KUNST DER FUGE CONTRAPUNCTUS I: THE MINERAL WORLD
Dernière mise à jour : 20 févr. 2018
Listen to Contrapunctus I: https://youtu.be/C82rGpPktCw
Read the score: http://hz.imslp.info/files/imglnks/usimg/5/5a/IMSLP121927-WIMA.c9c3-kfur.pdf
Many comments have been made about Kunst der fuge. This transcendental composition has always been a subject of discussions and doubts: for example the title may not come from the composer, or: how to know in which order the fugues should be played? Where are the scrolls that Bach’s son (Carl Philip Emmanuel) used for the second edition in 1751?
And as for the mystery of the unfinished fugue, it may not be the ultimate piece composed by J.S, but maybe the penultimate… In fact it is probable that the rest of this last fugue would have used the original theme, since it has been shown in 1881 that it can be combined with the 3 other soggetti, making 4 themes in all! By the way, in the first edition of Kunst der fuge, this last fugue was the 14th, a number frequently used by J.S.: indeed, check out that B+A+C+H=2+1+3+8=14!
Note the Fibonacci number sequence (1+2=3; 3+2=5, 5+3=8…) frequently used in art and music for proportions: for example there may be a climax at the 3/5 of the length of a piece, or a new section may begin at the 21th measure (13+8)…
But what is the message of this work? As the title says, and like many other music composed by J.S, there is an educational aspect in the Kunst der fuge. Maybe Kunst der fuge could also be heard as an act of resistance of counterpoint against the rising classicism and its accompanied melody…
What is sure is that J.S wrote it at the end of his life (1742-1750) and that it can be considered as a musical testament. At that time, J.S didn’t compose music for financial reasons anymore, or to answer an order. He even paid the printing of several scores himself. It is interesting to know that J.S got personally involved in this piece since he used his last name in several fugues (B.A.C.H corresponding to sib, la, do, si).
Does the original theme symbolize humanity and the various combinations in which it is played what it has been through?
Is it instrumental music or not?
Like many pure counterpoint pieces, no instrument is mentioned on the scroll. And as it is the case for every four parts pieces, Kunst der fuge can be played by a string quartet or other instrumental or vocal formations.
However, playing it on the piano, it cannot be denied that J.S paid minimum attention to keyboard possibilities. We should also add that in those days, knowing which instrument to use didn’t really make sense. Musicians probably used instruments which were available to them.
Moreover, about form, it is known that J.S taught rhetoric (thesis, antithesis and synthesis), and some aspects of Kunst der fuge particularly fit with it (for example the silences at the end of the first fugue). In the same way, some fugues written in French or Italian style sound like instrumental music.
Therefore, although there is thematic and tonal unity, contrapuntal texture everywhere in Kunst der fuge, it can’t be considered as only a pure, scientific counterpoint work.
The main theme:
The main theme of the Art of the fugue lasts 4 2/2 measures. It is based on a D (ré) minor chord arpeggio in the first 2 measures, with a raised seventh degree in the beginning of measure 3 (a “climax” halfway through the theme), and it ends with passing notes between the D minor chord tones. The first and last note of this theme is the tonic D. The first 2 measures contain intervals of 5th and 3rd and the 2 last one use stepwise motions. Moreover, note that the rhythm accelerates gradually and that measures 3 and 4 may almost be heard as a retrograde motion of 1 and 2.
So this theme shows important assets to write fugues: harmonic and melodic clarity, variety of intervals and rhythms and a tight ambitus (a minor 6th). Because of the choice of the ecclesiastical key of D minor, and the upward 5th at the beginning which sometimes symbolizes distance, this theme may sound archaic.
CONTRAPUNCTUS I: THE MINERAL WORLD
It’s the original idea, the number 1 which has the same shape as the crystal, the first of the 4 elements to appear on earth. The sunrise on a cliff lost in the mists of time. A raw fugue…
As regards the fugue, musical analysis helps us to make a distinction between which line is real thematic and which other one is only counterpoint, and so it makes it easier to play on keyboard.
