Mis à jour : 20 févr. 2018
Listen to Contrapunctus III: https://youtu.be/5DCPoyhwOsM
Mirrors have always been shrouded in mystery. The shape of cow horns itself is symmetric, and cell division too. The number 3 has the same shape as the horns. The third step of evolution, after flora has developed, is the animal. At this critical stage the only laws were survival instinct, predation and genetic mutations. Horns may also symbolize the devil and in music, chromatic patterns may represent the snake.
In this fugue, it is the mirror theme which is used. In this process, upward intervals become downward intervals, and downward intervals become upward intervals. But how is it possible to keep the tonic key? Which mirror tone must be chosen (the tone which will stay the same)?
If the tonic is chosen as a mirror tone, it transposes it in the subdominant key. Notice that the mirror theme in the dominant key may result directly from the original D minor theme by choosing the dominant (A) as a mirror tone. The only way to get a mirror theme in the tonic key is to choose the 3rd of the tonic chord as a mirror, in this case F:
The original theme and its mirror in the D minor key (tonic)
The original theme and its mirror in the dominant key (A minor)
Additional chromatic theme in the main key
This secondary theme and the original one are always played together (and built on the same key). They go hand in hand.
This theme is roughly a downward stepwise (and chromatic) motion from the tonic to the dominant, with almost a retrograde movement. It can also be considered as a mix of the different D minor scales, the last measure sounding in the upward melodic scale. The most treble tone is the 3rd of the tonic chord. Note that themes are often built on important tones like the tonic, dominant and the 3rd of the tonic chord.
As regards the role of the other tones, it can be either understood as passing tones (or neighbor tones like the sharp G at the beginning of the second measure above) or as tones belonging to a real chord of the moment, even if it implies a fast harmonic rhythm. Sometimes the two explanations are relevant.
Measures 1 to 23: tenor and alto, soprano and alto, bass and soprano
The mirror of the original theme is first played by the tenor from measures 1 to 4. Here it is built on the dominant (the mirror tone is C) but some modifications make it sound in the D minor key (the first tone D, the sharp C and the upward melodic scale of D minor in measure 4).
Measures 5 to 8: Then the tenor plays the additional theme in measure 5 while the alto plays the original mirror theme in its turn, but this time both are built on the tonic (the mirror tone is F). As it has been said above, the additional chromatic theme in the tenor line uses downward minor or major 2nd and is a mix of the melodic (natural B and C sharp), harmonic (C sharp and B flat) and natural (natural C and B flat) scales.
Measures 9 to 12: The mirror theme, built on the dominant, is played in the soprano and the additional theme in the alto. There is a short modulation to the dominant key (A minor) in measures 10 and 11.
Measures 12 to 15: to bring variety, there are imitations between soprano and alto in the tonic key.
Measures 15 to 18: the bass plays the mirror theme while the soprano plays the additional chromatic theme (the lowest and the highest lines, both in the tonic key). Note that this time, with the rhythmic modifications and the sharp C, there are only chromatic tones between the tonic and the dominant in the additional theme (D C# C B Bb A).
Measure 19 to 22: After the mirror theme has been played by every melodic line, there is a harmonic sequence with real transposed imitations between soprano and alto. For example: in measure 20 the alto is the exact transposition in the G minor key of the soprano in D minor in measure 19. And so the same patterns are played in several keys: in measure 19: in the D- key, 20: in the G- key, 21: C- key and 22: in the F- key.
All along this harmonic sequence, on the 2nd beat of each measure, the bass line uses the root of the VIth degree of the natural minor scale of the moment, before using the melodic scale, to provide a chromatic pattern. Note the beautiful delayed subdominant on the first beat of each measure resolving on a 3rd of each tonic chord. It should be added that the alto pattern in measure 19 (also played by the soprano in measure 20) comes from the beginning of the additional theme.
Measures 18 to 29: the tenor keeps silent.
Measure 4: note the sharp C, a surprising raised seventh degree.
Measure 8: look at the delayed E, resolving on a D on the second beat.
Measure 9: a passing G becomes a delayed 4th resolving on the 3rd of D-.
Measure 11: on the 2nd beat, note the A- chord without root to avoid a 2nd inversion since the tenor is playing E.
