Living Scores Learn - Jacob Druckman

In the doctoral dissertation of I-Jen Fang, there is an interesting use of tonal centers to analyse the different parts of the piece. We will compare it to our findings in every chapter of the harmonic analysis below. Also the formal analysis of the piece is worth looking at in this thesis.

Below (at the end of this document) is a list of resemblances between ‘Reflections on the Nature of Water’ by Druckman and both books of ‘Preludes’ by Debussy. When reviewing this list we can conclude the following harmonic structure per piece for ‘Reflections’:

All of the grace note groups that return three times throughout this first movement are combinations of two different chords. They form polychord clusters (1) of notes that have a very melodic and colorful result. Below are the combinations of chords of every group of notes and the resulting scale that comes out of the combination of those chords. You will see the scales often remind of the music of Debussy with pentatonic and whole-tone scale examples (insert of the technical exercises document).

As in the music of Debussy, the tonal functionality of the chords is less important than the color of the chords: most of the times the tension in dominant chords isn’t resolved, but the chords are used for their color, next to each other, al lot of the time in parallel motion. This is called ‘modal harmony’, as often used in jazz-theory.

The tonal centers of this piece as described in Fang’s thesis (2) and in the two articles about the use of tonal centers in the music of Claude Debussy (3)(4), are installed from the rolls in bar 6 on: the tonal center moves from G (Gmaj7 chord, Figure 1) in bar 7 (in the first 5 bars the tonal center isn’t really clear, also because of the repetition of this part with other tonal centers further on), over F (Fmaj7, Figure 1) in bar 10 to Bb (Bbmaj7, Figure 1) in bar 11. Druckman inserts other chords in the progression as well: Abmaj7, C# Quartal, … Figure 1 illustrates this chord progression.

Between bar 16 and 21 the tonal center is clearly A, with the returning octaves in the bass register (Figure 2, red). The section between bar 22 and 28 shows the same use of harmonic sequence as on the first page of the piece, with Maj7 chords and quartal (5) harmonies (Figure 2, green). The last part of the piece from bar 29 on centers on Bb in the bass register, and dissolves in B in the last bar. This dual tonal center is prepared in the bar before the last part, where this movement reaches its dynamic climax with two loud arpeggios that range the whole instrument, starting consequently on B and Bb (Figure 3).

Both MacDonald and Fang agree on the tonal centers as the note A for the entire movement, as stated in MacDonald’s analysis of the first movement (6). Druckman re-exposes the material three times, he rearranges the material in three different ways, once starting in bar 1, then bar 18, then bar 29. This re-exposition also clearly refers to the structure of quite a number of the preludes of Debussy (see below).

In this part, Druckman uses mainly major seventh chords, which mostly are the result of two stacked or combined fifths. These seventh chords are not used as a harmonic tension tool, but they are used in parallel motion for their intrinsic color, much resembling to the compositional style of Debussy and the impressionists (7).

Again, the harmony is structured by tonal centers, but here there are two possible structures to follow: the harmony of the major seventh chords or the single notes with or without accents. We personally prefer to think in harmonies to structure an analysis. Fang and MacDonald follow the accented single notes in this movement in order to define the tonal centers (8): sequence of the chords (always major seventh chords, figure 4 (red) illustrates the chords sequence of the first page of this movement: A - c# - Eb - Db - F11 (extension) - E (+extensions with C-G) - Db - Eb - D - D7-11# (m.12) - C9-11# - D4-7 - Eb - B4-7 - g#7-9 (+extensions with E-B) - C# - Db - f7, etc.

Sequence of single notes (Figure 4 illustrates the single notes of the first page of the movement in green circles): G#-B-G#-F#-G-D-A-Bb-C-….-C-E-A-B-C-C-E-G-B-Ab-Bb-B-C-F-B-G-D-G-E-F-G-C#, etc. The harmony doesn’t follow a classical pattern of tension and release — also typical for modal harmony in jazz for example — but uses the color of the chords and single notes to move through the harmonies, with a lot of parallelism, similar to the music of Claude Debussy. The piece ends in the last bar with a combination of 6 sets of fifths, using all twelve notes of a chromatic scale.

This part of ‘Reflections on the Nature of Water’ revolves around the A-B dyad that is presented in the first bar of the piece (Figure 5, red). This use of the dyad as key material is very similar to some of the preludes by Debussy (see below). Especially the ‘Tranquil’ mood of this third part resembles a lot to Des Pas sur la Neige from the first book of Preludes.

This part of ‘Reflections on the Nature of Water’ revolves around the A-B dyad that is presented in the first bar of the piece (Figure 5, red rectangles). This use of the dyad as key material is very similar to some of the preludes by Debussy (see below). Especially the ‘Tranquil’ mood of this third part resembles a lot to Des Pas sur la Neige from the first book of Preludes.

