3. Harmonic Analysis of the Etude Op. 65, No. 3

3. Harmonic Analysis of the Etude Op. 65, No. 3

Examining the Etude Op. 65, No. 3 (which is a study in playing right hand double

notes), one can notice that the slower-moving harmonic motion here is governed by the

limited number of possible sonorities which can be generated while the right hand

throughout this etude is restricted to perfect fifths. The harmony can easily be extracted

from the figuration. There is a striking lack of non-harmonic notes as the structure — G-F-E-A-B — is kept consistent throughout. 236 This sonority is transposed and

sequenced over the ascending bass notes G, A, B in measures 1-8 (see reduction in Ex.

108 below) and that whole section is transposed in the next eight-measure phrase (with

the main bass notes E-flat, F, G) which cycles back to the initial sonority.

Ex. 108. Harmonic reduction of mm. 1-8 (repetitions eliminated for clarity)

G is established as the tonal center at the end of that section. Note the presence of

the pitch A in the right hand, belonging to the acoustic mode built from G (Ex. 109).

Ex. 109. Op. 65, No. 3, mm. 15-16

236 This chord could be understood as a non-functional dominant seventh chord G-B-F with an added sixth (E) and ninth (A). Dominant chords with added dissonances are abundant in the romantic masterworks of Chopin, Schumann, Liszt and many others. As mentioned previously, Scriabin’s use of this sonority, however, removes all implication of a dominant (V) function.

In mm. 5-8, Scriabin introduces one new pitch in the left hand: the E-sharp, and makes it

prominent with a new rhythmical figuration in m. 8 (left hand, see Ex. 110).

Ex. 110. Scriabin Op. 65, No. 3, mm. 7-9

In the reduction of the harmony which the added E-sharp creates (Ex. 111 below),

the right hand is also shown closed position for easier comparison to the beginning of the

work:

Ex. 111. Op. 65, No. 3, reduction of m. 8 (closed position on the right)

This new chord serves as a link to the next eight-measure phrase, which is

transposition of the first phrase to E-flat. The E-sharp and B in the left hand of m. 8

expand out by a whole tone, creating the connection between the phrases (see Ex. 110

above). Note that in the transposed second phrase, m. 16 is not analogous to m. 8 of the

previous phrase, because the next Impérieux section (starting in m. 17) is in fact using the

same pitches as mm. 1-16, only with an inverted bass line. Therefore, additional

“foreign” pitches are not needed to accomplish that transition.

The prominent tritone featured in the B, E-sharp, A chord in the left hand (m. 8)

was actually hinted at in the first seven measures of the piece, if one (wisely) takes pedaling into account when examining the harmony.237 Playing the first measure on one

pedal produces a G, D-flat, F, B chord in the left hand. This is in fact that very same

harmonic structure which was made prominent by the new rhythmic figuration in m. 8.

Scriabin clearly expresses what has only been hinted at in the previous measures through

the blending of two dominant chords, a tritone apart:

This is important, as it is clear that Scriabin treats the tritone in m. 8 (and

elsewhere) as a free “added note”, as one might use the fifth scale degree in a diatonic

mode. This is a subtle way in which Scriabin uses the tritone relationship in place of the

traditional I-V motion in his late works. If one takes all the notes present in m. 1 and

stacks them in fourths, a seven-note chord will be produced. (There is also an E-flat

present, but not shown in the reduction because it is a non-harmonic note, functioning as

the lower neighbor to the E.) This is most likely how Scriabin built up the main harmony

of the piece (see Ex. 112 on the following page).

237 The prolongation (and blending) of notes using the pedal is integral to Scriabin’s piano writing. Scriabin does not indicate any piano markings but even the most ascetic tone-colorist would perform at least the first measure of the piece without changing the pedal (contemporary accounts of Scriabin’s performances noted his incredible tonal palette at the keyboard and inventive use of pedal-blurring effects).

Ex. 112. Scriabin Op. 65, No. 3. The pitches in m. 1 (except E-flat) neatly fit into a structure stacked by fourths, similar to the Prometheus chord

One should note that the “tritone link” is also an important motivic element in the

work. It connects the Molto vivace section (“Section A”, mm. 1-16) to the Impérieux

(“Section B” starting in m. 17), as the bass line in mm. 1-2: G, D-flat, G, becomes

C-sharp, G, C-sharp, in mm. 17-19. These are the same pitches, spelled enharmonically

and inverted. The continuous triplet rhythm established by the right hand in the first

section is now present in the left hand figuration starting from m. 17, which also helps to

link the two sections (Ex. 113).

