Analysis for Pianists

My new book: Reflections on the Water: One and Many in Myth and Music https://www.amazon.com/author/ishmaelwallace

  1. Rachmaninov’s Prelude in C Major, Op. 32, #1
  2. Liszt’s Sonetto 47 del Petrarca
  3. Schumann’s Aufschwung
  4. Chopin’s Mazurka in F, Op. 68, #3

1. Rachmaninov’s Prelude in C Major, Op. 32, #1

When I read a book, I read the thoughts of the author. The thoughts are expressed in words; the words are expressed in letters.

In a great performance, I hear the composer’s thoughts. The thoughts are expressed in harmonies; the harmonies are expressed in notes.

A piece may contain a million notes; to read the composer’s thoughts, I must perceive the harmonies.

A good way to begin is to make a harmonic reduction.

Below are my recording and harmonic reduction of Rachmaninov’s Prelude in C major, Op. 32, #1.

https://soundcloud.com/user-870249089/prelude-in-c-major-op-32-1-by-sergei-rachmaninov

The reduction shows two themes which Rachmaninov wove in to his work.

The first is a three note melody, the opening of his own Prelude in C# Minor, op. 3, #2: Ab, G, C (scale degrees 6, 5, 1 in minor). The Prelude in C# Minor was Rachmaninov’s best known composition. The resolution of scale degree 6 to scale degree 5 in minor is a basic motif in classical music which symbolises tragedy. The final Prelude in Op. 32, #13, returns to this motif, attempting to find victory over tragedy with a version in major, Bb — Ab — Db.

Another important theme, which also symbolises tragedy, in this case the descent to the land of death, is C, Bb, Ab, G (scale degrees 8, 7, 6, 5 in minor — a common passacaglia bass line).

That Rachmaninov weaves motifs from minor into a work in C major is his way of saying that, in life, light and dark are always interwoven.

2. Liszt’s Sonetto #47 del Petrarca

When I read a book, I read the thoughts of the author. The thoughts are expressed in words; the words are expressed in letters.

In a great performance, I hear the composer’s thoughts. The thoughts are expressed in harmonies; the harmonies are expressed in notes.

A piece may contain a million notes; to read the composer’s thoughts, perceive the harmonies.

A good way to begin is to make a harmonic reduction.

Below is my reduction of Sonetto 47 del Petrarca, by Franz Liszt. I’ve included all the harmonies, but taken out the figuration and most of the non-harmonic tones — neighbour notes, passing tones and appoggiaturas (those I did include are marked: passing notes or chords with P; neighbors with N).

The piece begins with a chromatic chord, an A major chord resolving to the tonic, C# major. The piece as a whole is in Db major, enharmonically the same as C#, so in the reduction I’ve written the C# as Db, and the A as Bbb. 

What does not belong attracts us. We want to understand it, and go back to it again and again until we can feel it does belong. The psychoanalyst Freud calls this “working through”. 

Liszt goes back again and again to Bbb. In measure 3 we hear it again already, as A, the third of an F major chord. A passing chord leads to A major in bar 4. 

In bar 6, we hear the Bbb harmony with an augmented sixth, G natural. Bbb and G resolving to Ab becomes the main idea of the piece. 

In Db major, the normal 6th scale degree is Bb. The Bbb is borrowed from minor; it doesn’t belong. So Liszt attempts to correct it to Bb. In measure 7, 8, and 9, Bb resolves to Ab; in measure 10, we hear first Bb, then Bbb — the two are competing.

In the melody which begins in measure 12, there are two ideas: a descent, Ab — Gb — F, and a neighbor note, Bb, which resolves to Ab. 

Beginning in measure 37, this melody is repeated, in a distant key, G major. Liszt is “working through” his memory of the G natural in bar 6. From measure 35 through measure 42, G is in the bass; in measure 57 the bass returns to this G (written as an F##) and leads it to Ab (written G#) in measure 60. 

