Listen to contrapunctus V: https://youtu.be/ALjSKpSfk54
As it has been said above, each fugue has its own character. But from this 5th fugue emerges an impression of compassion, standing back and awareness, regret, weariness, as if J-S was trying to describe us the fragility of life and the uselessness of suffering.
Measures 1 to 30:
From measures 1 to 12, the theme or a mirror of it is played a first time by each melodic line. Then there is a short harmonic sequence (measures 12 to 16). At last the theme is played once again by each line (17 to 30).
Measures 1 to 13: themes
This fugue begins with the mirror theme built on the D minor tonic key and played by the alto. Note that this time J-S adds passing tones between the tonic and the dominant (measures 1 and 2).
From measures 4 to 7, the original theme is played by the bass. It is built in the tonic key with passing tones too between the dominant and the 7th degree.
From measure 7 to 10, the soprano plays the original theme in the tonic key. In measures 11 and 12, the alto keeps silent on the last and first beat.
From measures 10 to 13, the tenor plays the mirror theme built in the dominant key. In measures 17 and 19, the tenor keeps silent.
Note that each theme begins one measure before the previous has ended, and so there is one measure of superposition or real canon.
Measures 1 to 13: harmonic context
From measures 4 to 6, note the nice melody over the bass theme, and the clarity of the 2 melodic lines. In measures 4 and 5, these 2 lines go in an opposite motion. Measures 5 and 6, the chords are D-, BbM, A7, D-. Note the delayed 7th on the 2nd beat of measure 5, and the delayed 4th on the 2nd beat of measure 6.
In measure 7, the chords are D-, GM and C#° (the +6 3 version of the dominant). What is interesting here is that the passing F in the bass at the end of the measure creates a F+ chord. Moreover, the alto (on the first beat) and the bass (last beat) are written in imitation.
In measure 8, the 7th of G (F) in the bass line and the 4th of A (D) are prepared.
In measure 9, chords alternate between A7 and GM (AM, GM, C#°). Note the complementary rhythms between the alto playing melodic 4th and the bass, and the delayed 9th above the first inversion of GM. Moreover, the bass follows the same rhythm as the soprano, the 2 lines being at a distance of 3rd.
In measure 10, note that the alto plays 4th again on the 2nd beat. Only built on a D- tonic chord, this measure is a good example of pure counterpoint. It also uses the upward melodic scale.
In measure 11, the degree V (A-) of the D minor natural scale is used. The soprano upward motion is an imitation of the alto in measure 10. In the soprano, note the G# which brings more tension and expression than a natural G. Moreover, this measure goes to a more treble register. It ends with the bass playing an imitation of the alto in measure 10.
Measures 12 and 13 consists in a melodic and harmonic sequence, with the chords BbM E-7b5 A7 D-.
Measure 12 uses the chords BbM and E-7b5, with continuity between soprano and alto. In measure 13, there are A7b9 and F+ chords thanks to a delayed minor 9th and augmented 5th. The 2nd beat of the alto is like the 1st of the bass. Note that the F+ chord is like the first inversion of tonic chord with the delayed 7th C#.
In measure 14, chords are D-, BbM, A7 or D-, BbM, E-7b5, A7 (+63). Note the delayed D in the tenor.
In measure 15, the alto is the same as in 10. In measure 16, the alto is the same as the tenor at the end of measure 14.
After each line has played the theme, the bass plays a dominant pedal in measures 15 and 16. By the way, there is a pedal 4th and 6th (2nd inversion) of the tonic chord on the 2nd beat of measure 15. This dominant pedal brings variety between two expositions. Note the 6th between the tenor and alto in measure 15 and the delayed 4th in the alto on the first beat of 16.
Measures 17 to 30:
Once again each melodic line plays the theme in its turn. This time again there is a one measure superposition.
From measures 17 to 21, the soprano plays the mirror theme built on the A minor key.
From measures 20 to 24, the tenor plays the original theme built on the A minor key.
From measures 23 to 27, the bass plays the mirror theme built on the D minor tonic key.
At last, from 26 to 30, the alto plays the original theme built on the D minor key.
Measures 17 to 30: harmonic context
From measures 17 to 23, the soprano and alto lines work together.
In measure 17, there is a D minor tonic chord. In measure 18, chords are FM, A-, CM. In measures 18 and 19, there is continuity between alto and bass. Measure 19 uses the following chords: a D- with a delayed 7th, B-7b5 and E7. This is a modulation to the dominant key A minor.
So in measure 20 there is a A- tonic chord and D- on the last beat (with a delayed 9th). In measure 21, there is a 4th and 6th inversion and a V/V (D#°) chord over the dominant pedal bass E.
