

Quartal harmony was utilised extensively in the 1960's by jazz musicians, in particular John Coltrane and McCoy Tyner, and just as the stacked 4th intervals permitted greater freedom from an improvisational standpoint so did the [027] chord for Zappa from the compositional. (The [027] chord or sus2 is merely an inversion of the sus4 chord, however the sus4 chord in its 2nd inversion contains stacked 4ths, so essentially it is an inversional choice from the same chord family).

For Zappa, the inherent ambiguity of these chords provided opportunities to explore a more extensive melodic application since one is not predetermined by the 3rd interval, be it major or minor. The [027] chord is fully exploited in Rollo Interior where the relationship between chord and melody is blurred at the discretion of the artistic whims of the composer.

To begin, I shall look at this interlude from the diatonic, purely for the fact that in the lead sheet Zappa has included specific chords. If we observe the chord melody relationship, we can see the chords do not change their structural value of [027] and therefore the melody implies a number of possibilities. For instance, in bar 15, the chord is Bb2 and the first 4 notes in the melody imply Bb harmonic minor with the natural 7 and b6, but then in the next 4 notes, the natural D appears momentarily implying a major chord, and in the next bar we have a b9 (B) and a b5 (E). I doubt that Zappa would have constructed the melodic content of this interlude on that premise, but I mention it just to illustrate the possibilities that Zappa was keen to exploit with the utilisation of the sus2 chord.

In our example you will notice that the melody often shifts to the next chord by a semitone, this practice appears in the Symmetrical Structures section pertaining to Zomby Woof; effortless scale/melodic connection between chord changes, a general rule of counterpoint. Zappa's indifference to traditional harmony and counterpoint is well documented so it comes as no surprise that there are wider interval shifts between chords in the interlude too, but the most prevelant shift is the semitone.

If we look at the contour of the interlude we notice that the highest contour occurrence is < - + - >, this CAS is quite significant because to the listener there is a recognisable rapid down and up motion throughout, so although significant, not so surprising. The creative part is the way this CAS is exploited with dynamic registral shifts that still maintain the CAS, reaching its highpoint with consecutive < - + - > at bars 25-27 and then descending with the inversion of the CAS, < + - + >, in bars 29-31. Variation is evident in the contour segments which are as follows; <2130> <2031> <1032> <3120> <3021>, with <2031> and <1032> appearing 3 times and <3120> twice, (not including bars 1-8 repeat at bars 17-24), as you can see the entire configurable mathematical possibilities have been used with the < - + - > CAS.

A point of interest is the CAS < - - + > CSEG <2103> or <3102>, out of the only two possible configurable numbers that could reside in the middle of this CAS, each one contains < 10 > not the other possible configuration < 20 >. The rotation occurs with the <2 3> and <3 2>, the outer intervals shuffle about in an alternating fashion almost constantly.

Our final observation is the repetition of 2 pitch class sets, 0236 and 0134. In bar 8, the first instance of 0236 is permutated in the second at bar 13 where the C# is an octave higher and the Bb and D are reversed, the 0236 immediately following is a further variation with the fourth at bar 15 being a transposition of the first. The 0134 set is realised at the end of bar 8 and it appears again in bar 14 but this time with the semitones paired next to each other [C# D - B A#]. In bar 15 we see an unfolding of 2 minor 3rd intervals which move up by a semitone [F D - F# D#]. This further shows how the idea of moving around the notes in little melodic segments can yield interesting results, an excellent micro example of compositional economy.

We now look at a 4 note broken quartal chord that appears in Greggery Peccary, Igor's Boogie and Music For Low Budget Orchestra. The application of the quartal broken chord in the first bar of our GP extract is in the descending, [B F# C# G#] with the whole descending sequence moving up a tone to [C# G# D# A#]. In-between this and the next 3 occurrences of the quartal chord at the end of bar 3 and the whole of bar 4 is a small whole tone collection and then 2 sets of 0134 on beat 2 of bar 2 and beat 1 of bar 3. Although the 0134 is fleeting and our attention at this point is on the quartal we should note again that the inherent use of economy of means plays a momentary role in the extract. The first of the 3 broken quartal chords beginning at bar 3 ascends with the remainding 2 descending in bar 4. Incidentally, the last 3 quartal chords reduced exhibit a form of chromatic saturation with 10 notes from the full chromatic realised, [0123456789], even using quartal harmony, Zappa manages to implement chromatic saturation.

The broken quartal chord also appears in Igor's Boogie and Music For Low Budget Orchestra. In MFLBO, 10 notes from the full chromatic are realised just as in the GP extract. In addition, each quartal chord can be seen to be part of a rotation, the last quartal broken chord, if placed in front of the 1st and 2nd would produce a succession of semitone descending quartal arpeggios, like this:

(Of course within the scheme of this hypothesis, the original retrograde of the 3rd quartal chord [F# B E A] would have to be assumed as being in the same position as the others, essentially descending.)

The utilisation of arpeggiated quartal chords is found in other Zappa pieces such as Zoot Allures or Brown For A Pound. However, the explicit manner in which it is used as melodic content in the 3 pieces here is not often heard in any other pieces.

Symmetrical Structures

In this section, we are going to look at a few symmetries found in three of Zappa's pieces. We shall discuss two examples of absolute symmetry in Greggery Peccary and Zomby Woof respectively, and then Echidna's Arf, which is more exemplar of interrupted symmetry.

Let's begin with Greggery Peccary; in the 3rd and 4th bars of our example we can see an interesting uninterrupted symmetrical structure. You will notice how the G# chromatically descends to the Eb whilst the A chromatically ascends to the D; a kind of contrary motion in one voice with outward dispersion of equal intervals. Assigning interval classes, we discover an expanding pitch-class interval series of, 1-2-3-4-5-6-7-8-9-10-11; although looking at it from this perspective does not really reveal the symmetry, it does somewhat demonstrate Zappa's unique ability to be creative with the total chromatic.

Clement identifies the employment of chromatic saturation to a much larger degree in his thesis, A Study Of The Instrumental Music Of Frank Zappa, illustrating a common compositional trait of this process, condensing the process in short spaces of time, Be-Bop Tango, and expanding it over longer periods of time, Pedro's Dowry.

Another example of uninterrupted symmetry can be found in Zomby Woof. Here are rhythmic groupings of 5's with some of them stated and then reinstated backwards (retrograde); you will notice the symmetry is found in the execution of the melody not in the melody itself. The symmetry is found from bar 2-5 which is then performed in retrograde uninterrupted until the beginning of the final bar in our example here.

There is a distinct jazz flavour to this section with the F major triad/D in bass descending chromatically from D to Bb and then ascending with the notes outling the minor tonality accordingly. The notes outline the chords in a diatonic fashion; a melodic line with each note at the end of every bar guided into the next with a tonal shift of a semitone (save the F# to Ab from bar 4 to 5), another characteristic of straight ahead jazz styles where melodic improvisation appears to be more effective if the chord changes are met by the soloist with little effort as possible in terms of intervallic scale connection. So ultimately, this example shows us a melodic line that is played and then played again but in reverse, a melodic palindrome if you like.

Our final example is another kind of symmetry that appears in Echidna's Arf. This interlude shows symmetrical displacement caused by the ascending C# and descending F#. The C# and F# act as a sort of pivot for the uninterrupted symmetry that resides outside of it. A stronger contender for the pivot would be the note B as it occurs every other note throughout the sequence, however from this perspective the symmetry becomes less apparent.