Measures 1 to 22: the main theme in 4 lines (alto/soprano and bass/tenor)
Measures 1 to 17: The first fugue of this cycle begins with a usual exposition: the original theme is played without modifications, except the regular change of the upward 5th turning into a 4th in the dominant key (in this case A minor). In the 8 first measures, the alto plays the original theme in the D minor key, and then the soprano plays it again in A minor. In the same way, from measures 9 to 17, the bass plays the D minor theme and the tenor plays it in its turn in A minor.
In measure 6, the A- chord may be a pivot chord, the Vth degree of the D natural minor scale and at the same time the Ist of the A minor scale. Or is the D minor chord in measure 5 a I of a D minor scale and IV of A minor? Anyway the modulation in A minor really appears in measure 7 with the EM chord.
In measures 6 and 7, the alto pattern is also played later in the bass (measures 14 and 15). In measure 8 the chords CM D7 G- bring the fugue back in the D minor key, the G- chord being a IV of the D minor scale.
In measures 10, 11 and 13 alto and soprano rhythms are complementary. This “rhythmic conversation” between different melodic lines is the most important aspect of the fugue process. One line can also take over from another line: this is the case in measure 11: the alto continues the soprano line.
In measure 12 occurs an amazing short modulation in the key of CM, thanks to a D- chord in measure 11, which is both I- chord of D minor and II- of C major. Moreover, this modulation is embellished with the delayed C in the soprano, a minor 7th of the D- chord becoming a 3rd of G7. In the bass line, the delayed F gives the impression of a suspended sound.
In measure 13, the fugue goes to the A minor key thanks to a B-7b5 and EM chord. From measure 14 to 16, so as to emphasize the theme in the tenor line, soprano and tenor have the same rhythm. Notice that the alto line, which was the first to play the theme, stops playing from measure 16.
Examples of interesting contrapuntal combinations:
In measure 11, in the soprano, the delayed Bb becomes a diminished 7th of C#°7, seventh degree of the D harmonic minor scale, before resolving on a A to make a V7 of D minor.
In measure 15, in the bass line, the root of E7 becomes a major 7th of a FM7 chord.
And in measure 12 as seen above.
Measures 17 to 22: After each line has played the theme, there is a motivic sequence between soprano and tenor on one hand and bass on the other. These imitations, from measure 18 to 20, are built on the following harmonic progression: C7 FM, D7 GM, E7 A-, FM BbM, G7 CM, A7 D-. In other words, it consists in playing each secondary dominant and each chord of the natural minor scale of D minor. It can be also understood as successive short modulations in each neighbor tones of D- (except the GM chord which is from the melodic scale of D-).
Note that from measures 17 to 20, the bass line can be summed up as an upward stepwise chromatic motion from the tonic to the tonic. In measure 22, note the use of the D- melodic scale with the G7 chord, and the C#° dominant chord just before the alto begins to play the theme again in the D- key.
Measures 23 to 39: the theme in 3 lines (alto, soprano, bass)
At the end of measure 23 and 24, the continuous flow of quarter notes stops briefly to highlight the theme in the alto after the harmonic sequence of measures 17 to 22. .
In measure 27 and 28, a short harmonic sequence (G-, D-, and A-, E- in the E- key) sounds like a medieval, archaic music. On this chord progression, there are imitations between alto and tenor.
After having kept silent during 4 measures, the soprano plays the theme in measure 29 in the A- key, but without modifications (except at the end with the Bb in measure 32). Modulation from the previous key E- to A- occurs thanks to a DM chord (melodic scale of A-).
In measure 29 and 30, intervals and rhythm in the bass line may suggest a fake theme, whereas in measure 32, a real theme appears in the bass, but with many modifications. This is probably to avoid repetition, because this time the theme starts from the same pitch as the previous (in measure 29). Moreover, for the first time, there is a one measure superposition between the last of the soprano and the first of the bass (measure 32).