In measure 22, there are E7 and A- with a delayed 9th and continuity between soprano and alto.
In measure 23, the Bb and natural G in the soprano shows that the fugue comes back in the tonic key. Chords are A-, D- and E-7b5. Note the intervals of 6th between tenor and soprano and the delayed 7th on the 2nd beat.
In measure 24, chords are FM, D-, FM, AM. In measures 24 and 25, the alto keeps silent.
In measure 25, chords are BbM, D- and A7. Note the delayed 4th on the 2nd beat. Moreover, this delayed 4th in the tenor with the neighbor tone F in the soprano form a 4th and 6th (a fake 2nd inversion of D-).
Measure 26 uses a D- chord. In measure 27, there are two delayed 4th in the tenor and the soprano forming a 4th and 6th (2nd inversion) of D-. Note the beautiful 4th between alto and soprano, which highlights the alto theme. Chords are D- (2nd inversion), A- and G-. Note the continuity between tenor and bass.
In measure 28, chords are C#°7, D- with a delayed 4th and BbM.
Measures 29 to 46: 2 lines canons with the original and mirror theme
From measures 29 to 32, the end of the alto theme merges with the beginning of a beautiful desperate sequence in which each line goes downward to a low and deep register.
From measures 33 to 37, there is a canon between the bass and soprano. The bass theme begins on the first beat of measure 33 and is built on the F major key (the relative key). The soprano begins on the 2nd beat and plays the mirror theme built on the same F major key.
From measures 38 to 40, there is a harmonic sequence in which the alto and soprano use delayed 7th and 6th and the bass plays quarter notes in stepwise motion.
From measures 41 to 45, there is a canon between the tenor and the alto. The tenor begins to play the mirror theme on the first beat of measure 41, which is built on the G minor key (the subdominant key). The alto begins to play the original theme (built on the G minor key again) on the 2nd beat of the same measure.
Measures 29 to 32: harmonic sequence
In measure 29 chords are D- and F7. In measure 30 there is a BbM with a delayed 9th and so a short modulation to the Bb major key.
The harmonic sequence consists in the transposition of the chords D- F7 and BbM (measures 29 and 30) to BbM D7b9 and G-. Indeed, note that the imitations between bass, alto and tenor in measures 29 and 30 are based on the same chord tones as those in measures 30 and 31. Moreover, this sequence modulates from the Bb major key to its relative G minor.
Measures 33 to 37:
Thanks to a C7 chord at the end of measure 32, the fugue modulates to the F major key in measure 33 (the relative key of D minor). Note the delayed 4th on the C7 chord and the continuity of the stepwise motion between alto and tenor.
In measure 34, chords are FM and D-, since the Bb on the last quarter note in the soprano is a passing tone.
Measure 35 is based on the chords C7, BbM, D- and E-7b5. Note the 2nd inversion of the BbM created by a delayed 4th on the 2nd beat (F-Bb). The last quarter note is a good example of the use of the VII-7b5 chord of a major key as a dominant (here E7b5). The 7th D is prepared and resolves on the C on the first beat of the next measure.
So measure 36 uses the chord FM. In measure 37 and 38, the last part of the theme is enlightened since the soprano, alto and tenor uses the same rhythm. However, the tenor on one hand and the soprano and alto on the other hand follow an opposite motion.
Measures 39 and 40 consist in a nice melodic sequence in which the soprano plays delayed notes. It sounds in the C major key (at least until the G- chord). Chords are G7, CM, FM, G7, CM, G-.
Delayed notes in the soprano are the 7th of G7, 7th of FM7, 7th of G7, 9th of CM, 4th of G-.
The bass is playing a continuity of quarter notes in a stepwise motion while alto and soprano alternate between 6th and 7th with a note rhythm.
Measure 41 to 46:
In the beginning of measure 41, appears a short modulation to the F major key. Chords are C7 with a delayed 7th and FM. However on the 2nd beat there is a C- chord with a delayed 4th in the bass. Note the nice downward chromatic embellishment in the soprano (with the natural B).
Measure 42 consists in a dominant pedal of the G minor key in the bass (so D). This measure uses the following chords: Bb+ (the 3rd degree of the G minor harmonic scale), G- (a pedal 2nd inversion of the tonic chord), and BbM (3rd degree of the G minor natural scale). Note that the soprano pattern on the first beat of 42 looks like those used in the first fugue, with the raised 7th degree (the augmented 5th) going to the tonic. Moreover the upward 4th D-G recalls the first fugue too.