Measure 15: to highlight the theme in the bass line, the tenor is playing the same rhythm. Also note the delayed D resolving on a C#. On the 2nd beat, the delayed C in the soprano becomes a 7th of the bass D, resolving on a B.
Measure 17: there is a diminished form of the dominant chord (Bb°).
Also note the delayed D becoming a 4th of a 2nd inversion of the tonic chord (the bass playing A).
In the tenor line on the 2nd beat, note the raised seventh degree C# going to the dominant (the 5th of the tonic chord) instead of going to the tonic in measure 18.
During the harmonic sequence from measure 19 to 22, on each first beat, this seventh degree first goes to the 3rd of the tonic chord of the moment, and then to the tonic (on the 2nd beat).
Measure 19: as it is the case on the second half of each first beat of the harmonic sequence, note the tonic chord without root. In the end of measure 19, note the passing chromatic G# which forms a V/V chord (G#° or +63) and G which forms a dominant chord (C#°).
Measures 23 to 43: soprano/alto, tenor/alto, tenor:
From measure 23 to 26, the mirror theme, built on the tonic, is played by the soprano with rhythmic modifications and passing tones. At the same time the alto plays the additional theme. In measure 23, the key is F major, but in the end of measure 24, the fugue comes back in D minor.
In measures 27 and 28, there is a short harmonic sequence (D7 G- and A7 D-) with imitations between soprano and alto (soprano in measure 27 is almost the same as the alto in 28). In the bass line, note the trille on the raised seventh degree of the key of the moment (or else the 3rd of each dominant chord).
From measure 29 to 32, the mirror theme built on the dominant and harmonized in the dominant key (A minor) appears in the tenor line, with the same modifications as in measure 23 (passing tones, rhythm). At the same time, the alto plays once again the chromatic additional theme, with almost the same modifications as in measure 23, except at the beginning and on the 2nd beat of measure 29 (the B to fit with the E7b9 chord and the 16th notes).
From measures 30 to 42, the soprano keeps silent.
From measure 33 to 35, there is a short harmonic sequence (A7 D7 B°, G7 C7 A°) in which each line (alto, tenor and bass) keeps the same motif, but goes to opposite directions. This motif is based on the end of the mirror theme. Note the chromatic downward motion on the second half of each measure. It sounds like continuous modulation.
From measure 35 to 38, the mirror theme built on F major is played by the tenor, but this time there is no secondary theme, even if the alto pitch contour and rhythm sometimes echoes that of the additional theme (particularly in measure 36). In measure 35, the key is Bb major but soon goes to F major in measure 36.
From measure 39 to 42, there are 2 harmonic sequences based on the following chords CM DbM B° E° and FM BbM G#° C#°, then DM EbM C#° F#° and GM CM A#° D#°. In those 2 sequences bass, tenor and alto play the same patterns as in measures 19 to 22. There are also imitations between tenor and alto (particularly in measures 40 and 41).
Note that measures 41 and 42 are the transposition to an upward major 2nd of measures 39 and 40. That’s why the sharp F on the first beat of measure 41 is so surprising.
Moreover, each second half of each measure is the same as in measures 19 to 22, but each first half is not. Indeed, this time the first chord of each measure isn’t a dominant of a minor chord, but a tonic major chord. As a result, in measures 39 and 41, there is a contrast between a major tonic chord (I) and a bVIM of a natural minor scale of the next (major) tonic.
Measure 26: the soprano continues the alto
Measure 36: the alto echoes the tenor
Measure 36: the bass plays the same as the alto in the 2nd part of measure 35
Measure 38: the tenor line continues the alto
Measures 43 to 50: soprano/alto
The soprano plays the mirror theme and the alto the additional theme, both are built on the dominant. In measure 43, it begins in the key of E minor and goes to the key of A minor in measure 44.
In measures 46 and 47, there is a little Canon between alto, soprano and tenor based on the stepwise upward movement from the dominant E of the A minor melodic scale to its tonic A (the end of the mirror theme, like in measure 32), and the downward stepwise motion from the tonic to the dominant in the A minor natural scale. This pattern is transposed to an upward 4th (or a downward 5th). As a result, the fugue goes through the keys of A minor, D minor and G major.