On the second beat of measure 32, there is a IV 7 chord of the A minor melodic scale followed by a passing G- chord. These chords bring the music back in the D- key in measure 33 with the A7 chord. But in measure 34, there is a modulation in the G- key, the I- chord of D minor becoming a V7.
From measure 34 to 39, the tenor keeps silent.
Measures 36 to 39:
Here is another motivic sequence based on the following harmonic progression: G- E°, A7 F+, BbM G- (harmonic scale of D minor), C7 A-, D- B°, E-7 CM, FM7 D-, G7 E- (natural or melodic scale of D minor).
In this sequence there are imitations between alto and bass, with delayed chord roots becoming 7th of the second next chord. Note that the soprano line can be summed up as a stepwise upward motion from C# to C# in the D minor melodic scale (as it is rising towards the treble).
There are similarities between measures 36 to 39 and the first motivic sequence from measures 17 to 20. First, the harmonic rhythm is the same, and the two harmonic progressions are based on upward chords of one or another of the D minor scales. Moreover, melodic lines go up in the two cases, and in the second motivic sequence, the bass and alto pattern are the same as those of the soprano and tenor in the first progression.
Nevertheless, there is a difference between these two sequences: the first alternates secondary dominant chords and D minor scales chords whereas the second only uses D minor scales chords.
Examples of interesting contrapuntal combinations:
The rhythm and intervals of the tenor line in measure 25 are the same as those of the alto in measures 25 and 26, and may give the impression of a real canon.
The amazing harmonic sequence in measures 27 and 28.
End of measure 32 in the tenor: the passing G becomes a delayed note.
Second time of measure 33: the F in the tenor is used as a neighbor tone of E, 5th of A7.
In measure 34, the soprano downward motion echoes the tenor in measure 33.
Modern intervals and rhythm of measure 35 (between alto and soprano).
Measure 36: delayed C# going up to D on the V I chords change.
Measure 39: use of the augmented 5th of a F chord (C#) as an approach note to D.
Measures 40 to 62: the theme in 3 lines (tenor, soprano, bass)
This motivic sequence (36 to 39) leads to a A7 dominant chord in measure 40, and that’s why the theme in the tenor begins by a E instead of a D.
Measure 42-43: there is a short dominant pedal bass, with a passing D- chord on the second beat of measure 43. On the first beat of measure 43, there is a F+ chord followed by a “pedal 4th and 6th” D- chord, a “second inversion” (and a Bb+ on the first beat of measure 44).
In measure 44, the alto is a transposition of the soprano in measure 43. The two first chords in measure 44 are also a transposition of those in measure 43: indeed there are F+ D- and then Bb+ G-.
Note that in measure 44, the alto plays the same notes as in measure 66.
From measure 45 to 48, the soprano keeps silent.
Measures 44 to 48:
There is a harmonic progression using the D natural minor scale (D-, BbM, E°, CM, FM, D-) and imitations between alto and tenor. The melodic pattern played here by the alto and tenor (the upward 4th) looks like that of the first motivic sequence from measure 17 to 21. In measure 46 and 47 is another harmonic progression with a short modulation in the F major key (D- G- C7 FM BbM E- A7 D-), and using imitations between alto and bass, while the tenor is playing chord roots. As for the alto, it can be summed up as follows: fa, sol, la, sib, la, sol, fa.
Measures 49 to 59:
In measure 48, intervals and rhythm in the alto line may suggest the beginning of the theme, but in measure 49, it’s the soprano which plays it for real, the first note D turning into E, to fit with the A7 chord. Note that the D natural minor scale is used (with its minor V chord) on the first beat of measure 48, followed by a G#° chord, dominant of V.
On the first beat of measure 49, the alto is a transposition of the tenor on the second beat of measure 48. In measure 50, the tenor pattern looks like that of the alto in measure 6 and 7 and that of the soprano in measure 17. At the end of measure 51, tenor and soprano follow the same rhythm.
From measure 49 to 55, the bass keeps silent.
In measure 56, the theme is played a last time without modifications in the bass line.
Measure 40: in the alto, the 7th (G) of the A7 chord can go upward because it’s going downward in the bass line.