Liszt has explored the sound of G natural and found how it belongs: G natural is the raised fourth in Db, and leads to the dominant.

(This experience has been prepared by an odd moment; in measures 43 — 47, the melody rises from G through Ab to A natural. These three notes are a memory of the G, Bbb, and A flat from measure 6. In measure 47, the A is not heard as a Bbb — it’s still heard as the second scale degree in G major. But the A cannot feel secure; the Ab has been emphasised in a way that is not normal in G major. And right away, A sinks down to Ab (measure 54, written as G#)). 

In measures 68 — 88, as the music prepares to resolve to Db, Bb and Bbb are still in competition.

At the end of measure 88, Bbb is corrected to Bb — the reverse of measure 10.

The sound Bbb to Ab appears one last time in measure 93. But now, as in measure 3, the Bbb is an A, the third of a F major chord; that sound which haunted the piece is still there, but its meaning has changed. 

https://soundcloud.com/user-870249089/sonetto-47-del-petrarca-franz-liszt

3. Schumann’s Aufschwung

When I read a book, I read the thoughts of the author. The thoughts are expressed in words; the words are expressed in letters.

In a great performance, I hear the composer’s thoughts. The thoughts are expressed in harmonies; the harmonies are expressed in notes.

A piece may contain a million notes; to read the composer’s thoughts, perceive the harmonies.

A good way to begin is to make a harmonic reduction.

Below is my reduction of Schumann’s Aufschwung, the second of his Phantasiestücke, op. 12. It includes all the harmonies but none of the figuration or non-harmonic tones. Notes of the harmony which are passing tones, neighbour tones, or incomplete neighbours are marked P, N, or IN.

“Aufschwung” means “Soaring up”; the piece has two themes —

the heaviness of bars 1 — 4, with its sighing Db to C (scale degree 6 to scale degree 5 in minor traditionally indicates tragedy)

and the weightlessness of bars 5 — 8, with its motion up a third, C — Db — Eb, and cadence on III.

(An important aspect of this weightlessness is that, in bars 1 — 8, the tonic, F minor, never appears in root position.)

The opening sound, Bb and Db, is odd in that there is no fifth (the F in parentheses is only in our minds, remembered from the end of the last piece). What is odd is held in our memory; we want to explore it. Schumann explores each note in turn — first Db, the tonic of the B section (measures 17 — 40), then Bb, the tonic of the C section (measures 51 — 112).

Both the B and C sections are permeated with the rising third of measures 5 — 8.

In measures 16 — 18, the beginning of the B section, the third is in the soprano, F — Gb — Ab; this third is then inverted to make a descending 6th (measures 20 — 24, F to Ab).

In measures 51 — 58, the beginning of the C section, these ideas are worked out with especial beauty:

the soprano begins with a descending sixth, Bb to F (measures 51 to 53), while the tenor rises a third from D to F and descends again. The tenor’s rising third is doubled in the bass, a tenth lower. As Heinrich Schenker wrote, passing tones like to move in pairs.

The overall harmony of measures 51 — 54 is Bb major; in measures 55 — 57, it is a dominant seventh on F. The bass arpeggiates this dominant seventh chord, from Eb to F, in a series of descending thirds.

Meanwhile, the tenor moves from F to its upper neighbor, G (measure 56) and back to F (measure 57).

The soprano moves from an implied F in measure 55 (expected as a resolution of the soprano’s G in measure 54) through an Eb in measure 56, to D in measure 58. (I have connected the F, Eb, and D with a beam to show this descending third.)

The combination of the soprano’s Eb and the tenor’s G in measure 56 creates, within the overall harmony of F, a local harmony of C minor. This is a very poignant moment.

A rising third, C — D — Eb, leads to the soprano’s Eb (measures 55 and 56); it is doubled in the alto, A — B natural — C. From the Eb, a passing E natural leads to F; this is harmonised by a neighbour motion, C — Db — C, in the alto, which, together with Bb in the bass, creates a harmony of the diminished seventh.