Measure 43 is based on a EbM chord with a delayed 7th in the bass, followed by a degree II (A-7b5) with a delayed 7th in the alto and a dominant chord with a delayed 7th in the bass.
Remark that this G minor subdominant key appears relatively soon (in half-fugue).
Measure 43 only uses the tonic chord of the moment. There is a continuity of a stepwise motion between bass and tenor (upward melodic G minor scale).
In measure 45 the soprano plays a nice little contrechant. This measure is built on G- and C- (with a delayed 9th and a passing F7).
The F7 and BbM chords of measure 46 announce the advent of the next theme in the Bb major key. Note the delayed 7th in the bass (Eb) and the delayed 9th in the tenor.
Measures 47 to 68: octave canons and double tightened canons (2 different ones)
From measures 47 to 52, there is a canon between bass and tenor and both are playing the mirror theme built on the Bb major key (the major relative of the minor subdominant key). So the tenor plays it an octave higher than the bass.
From measures 53 to 56, there is a double tightened canon between soprano and tenor on one hand, and alto and bass on the other hand. They are both reproduced at an octave interval and a half note of distance. The canon between soprano and tenor uses the mirror theme built on the C minor scale. The canon between alto and bass plays the mirror theme built on the G minor scale. These 2 canons are exact until measure 56.
From measures 57 to 62, the original theme built on the D minor key is played in canon between soprano and alto.
Measures 47 to 52: the first octave canon
In measure 47, there is a prepared 4th and 6th inversion of BbM. The 4th (the tonic Bb) resolves on a A, 3rd of a F7 chord. On the 2nd beat of measure 47, there is a tonic chord.
Measure 48 uses the first inversion BbM, its 2nd inversion (with the prepared Bb in the soprano) and the dominant chord.
This dominant chord is followed in measure 49 by a G- chord (VI degree of the Bb major key) with the tonic in the soprano. Note the passing 7th on the 2nd beat in the bass. Note that the soprano uses a rhythmic diminution of the theme played by the tenor. This process creates the impression of an echo.
In measures 50, the tonic chord is used. Note the parallel motion of 3rd between soprano and alto.
In measure 51, we can hear a prepared 4th and 6th 2nd inversion of BbM over a dominant pedal. This chord is followed by a F7 and a D-.
Measure 52 begins with a pedal 4th and 6th and continues with a C7 (V/V) over a dominant pedal. This measure ends with the dominant chord with a delayed 4th.
For the first time, as it can be found in the first fugue, the continuous flow of quarter notes stops briefly on the dominant chord of the Bb major key in measure 53.
Measures 53 to 56: the first double canon
In measure 54, chords are C-, EbM and G-. Then in measure 55, there are BbM, D-, FM. In fact, the roots of these chords follow a harmonic sequence since their roots are separated by the same interval of 3rd (it is roughly the alto line without the passing tones). Note that in measure 55 the soprano is a transposition of itself in measures 52-53 a major second up.
Measures 57 to 62: the second octave canon
In measure 56, the chords A-, E°, G- and D- prepare the return of the tonic key D minor. Indeed in measure 57, there is a A7 chord with a delayed 4th and passing tones derived from the E7 chord (G#, B and D of the V/V).
In measure 58, there are D- and G-. Note the 7th (C) of D- played after the apparition of the chord. Then this note becomes a delayed 4th of the G- chord.
In measure 59, a A7 chord is followed by a F+ (a D- chord without root) and a D-.
In measure 61 note the G- chord with the delayed 9th A in the bass. Or else it could be understood like a BbM7 chord with the delayed 7th, since it sounds a little like a V VI progression.
Measure 61 ends with G- and D-.
Measure 62 to 64:
This harmonic and melodic sequence includes the following chords: F7, BbM, G7, C7, A7, D-. It consist in a succession of V – I progressions with an upward chromatic bass from A (the dominant) to D (the tonic). During the whole sequence, there are imitations between alto, tenor and soprano: a continuity of a stepwise downward motion between these 3 lines. This motion begins on each 9th of each chord. In measure 64, chords are A7 with a delayed 7th and D- with a delayed 9th. Over the D- chord, note the beautiful embellishment (G#) of A in the alto, which forms a D° V/V chord!
In measure 65, there is a pause on the AM dominant chord, as it was the case in measure 53: the flow of quarter notes stops.
Measures 65 to 68: the second double canon
This sequence is based on the beginning of the original theme with additional passing notes. The first canon is built on the D minor key between soprano and bass. Note the modification of the first note in the soprano because of the AM chord on the first beat of measure 65 (E instead of D). The bass plays the same thing as the soprano a 5th lower.