The tonal center shifts towards Ab-Bb (Figure 5, green) in bar 9 of the piece, then starts to move around in a similar way as in the second movement of Reflections, following the rolled single notes consequently (Figure 6, red): F#-C#-Eb-G-A-F#-C#, to come back to major dyads in bar 19 with B-C# and Eb-F (in a seventh voicing, Figure 6, green).

From bar 20 on the tonal center moves back again to A-B until the end of this movement.

Fang states that the overall tonal center of this movement is F, because of it recurring nature throughout this movement (9). The surrounding harmony and note-slurs have different kinds of provenance:

• extended chords and parallelism as described in Part II (for example the chords in bar 21 and following)

• Opening and closing of intervals (for example bar 5, second half: 7-6-5th)
• Some slurs seem to be combinations of both of the described techniques.
• Quartal harmony.

This part consists of a clear superimposition of a left-hand harmonic pattern over a right hand melody. This reoccurs in three parts of the movement, the tonal center following the harmony in every part.

Left hand:

• Bar 1-8: combination of diminished chord C#-E-G-Bb (Figure 7, red) and augmented triad D-F#-A# (Figure 7, green), resulting in a hexachord: C#-D-E-F#-G-Bb.

• Bar 9-17: combination of a diminished chord C-Eb-F# (Figure 8, red) and major chord Db-F-Ab (Figure 8, green), resulting in a hexachord: C-C#-Eb-F-F#-Ab. This can also be seen as a combination of twice a semitone and a wholestep, a symmetric scale: C-C#-Eb and F-F#-Ab.

• Bar 18-26: combination of twice a combination of an augmented fourth and a fourth (symmetric scale): F-B-E (Figure 9, red) and Eb-A-D (Figure 9, green), resulting in a hexachord: D-Eb-E-F-A-B.

Right hand:

• Bar 1-8: FMaj7 chord (Figure 7, blue) with 9 and 11th extensions and some alterations at the end of the phrase.

• Bar 9-17: Cmin7 (Figure 8, blue) with added chromaticism in the melody.

• Bar 18-26: Introduction of the combination of black and white keys, as used at the end of the exposition. Parallel intervals, idiomatic writing (Figure 9, blue).

In bar 27-30, this combination of black and white keys and parallelism is further elaborated (Figure 10).

In this movement, the tonal centers are very clear, they evolve around the held notes in the rolls, changing tonality with the added faded-in notes in both hands. The tonality moves from D, over F (with its fifth C) to G# (with its third B). (Figure 11, red).

The grace notes interjections and the roll passages in the middle and at the end of the piece are idiomatically written, mostly constructed out of quasi-parallel centripetal chord-progressions that follow quasi-regular intervals between the chords. A beautiful example of this parallelism is the last event on page 1 of Movement 5: a superimposition of parallel fourths in the left hand on white keys and parallel fifths in the right hand on black keys, resulting in a beautiful blurry shimmering chord. This kind of writing works extremely well on the marimba, especially in this specific range of the instrument (Figure 12).

The tonal center moves back to F (with its fifth C) throughout the second page, ending with the tonal center D of the beginning of the piece and a quintal harmony chord to end the piece. There is no mention of tonal center in Fang’s thesis for this movement.

The harmony in this part of the piece is mostly structured by the accompanying notes in the right hand, that form the second and third note of each sixteenth note triplet. These tonal centers are interjected with some idiomatically written parallel chord progressions that are divided over the two hands, and quartal harmony chords. Exercises on the most difficult of these chord progressions can be found in the technical exercises addendum. The material is exposed twice in the piece, the re-exposition of this movement starts at the end of bar 25, where the tonal center moves back to F.

The tonal centers moves over the following notes (Figure 13-14, red):

• F in measure 1

• Gb-Db from measure 3 on

• G-D from measure 8 on

• F-C from measure 11 on

• C#-G# from measure 16 on

• C-Ab from measure 18 on

• C#-A from measure 22 on

• F from bar 25 on

• Gb-Db from measure 29 on

• C-G# from measure 36 on (Figure 15, red)

• Measures 36-39 are then elaborated and extended 4 times (Figure 15, green arrows) over the third page of this movement, resulting in a parallel cord progression at the last bar of page 3 and the first bar of page 4 of the movement.

• Db-Ab from measure 52 on (Figure 16, red)

• The coda from measure 58 on starts back in tonal center F (Figure 16, green), moves over tonal center C-G (Figure 16, blue), over a parallel chord progression (Figure 16, yellow) towards the last quartal harmony chord of the piece (Figure 16, orange).

There is no mention of tonal center in Fang’s thesis for this movement.