From measure 48, there are no more Canon and each line keeps its own pattern transposed in several keys. So it can be considered as a short harmonic sequence: indeed in measure 48 the soprano plays the pattern of measures 46 and 47 “transposed” in the C major key (or harmonized with a G7 and C7 chords) and measure 49 is the transposition of 47 and 48 in the Bb major key. This harmonic progression can be summed up as: D7 G7 C7 F7 Bb7 EbM. Note that this way down keys with more flats announces the last part of the fugue.
From measures 47 to 50, as every line almost have the same rhythm, note the use of the opposite movement: 2 lines in 3rd going upward or downward, whereas the other is going downward or upward.
From measures 46 to 50, the bass keeps silent.
Measure 45: passing and delayed notes.
Measures 51 to 67: bass/soprano, alto/tenor, soprano/bass, tenor/bass
From measures 51 to 54, the bass plays the mirror theme in the G minor key (the subdominant key). The additional theme only appears from measure 52 in the soprano line, measure 51 being an imitation of the first beat of 52. Note that measures 52 and 53 are almost the transposition of 16 and 17 in the G minor key! It is also the case with the soprano and bass between measures 54 and 19. In measure 51, the soprano continues the tenor of the second beat of measure 50.
Measure 53: on the second beat, note the 4 and 6 inversion on the G- chord thanks to a delayed G in the alto.
Measures 55 to 58: The mirror theme built on the tonic (and mostly harmonized in the tonic key) is played by the alto, the additional theme by the tenor (note the rhythmic modifications). In measure 55, thanks to a E in the bass used in a stepwise motion (a +6 inversion of the dominant A7), the G in the soprano, which is the 7th of the A7 chord, can go upward.
In measure 58: note the continuation between tenor and alto.
Measures 58 to 61: The soprano plays the mirror theme built on the dominant, and from measure 59 the tenor plays the additional theme. In measure 58, the key is D minor, and at the beginning of measure 59, the key is A minor.
Measure 63 to 66: the mirror theme appears (a last time) in the tenor, and the chromatic secondary theme in the bass, both built on the tonic key.
In measure 61, on the 2nd beat, the soprano pattern is the same as that of the little canon in 46, or that of measures 12 to 14. The alto pattern at the beginning of 62 also recalls measures 12 to 14. But this time, instead of subsiding, the music increases in strength and intensity.
In measure 63: On the second beat, thanks to the opposite stepwise motion between bass and alto on the G- (or GM chord?) it is possible for the delayed note (C) to be under the real note (Bb).
The harmonic context of measure 63 is interesting: in the first beat, the A7 chord goes to a A-7b5 chord (the dominant of the D minor key goes to the 2nd degree of the G minor key!). Maybe the climax of this 3rd fugue is the first beat of measure 64.
At the end of measure 63, the flat B in the bass and the sharp G in the soprano would be understood nowadays as a Bb7 chord. They are both resolving on the dominant tone and on a second inversion of D- in measure 64. It is also the case between measures 59 and 60, Bb and G# go to A (A belonging here to a first inversion of F+).
Measure 66 and 67: the alto echoes the tenor.
Measures 68 to 72: there is the coda with the usual tonic pedal, but no dominant pedal before. Note the usual chord progression from measure 68: G-, D7, A7/D (a +7 chord: a dominant chord over the tonic pedal), D7, G-, DM.
Summary and characteristics of the 3rd fugue:
This fugue of great intensity differs from the others by the chromatic secondary theme, the use of chromatic tones, amazing chord progressions and modulations and unusual resolutions. All of this gives the tragic impression of an anomaly or a painful transformation.
1-23: The mirror and secondary chromatic theme appear 3 times. This part begins in the medium and ends with a larger register from the bass to the soprano.
23-43: The mirror and the secondary themes appear 3 times with rhythmic modifications and additional tones, the secondary theme may not appear completely. This part ends in a lower register.
43-50: A central part where the theme only appears one time.
51-67: A last part with more and more intensity, with a dense 4 lines counterpoint and more closely spaced themes, and a climax in measure 64. Note that almost every lines speak, except the 2 measures before the soprano and tenor theme (measures 56-57 and 61-32).
68-72: A relatively short end.
To conclude, it may be said that in this fugue J-S managed to write a piece in which almost every moments are important.