The canon between alto and tenor is built on the G minor key and the 2 lines are at a distance of 5th. Like in the soprano line, there is the same modification at the beginning of the alto: a A instead of a G, as a result of the D- chord at the end of measure 65.
In measure 66, chords are D-, G- with a delayed 7th and a +6/3 inversion of E°. Measure 67 uses C7 and FM with a delayed 7th. Note the short modulation in the F major key.
So the harmonic sequence is D-, G-, E° then C7, FM and D-, BbM, G-, C7. The canon between soprano and bass lasts until the end of measure 68.
Measures 69 to 85: 2 lines canon with the mirror and original theme
From measures 69 to 72, the soprano plays the mirror theme based on the D minor key. One measure after (from measures 70 to 73) the tenor uses the same mirror theme an octave lower.
From measures 77 to 80, the tenor plays the original theme in the tonic key and one measure later, it is the alto which plays the same theme an octave upper.
Harmonic context:
After the C7 chord in measure 68, measure 69 uses a A- chord which becomes a +63 inversion of F#°, dominant of the G minor key. Then there is a G- chord with a delayed 4th.
In measure 70, the 4 melodic lines go to a relative high register on a D- chord.
Measure 71 uses BbM and A7 with a delayed 4th in the bass.
In measure 72 chords are BbM, G-, a 2nd inversion of FM (thanks to a delayed 4th), A-, D- and E°. So in measure 73 there is a short modulation to the F major key.
In measure 73, there are a FM and a BbM chord with a passing D7 chord in the +6 inversion.
There is an imitation between soprano and tenor from measures 72 to 74. The soprano motif is in the F major key and the tenor motif in the G minor key.
In measure 74 there are a D7 and a G- chord with a delayed 4th.
Measure 75 uses a D- chord with a passing +6 inversion of A7, a G- chord with a delayed 9th and a E° chord. In measures 76 there are the chords A7, D- with a delayed 9th and BbM. Note that in measures 76 and 77 the bass plays a melodic sequence.
In measure 77, there is a short modulation to the A minor key thanks to the chords E7 (with a delayed 7th) and A-.
Measure 78 is made of a D- and G- chord (with a delayed 9th). In measure 78, there is a F+ chord thanks to a passing F over a AM chord in the soprano and alto. On the 2nd beat of this measure there are a D- and a BbM chord.
In measure 80, there is a F+ chord which plays a dominant role. The last quarter note is a C#° preceded by a B-7b5 chord (a degree VI of the melodic D minor key). Note the pedal 2nd inversion of D- on the 2nd beat.
Measure 81 uses D- and BbM.
In measure 82 there is a chromatic bass. Chords are a 4th and 6th 2nd inversion of BbM thanks to a prepared 4th (Bb) in the tenor. Then with the F# in the bass there is a D7 chord (dominant of the G minor key). At last appears a G- chord.
Measure 83 is made of EbM, G- and G7 (with the chromatic upward bass).
In measure 84, chords are A7 with a delayed 7th and D-, B-7b5, and G-.
Measure 85 uses the chords C#° (with a delayed 7th), BbM with a delayed 7th, Bb7 and A7 with a delayed 4th.
Note that the chord Bb7 appears thanks to the G#, the embellishment of the A in the bass line.
This is the final I – V progression, with the DM tonic chord in measure 86 (with a delayed 4th).
Measures 86 to 90: original and mirror themes in the coda
During this coda, the original theme is played by the alto, while the mirror theme is played by the bass at the same time. Both are built on the D minor key. Measures 86 and 87 use the D7 chord (dominant of the degree IV). In measure 88, there is a C#° dominant chord over the tonic pedal bass on the first beat. On the second beat we can hear a +6 (2nd) inversion of the D7 chord. As it is not the last inversion of the chord, this inversion can be used. Moreover the bass follows a stepwise motion.
In measure 89, there is a 6th and 5° 1st inversion of D7. On the 2nd beat, over the G subdominant bass, there are passing chords: C#°, DM and C#° (V, I, V over the G bass).
Note that in this coda, there are sometimes 5 or 6 melodic lines (measures 86, 89). Also remark that soprano and tenor are written in mirror (measures 86 and 87), the mirror tone being A.
Finally, this fugue includes 4 parts and a coda. From measures 1 to 29, a first part consists in playing the theme by each melodic line 2 times. Measures 30 to 46 use 2 real canons. Measures 47 to 68 make us ear 2 octave canons and 2 double tightened canons. The last part from 69 to 85 is made of 2 canons. The 4 measures coda uses 2 times the mirror process: with the original and mirror theme and with an additional pattern and its mirror, both played at the same time.