J.S.Bach's 2 voices Invention manuscript.

J.S. Bach's 2 Voices Invention n.13 - Analysis

Bandoneón score, formal and harmonic analysis

The two-part invention n.13 by J.S. Bach is part of the program of the exam of bandoneĆ³n pregrado II in the Buenos Aires Conservatory "Manuel de Falla", corresponding to the fourth year of study of the initial cycle. It is therefore part of my study program this year, and I decided to study it through a formal and harmonic analysis to improve the execution through a more in-depth knowledge of the work.

The work is really very beautiful, a little gem among Bach's compositions (like all two-voices inventions, actually).

I share the score for bandoneón (from the wesite of M. Rodolfo Daluisio). In the score, the letter A stands for "open" and C stands for "close".


Download J.S.Bach - 2 voices Invention n.13 - PDF

Some history

The two and three-part inventions are born for educational purposes for Wilhelm Friedemann's musical education, Johann Sebastian's eldest son, and the other sons of the great composer. They date back to the period between 1720 and 1723, when Bach was chapel master in Köthen. Emblematic case in the history of music, it is a collection of compositions today universally famous, originally born for the musical training of Bach's children and closest relatives.

The frontispiece from 1723 edition says:

"Effective method with which it is presented in a clear form to lovers of the harpsichord and especially to those who are eager to learn [...] and thus obtain not only good inventions, but also to be able to perform them well and above all to achieve the art of cantabile and the taste of the composition."

With this declaration, Bach clarifies his pedagogical intent:

  • provide several examples of two-part pieces, to be able to play them on the keyboard until complete independence is achieved in both hands.
  • Show how to use simple musical ideas in various ways, that's to say, to compose "good inventions".

The invention as a compositional form is strongly related to Bach, who drew heavily from the Italian counterpoint improvisation.In particular Bach was inspired by the works of Francesco Antonio Bonporti, whose Opera X is called "Inventions" (some of Bach's works are nothing but transcriptions of this work).

The meaning of "invention"

The word "invention" is from latin "invenire" that means "find by investigating".

The invention start with theme exposition and continues with the melodic and harmonic reworking of the subject. This is what "finding" means, that is, meeting original and creative musical solutions in the possibilities offered by the subject.

The subject in Invention n.13

In Invention 13 the theme is exposed in the first two bars, in a sentence composed of a antecedent and a consequent.

Here is the antecedent at the melody:

And here is the consequent:

What can we notice immediately? These are basically arpeggios: in the antecedent we have the arpeggio of the fundamental in the facing position, followed immediately after four notes by an eighth playing on the dominant, and then resolving on the fundamental chord with another arpeggio game. Bach is already telling us what his "magic formula" will be for the composition of the entire piece: basically permutations of arpeggiated notes.

The subject of the melodic line is echoed by the counterpoint of the accompaniment, with an imitative form at the lower octave. Below is the first bar for the 2nd voice line:

Compositional technique and structure

Compositional technique is the double counterpoint.

The structure is quite simple: the theme exposition is followed by a development, which can be divided into two parts, "Development A" and "Development B". Theconclusion follows the development.

Structural analysis of J.S.Bach's two-part invention n.13, in the image the score is divided into its the structural elements.

I decided to divide the development into two parts because the cadence at E minor of bar 13 marks a certain detachment, as if introducing a moment of pause. Development B has its own identity and with harmonic and phrasing characterization that we are now going to analyze.

Harmonic analysis: overview

In bars 3-6 we have the first progression that leads us to the first modulation at C major. In bar 7 the theme is re-exposed in the new key, and a second progression begins which modulates to G major (bar 10) and which ends with the affirmation of E minor (bar 13). Development A also closes with this modulation, characterized by a frequent re-exposure of the subject declined in the various harmonic "nuances".

Development B starts immediately with a third progression that crosses the chords of D minor, C major and E minor before reaffirming the dominant E7 in view of a resolution on the starting key (bar 18.) The peculiarity of this progression is that to use diminished seventh chords instead of dominant ones. This choice makes harmony more tense. Even the structures become more tense, concentrated: let's observe for example this structure (bar 14)

the melodic phrase is entrusted to the first half of the measure, while in the second half we already have the element of tension (diminished chord) which wants resolution at the new tonal center. All the musical discourse is now concentrated in one bar instead of two, as we have seen so far in the subject and in the previous progressions.

In this progression, the various passing tonal centers are underlined by a little descending scale in the 2nd voice line, as can be seen in this bar (the 14th, again)

and that ends at a D note. This same structure is "declined" throughout the progression, from bars 14 to 18.

At bar 18 we have a first reprise of the subject, which gives us a taste of conclusion. But it is still far away: Bach has not finished yet the musical discourse.

The reprise of the theme serves to introduce the fourth and final progression (bar 19). The musical discourse becomes even more dense and concentrated: the melodic line is now divided into sixteenth notes (measures 19, 20, 21).

Finally we reach the conclusion (bar 21): a last reprise of the theme confirms us that we are going right to the end. The "conclusive process" has already started in sixteenths and with this rhytmic subdivision we reach the conclusion . A perfect cadence in the last bar underlines the ending. Interesting note: the B flat that appears in the bass part at bar 23 belongs to a second Neapolitan.

What does the work say?

The brevity of the work clearly shows its didactic character. The theme is very interesting in relation with its development, probable intention by J.S. Bach to familiarize the student with arpeggios and melodic connections between the various chords. I personally recognize a certain crescendo of intensity and tension, which accumulates in "Development B" and unleashes itself in the conclusion: a conclusive musical discourse concentrated it in 4 bars.

Binary elements often occur, as well as musical ideas divided into two bars (or in one bar but divided into two) and musical macro-structures that develop in groups of 4 bars. Symmetry elements balance the musical discourse along the whole course of the composition.

Conclusion and comments

Much more could be said about this splendid composition, however I hope that my analysis has served and inspired you with reflections. if this article intrigued you, left you questions, and you feel that you want to share your opinions with me, I invite you to contact me by email - or using social networks (links below). I will be thrilled to hear your point of view!

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