Ex. 113. Scriabin Op. 65, No. 3, mm 1-2 and mm. 17-19.

The Impérieux section (from m. 17) is the first time that a recognizably melodic element (in the right hand) is introduced in the piece.238 Scriabin emphasizes the contrast

in texture and dynamics with a slower tempo marking (Ex. 114).

238 However, the melody in this etude is rather minimalist.

Ex. 114. Op. 65, No. 3. Measures 17-20, right hand melody.

In a conversation with me, Dr. Edward Green (the advisor of this thesis), noted

that the melody seems to be an allusion to La Marseillaise (below), which may connect with Scriabin’s use of the Impérieux marking.239

The markings Impérieux and Imperioso (which may be translated as “magistral”,

“authoritative” and even “pompous”) are found in several other Scriabin works in

addition to the Etude Op. 65, No. 3 (see Ex. 115). Ballard writes “Scriabin is fond of

kingly, assertive gestures marked Imperioso or Impérieux. These brands of royalty are self-important to the extent that they can disrupt metric flow.” 240

239 Tchaikovsky’s famous 1812 Solemn Overture, composed in 1880 (referencing the successful Russian defense against Napoleon’s army in 1812) also quotes La Marseillaise. 240 Ballard, Companion, 312.

Sonata No. 5, Op. 53 (1907):

Sonata No. 7, Op. 64 (1911-1912), written at the same time as the 3 Etudes Op. 65:

Ex. 115. Other instances of the Impérieux and Imperioso marking in Scriabin works.

The Scriabin Etude Op. 65, No. 3 reveals an increasingly minimalist approach to

harmony and texture. While the sonorities have become more dissonant, there is less

contrapuntal activity and the music strikingly less “melodic”.

Returning to the Impérieux (m. 17), note that all of the “added note dissonances”

are in the right hand in this section, above the alternating left hand seventh chords a

tritone apart.

Ex. 116. A reduction of mm. 17-22.

As observed in the previous two etudes in this set, the top note of the right hand is treated

as a melody, with the lower note in the right hand (along with the left hand harmonies)

tailored to it. The lower notes in the right hand inevitably tend to create an abundance of

non-harmonic notes because the right hand is restricted to playing perfect fifths in this

etude, with no exceptions.

This explains why the E-flat in the right hand in the first measure of the piece

does not belong to any mode over the bass G. The E-flat would have belonged to the

acoustic scale mode above the preceding C-sharp/D-flat bass, which also confirms how

Scriabin used both the acoustic and octatonic scale interchangeably to add seemingly

foreign harmonic notes. In m. 1, the E-flat is in a rhythmically weak position and is best

understood as being “non-harmonic”, precisely because of Scriabin’s self-imposed

restriction of the fifth. Scriabin must have been aware of it, as he also uses the “non-

harmonic” E-flat in a similar fashion in the Impérieux section (see Ex. 117). This is yet

another connection between the two seemingly contrasting sections, relating to Scriabin’s

ideas of Unity and Multiplicity.

Ex. 117. Op. 65, No. 1: m. 1 and mm. 17-18.

There are several other things to consider. Late Scriabin’s chord “spellings” are

often made as easy to read as possible and avoid extra accidentals in the notation. This is

noticeable when one examines the way Scriabin notates (or “spells”) many of the cross-

relations in this etude. For instance, the left hand B-natural in the Impérieux (m. 17, see

Ex. 117 on the previous page) is first notated as a B-natural and then as a C-flat in m. 18,

in order to prevent confusion with the prominent B-flat in the right hand in that measure.

The harmonic function of that pitch in that context, however, supports the B-natural

spelling (a major third above the G bass would be spelled “correctly” as a B than as

C-flat in that instance).

In m. 17, the C-sharp, F, B sonority in the left hand is in fact the same pitches

which are spelled D-flat, F, C-flat in the second figuration of measure 1, and could have

been spelled the same way in measure 17. However, that would have made it necessary

for Scriabin to add the natural symbol to the D in the right hand of that measure.

The harmonic function of each note was something that Scriabin was acutely

aware of. In many of the Etudes Op. 8, Scriabin resorts to using double-sharps quite often to notate the sonorities with the “correct” harmonic function for every note. 241

The previous generation of composers who had influenced Scriabin in his late

period harmonic innovations were not known for using enharmonic spellings in their

notation (see Ex. 118 on the next page). However, the presence of cross-relations

throughout the Op. 65, No. 3 created the need to notate some of the pitches

enharmonically (despite their actual harmonic function) in order to preserve a clear,

elegant and readable notation.