In measures 59 — 62, the basic progression is Bb major — G major — C minor. The Bb harmony is expanded with rising thirds in soprano and bass (soprano, D — Eb — F in measures 59 — 61, bass, Bb — C — D in the same measures). Again, poignantly, when the upper notes of the rising third arrive in measure 61, the local harmony is no longer Bb, but D minor.

In Schumann, the basic ideas are very simple, but expressed in poetic ways. When hear the underlying simplicity, the poetry is even more moving.

https://soundcloud.com/user-870249089/aufschwung-op-12-2-by-robert-schumann

4. Chopin’s Mazurka in F, Op. 68 #3

When I read a book, I read the thoughts of the author. The thoughts are expressed in words; the words are expressed in letters.

In a great performance, I hear the composer’s thoughts. The thoughts are expressed in harmonies; the harmonies are expressed in notes.

A piece may contain a million notes; to read the composer’s thoughts, perceive the harmonies!

A good way to begin is to make a harmonic reduction.

Below is my reduction of Chopin’s Mazurka in F Major, op. 68 no. 3. It includes all the harmonies, but none of the figuration or non-harmonic tones, except a few which are motivically important. Notes of the harmony which are passing tones or neighbour tones are marked P or N.

It is possible to reduce the music even more. A piece has a foreground (its surface), and a background (its basic structure). In between is a middle ground. I have included a graph of the middle ground, following Heinrich Schenker’s approach.

An important point is that the melody goes back and forth between the voices of the basic harmony: in measures 1 — 16, 25 — 32, and 45 — 60, between soprano and alto; in measures 17 — 24 and 33 — 44, between soprano, alto, and tenor. A melody like this is called by Schenker a “polyphonic melody”.

The piece develops three basic figures:

A — Bb — A;

F — E — F;

and F — D — Bb.

The piece begins with (3); soprano and bass move down in octaves, F — D — Bb (measures 1, 3, and 5). In between, (measures 2, and 4) are harmonies which support passing tones in the soprano.

The Bb in measure 5 is a neighbor to the A in measure 6. It connects with the A in measure 1 (inner voice), so measures 1 — 7 are a full statement of idea (1). Idea (1) is then echoed in measures 6 — 7.

The A in measure 6 is an important arrival. It’s the third scale degree in F major: stable, but not as stable as the tonic. It longs to descend to the tonic; in measure 8, it gets part way there with a half cadence.

The music begins again in measure 9, and reaches a full cadence in measure 16.

But A is still in our ear as the upper voice. Chopin asserts it strongly in measure 17, an octave higher and supported by an A major chord.

In measures 16 — 25, the bass arpeggiates an F major chord. Beneath the soprano A, F moves to E and then (measure 25) back to F — idea (2).

After a return of the beginning and a full cadence (in measure 32), measures 33 — 44 sound very different. The fifth, Bb and F, without a third to soften it, and the repetitions in the melody suggest folk music.

Folk music from the Podhale area in Poland has a scale with sharpened fourth (the Lydian mode); at first it sounds like Bb is now the tonic, and the E naturals in the melody are sharpened fourths.

Chopin has accomplished a miracle; it sounds like we have traveled to the countryside, and yet the music of these measures is closely related to the rest. The Bb in the melody is the neighbour note from measure 5; F — E — F in measures 37 — 44 is idea (2).

In measure 44, the bass moves up to C, and we realize the Bb in the bass from 33 to 44 was an expansion of IV. The A in measure 45 (inner voice) is a resolution of the treble Bb (measures 38 to 44).

In measures 59 and 60, the notes are the same as in measures 31 — 32, but the meaning is different. In measures 31 — 32, a section ends; in measures 59 — 60, the piece ends. In measures 59 and 60, the pianist must feel that the A, which had always wanted to resolve to F, is able to do so for the first time.

https://soundcloud.com/user-870249089/mazurka-in-f-op-68-3-chopin

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