Measure 51: melodic scale of D-.
Measure 52: short modulation in the CM key and the FM key.
Measures 52 and 53: on the first beat of measure 53, the delayed C implies a BbM chord. The last F in the tenor prepares the 7th of the G-7 chord.
Measure 55: D and the delayed E and F: a cluster chord!
Measure 57: with the two delayed notes E and C#, there is an ambiguity between F+ and D-, or a dominant over the 3rd of the chord….
End of measure 57: How to explain this “2nd inversion” of G-? is the G- over the D bass a part of a dominant over a tonic bass?
Measure 59: the tenor is an echo of the bass in measure 58.
Measure 58: bass and tenor follow the same rhythm.
Measure 60: the silences in the alto and tenor lines, the key of G- (subdominant of D-) are announcing the end.
Measure 61: a +6 3 chord (first inversion of F#°) in which the subdominant (C) can go upward.
Measures 63 to 78: dominant pedal, tonic pedal with the theme in 1 line (tenor)
From measure 63 to 66: the soprano line can be summed up as: la sol fa mi ré do sib la (A G F E D C Bb A), a stepwise downward motion from the dominant to the dominant.
Measure 63 to 65: the usual dominant pedal bass, just after the first inversion of the bIIM chord in measure 62 (the sixte napolitaine between the bass G and the soprano Eb).
Measure 64 and 65: tenor and alto follow the same rhythm and are an imitation of the soprano in measure 63.
From measure 67 to 69: note the harmonic progression IV V I played in the key of FM (BbM C7 FM), A- (D- E7 A-) and C- (FM G7 C-), and the melodic pattern coming from measures 17 to 21 played by the bass and tenor.
Measure 71 and 72: the 4 lines play plated chords interspersed with silences. Note the passing 4th and 6th chord of D- in measure 71 (2nd inversion).
Measure 74: here are the two final V I chords, with the usual major 3rd and the octave interval between the bass and the soprano on the tonic chord. Note the usual tonic pedal bass typical of the (baroque) codas.
From measure 74 till the end, the tenor plays the theme a last time but with many modifications, to fit with the usual baroque harmonic progression above the tonic pedal (D7 G- A° D7b9 G-…G° DM).
Measure 75-76: the soprano continues the alto pattern on the first beat.
Measure 76: alto and tenor follow the same rhythm.
Measure 68: in the soprano, approach notes F and D of the E, 5th of the A chord-.
Measure 66: the Bb+ chord with the delayed C and the F# resolving on a G- chord will be used later by F. Schubert and Romantic composers as a slash chord: D7b9/Bb or F#°7/Bb, a dominant of a chord above the 3rd of this chord.
Characteristic elements of the first fugue:
A rather free inner formal structure, with more and more spaced out themes, with no real modulations, no real canon, fake beginnings of the theme, the use in each motivic sequence of the upward 4th coming from the alto pattern in measures 6 and 7 (and from the first motivic sequence), the use of 5+ chords (or at least chromatic approach notes of a root).
Recurrent patterns: Note that the downward motif in the end of the main theme is used several times in different lines of the fugue: measure 4, 7, 11, 15, 16, 25, 29, 32, 33, 34, 35…
The archaic sounding upward 4th in measures 7, 11, 12, 15, 17, 18, 19, 27, 20, 22, 25, 27, 28, 29, 32, 35, 37, 38, 39, 43, 44, 45, 46, 47, 48, 49, 50, …
Summary of the first fugue: 4 parts
1-16: a usual first part: the theme in the tonic and dominant keys in the 4 lines.
17-22: long motivic sequence: repetition of a specific melodic pattern on a harmonic progression.
23-35: theme with mutations, but in only 3 lines, with a short motivic sequence (27-28)
36-39: long motivic sequence: repetition of a specific melodic pattern on a harmonic progression.
40-59: theme in 3 lines with a short motivic sequence (44-48)
60-78: the usual dominant pedal (a climax in measure 63?), final V I chords, tonic pedal with the usual V/IV…