241 Especially Etudes Op. 8 Nos: 1 in C-sharp major, 9 in G-sharp minor and 12 in D-sharp minor.

Balakirev Islamey (1869). The B minor chords are “spelled” correctly within the D-flat major key signature:

Mussorgsky Pictures at an Exhibition (1874): The Great Gate of Kiev

Ex. 118. The composers of the Mighty Handful tended to avoid “simplified” enharmonic spellings when notating remote key-areas.

In the Impérieux section of this etude (starting in m. 17), the harmony is static

from measure 17 through 30 until the bass note changes to an E in measure 31. Note that

due to the “tritone link” between the bass notes C-sharp and G in this section, these bass

notes are essentially interchangeable. The harmony produced is identical to the first

Vivace section (mm. 1-16), only inverted (see Ex. 119 on the next page). Once again, it

connects to Scriabin’s ideas about Unity and Multiplicity. Significantly, it also reveals

that Scriabin’s tritone-link is based on the properties of the French augmented sixth

chord, as discussed previously (see page 127).

Vivace section mm. 1-2: Imperieux section: mm. 17-19:

Ex. 119. The main harmonies of the Vivace and Impérieux sections use the same pitches, and intervallic structure, this is possible due to the unusual properties of the French Augmented 6th chord, as discussed earlier.

Measures 29-32 are important to examine in order to understand how transitions

between tonal areas are accomplished in this late-period work (Ex. 120). While there is

no defined “key” (in the diatonic sense) in late Scriabin, the bass-line nevertheless

establishes some very specific tonal centers. As mentioned previously, this etude is based

around the seventh chord built from two pitches linked by tritone, namely G and C-sharp.

Ex. 120. Op. 65, No. 3, mm. 29-32. Transitioning to a bass note not heard previously

As made clear in the reduction of mm. 29-32 (see Ex. 121 on the following page),

the progression is based on a voice exchange: the bass G natural is picked up by the top

voice in the next measure. Note the cross-relation to the G-sharp in the left hand. Scriabin

once again uses the tritone link between seventh chords freely. While the bass note

changes, it is not treated as a new harmonic note.

The underlying bass motion is best understood as an ascent by minor third from

D-flat/C-sharp to E. One can often find this kind of octatonic-based progression in Scriabin’s late works. 242 In addition, the bottom notes in the right hand double-note

figuration in each measure (Ex. 121) outline a chromatic scale—D, E-flat, E-natural, F—

in that register, which helps to link the progression contrapuntally.

Ex. 121. Op. 65, No. 3, mm. 29-32, reduction

Despite (or in addition to) the innovative approach to harmony, Scriabin writes in

short, clear eight measure phrases, just as in his early and middle period etudes. The

phrase structure in the first section (mm. 1-16) is very clear, with each of the two phrases

being eight measures long. The sparseness of pianistic texture is apparent in this work,

and Scriabin’s restrictive use of intervals certainly contributes to it.

Examining the Impérieux section (from mm. 17) one can discern that it is

structured in four-measure phrases, heard in sets of two: mm. 17-20 and 21-24 plus 25-28

and 29-32. Starting from mm. 33 however, the phrases shortened to two-measures in

length, as Scriabin starts interpolating material from the first Vivace section (mm. 1-16,

see Ex. 122 on the next page).

242 The bass-line of progressions by minor third (outlining a diminished chord) can be filled in with an octatonic scale. This can be found in works of Liszt, Rimsky-Korsakov and other composers who influenced Scriabin.

Ex. 122. Scriabin Op. 65, No. 3, mm. 33-40. Phrases are now two measures long, as Scriabin starts interpolating material from the Vivace in mm. 1-16

This may also connect with Scriabin’s ideas of polarity, as he is now rapidly

switching between the two contrasting textures based on the Vivace and the Impérieux

material.243 Note that Scriabin now uses a whole-tone element in the material derived

from the Vivace, instead of the chromatic element heard in m. 1 (see Ex. 123). The

whole-tone element generates a harmony which was not heard previously in the piece.

m. 1: mm. 33-34:

Ex. 123. Op 65, No. 3, m. 1 compared with the modified material in m. 33

243 It is similar to the procedures typically used in a development section of a traditional sonata form.

The initial harmony in m. 1: m. 33: m. 33 transposed to the initial tonal area for easier comparison:

Ex. 124. Op. 65, No. 3. The m. 1 harmony compared with the modified m. 33 material.

It is easier to understand the harmony in m. 33 when it is transposed to the

G/D-flat tonal area of m. 1 (the tonal center or “tonic” of the piece). Examining the

transposed version of m. 33 (on the right of Ex. 124), the E-flat and A-flat in that

transposition now produce a new harmony of four note, stacked in fourths: F, B-flat,

E-flat and A-flat, which is related to the initial harmony of the work. Thus, the harmony

in mm. 33 is derived from the opening harmony, transposed down a minor third (from

G/D-flat to the tonal center of E/B-flat).

Measures 35-36 are a fragmented repeat of the phrase in mm. 29-32, and mm. 37-

38 serve as a transition from the bass E to a new F-sharp bass note in m. 39, a progression

which moves by ascending whole-step (E/B-flat—F-sharp/C), as illustrated in Ex. 125. Note that mm. 37-38 is the material from mm. 3-4, transposed down a minor third.244

This is yet another example of the overarching integration of material in this work, to an

extent not found in the earlier etudes.

244 The phrase in mm. 37-38 is a two-measure fragment derived from the longer phrase in mm. 3-6.

Ex. 125. mm. 37-39, note the underlying bass motion by whole step, E—F-sharp. Scriabin pairs each bass note with its “inversion” a tritone away.

The subito meno vivo section in m. 39 arrives unexpectedly due to an accelerando

in the previous measure (see Ex. 125). In addition, the transition in measures 33-38 was

only six measures long, with three fragmented phrases (organized as 2+2+2), which

contrasts the symmetrical four-bar phrasing heard previously. The molto vivace section in

mm. 1-16 had was grouped into two phrases, each eight measures long. Aside from the

anomaly in m. 39, the Imperieux section was mostly divided into four-measure phrases.

However, the three fragmented phrases in mm. 33-38 were two measures each, heard as a

total of six measures and not the expected eight measures.

The section marked subito meno vivo (m. 39, see Ex. 126) is in fact the Imperieux

material heard previously, transposed up a perfect fourth, from C-sharp/G to F-sharp/C.

mm. 17-18 mm. 39-40

Ex. 126. Scriabin Op. 65 No. 3. The section starting in m. 39 is a transposition of the Impérieux in m. 17

This section starting from m. 39 (identified as “B-1” in the analysis of the form on

pg. 134) is analogous to the second and not the first phrase of the Impérieux heard earlier.245 This entire section, which features interpolations from the “Section A” Vivace

material, lasts a total of 24 measures (this was the expected length of the Section B

Impérieux in mm. 17-38, which was only 22 measures long due to the incomplete phrase

discussed earlier).

Examining the overall structure and tonal scheme again (shown below, identical

to pg. 134), it is possible to understand this entire subito meno vivo section transposed to

F#/C (labeled B-1) as being in the structural spot of a development section within a

sonata form.

Structure and Tonal Scheme of Scriabin’s Etude Op. 65, No. 3:

Section A: Vivace. Tonal center: G/D-flat (mm. 1-16) 16 measures total, 2 phrases 8 bars each

Section B: Impérieux. Tonal Center: C-sharp/G (mm 17-38) 22 measures (**2 measures missing due to incomplete sequence)

Section B-1: Subito meno vivo. F-sharp/C (mm. 39-62) 24 measures, with interpolated elements from the A section This is a transposition of Impérieux to F-sharp/C

Section A: Prestissimo. G/D-flat (mm. 63-78) 16 measures. Modified return of the Vivace material

Section B: Meno Vivo. C-sharp/G (mm. 79-102) 24 measures. Return of the Imperieux plus a coda

The transposed statement of the Impérieux material (section B-1) is likely placed there to

provide a fresh new tonal area in work otherwise centered around two main bass notes,

namely: G and C-sharp/D-flat.

245 It is essentially a transposition of the phrase which started in measure 25 and not 17.

Much of the Subito meno vivo section (m. 39) is in fact an exact transposition of

the Impérieux section (m. 17), as illustrated in Ex. 127 below. The shifts to new tonal

areas are accomplished in the same way as discussed on pages 146-147.

Op. 65, No. 3 mm. 29-32:

Op. 65, No. 3 mm. 43-46 is the same material, up a fourth:

Ex. 127. Scriabin Op. 65, No. 3. A comparison of two analogous sections

The two-measure fragment previously heard in measures 37-38 is used in this

section to modulate up a whole-step to the main bass note B (see Ex. 128 below).

mm. 51-52 (left). This is a transposition (up a fourth) of mm. 37-38 (right).

Ex. 128. Scriabin Op. 65, No. 3. Another comparison of two analogous sections

Note that the underlying upward chromatic motion in the right hand is supported by the

slower-moving whole tone bass motion. Each bass note is complemented by a note a

tritone away.

In mm. 57-62, at the end of this entire Subito meno vivo section, Scriabin uses a

harmonic progression which was not heard previously in the work (Ex. 129). It serves as

a transition to the modified return of the A-section, in the G/D-flat “tonic” area.

By m. 62, Scriabin returns to the original “tonic” harmony of the piece: 246

Ex. 129. Op. 65, No. 3, mm-57-62, reduction

246 Note that the pitches in measure 61-62 are exactly the same as in the first measure of the piece, only missing of the chromatic neighboring notes Eb and Bb present in measure 1.

Note that the bass is moving down a major third from B to G, a progression which

makes sense to the listener because of the B (common-tone) present in both harmonies.

The right hand material at that point features an ascending sequence by whole step. The

presence of the major ninths (A-B) in mm. 61-62 (right hand) could be a reference to the

Op. 65, No. 1. The harmonic progression with a motion of the root by major third is an

influence of Rimsky-Korsakov and by extension, Franz Liszt. One of many examples of a

progression where the bass moves by major third in Liszt’s music can be found in his

Mephisto Waltz No. 1, S. 514 (1862), as demonstrated in Ex. 130 below.

Free harmonic reduction:

The same progression but reduced to root-position:

Ex. 130. Liszt, Mephisto Waltz No. 1, mm. 750-756

Note that in Ex. 130, every chord is connected through a common-tone, which is

sometimes spelled enharmonically. Another subtle detail in the Liszt example is the

presence of a whole-tone element in the right hand (mm. 750-751: F-sharp, E, D, C), and

also in the left hand bass line: E, G-sharp, F-sharp, B-flat (those four notes belong to a

whole-tone collection ). This is one of many examples in Scriabin’s late-period music

where elements of his harmonic innovations can be traced back to earlier composers.

Returning to the Scriabin Etude Op. 65, No. 3, mm. 63-78 serve as a

recapitulation of the “A section”. The only difference is the increased tempo

(Prestissimo), and the rhythm.

Ex. 131. The rhythm of the Vivace (m. 1) and the Prestissimo “recapitulation” (m. 63)

Interestingly, in first measure of the etude (see example above), Scriabin notates

the two-note motive in the left hand as two sixteenth notes, and not as an incomplete

triplet. In tempo, this rhythmic subtlety is not audible at all in m. 1 (and is not meant to

be). However, this rhythmic figuration becomes prominent in the frenzied return of the

opening material in m. 16. This is yet another detail which suggests Scriabin’s meticulous

attention to the overall unity of all the various components within his compositions,

especially in his late period works.

Besides the rhythmic change, the Prestissimo recapitulation is an exact repeat of

mm. 1-16. Likewise, the next section in mm. 79-86 is an exact repeat of mm. 17-24. The

final 16-measure phrase (starting in m. 87) serves as a coda to the etude. It starts out as a

continuation of the Impérieux material, and finishes with an eight-measure reference to

the opening of the Etude Op. 65, No. 1, confirming that the Three Etudes Op. 65 were

indeed envisioned as a cycle by Scriabin (see Ex. 117).

The ending of the Etude Op. 65, No. 3:

The beginning of the Etude Op. 65, No. 1:

Ex. 117. The ending of the Op. 65/1 is related thematically to the opening of the Op. 65/3

Examining Ex. 117, note that while the right hand in the ending passage of the

Etude Op. 65, No. 3 is composed of perfect fifths with a bottom octave added, it is

nevertheless a clear reference to the beginning of the Etude Op. 65, No. 1. The top line

of the right hand in the Etude Op. 65, No. 3 now spans two octaves and is transposed up a

half-step. The left hand bass notes, however, are the same exact pitches in both etudes. In

the Op. 65, No. 3 ending, the main bass notes expand a full octave down, outlining the

diminished chord: C-sharp, A-sharp, G, E. In the opening of the Etude Op. 65, No. 1, the

main bass notes (E, C-sharp, A-sharp, G) belong to the same collection.

Tonal Centers of The Etudes Op. 65

Op. 65, No. 1 Op. 65, No. 2 Op. 65, No 3

The same collection is outlined by the main tonal centers of the three etudes in the

cycle. This is Scriabin’s only set of etudes with an apparent overarching plan of tonal

organization.