counterpoint miguel vicente
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18th century counterpoint The first two pieces presented here are based on Bachs models, using the same bass line of used by Bach. This procedure of writing new upper voices on a given bass has been employed as a learning exercise since Bach time. As Mattheson suggested one hereby proceeds (...) by means of choosing one or another piece already written by a competent master and keeping the upper voice secret until one can compare the melody invented over the bass alone with the original. 1 One example of this kind of recycling of a bassline is found in Bachs oeuvre. The bass line of the sonata for violin and continuo in G major, BWV 1021 is used again (with minor modifications) in the sonata for violin and obligato harpsichord in F major, BWV 1022 (this last piece exists also as a trio sonata in G Major for flute, violin and continuo, BWV 1038). For my first exercise I took as a model the 9th movmement of the motet Jesu, meine Freude, BWV 227.
Initially I took the bass line to write two upper parts above it, but the fact that the model was a chorale prelude made that using only the bass without the choral melody made the result lack of direction, so finally I decided to write a quartet, keeping the chorale prelude texture. This kind of texture can be found sometimes in the cantatas, as in Jauchzet Gott in allen Landen (Praise God in all lands), BWV 51.
Quoted from Mattheson, Der vollkommene Capellmeister in Schubert & Neidhfer, Baroque counterpoint, Upper Saddle River, N.J.: Pearson Education, 2006, p. 3
For the second exercise I chose the bass from the second movement of the organ trio sonata in G, BWV 530.
I wrote two upper parts above this bass and I added the figures for the continuo. The possibility of realize or not of continuo seems to be a not decisive factor for Bach. He wrote a trio sonata for two flutes and continuo in G major that was later adapted for
viola da gamba and harpsichord (BWV 1027) in which the left hand of the harpsichord plays the bass line and the right hand plays the 2nd flute part, leaving out the continuo realization. Altough trio sonatas were present in Bachs oeuvre (in addition to the two mentioned above BWV 1038 and 1039 there is a trio sonata for flute, violin and continuo in c minor in The musical offering, BWV 1079) this genre was much more exploited by other composers such us Telemann. Telemanns style differs from Bachs in several ways. The thematic material is usually more varied and not as compact as in Bach. This variety can be achieved by the change of rhythmic figuration (series of sixteenths, triplets, dotted rhythms). Telemann also writes more passagi (fast scales, arpeggios and broken chords) and much more fragments in which the upper parts move in parallel thirds or sixths. 2 The bass line tends to be simpler and less melodic than in Bach, although occassionally takes over the passage-work of the upper voices. The third exercise presented here is written according to these premises.
In Versuch einer Anweisung die Flte traversiere zu spielen Quantz gives some guidelines for writing a trio, where he warns us against the excesive use of passages in thirds and sixths explaining that although they are one of the ornaments of a trio, they must be not abused or dragged on ad nauseam; they must be regularily interrupted with passage-work or other imitations.
Counterpoint alla Shostakovich Looking to the fugues of Shostakovichs cycle of 24 Preludes and fugues, op. 87 we find a great variety in the style of the the themes and the pieces themselves. First of all I tried to find common elements and classify the different fugues. The first aspect I considered was the quality of the theme, and I distinguished between the fugues with a more vocal treatment (moving mostly stepwise and with singable leaps, and with a slow or moderated tempo), and the fugues with a more instrumental character (with more leaps, arpeggios, faster movement). Examples of the vocal type are the fugues in C major, e minor, F# major and c minor. Examples of the more instrumental approach are, among others, the following ones: a minor, A major, E major, g# minor and D major. Another aspect I considered was if the theme was diatonic or not. Most of the themes used only diatonic pitches, but the ones that included non-diatonic pitches (D major, E major, g# minor, f# minor) produced a very characteristic sound. The non-diatonic pitches are used mainly in two different contexts. As part of chromatic scalar movement, as in the fugue in D major (one of the elements of this theme is the compound melody of chromatic scales in contrary motion), or more often as a modification of a diatonic step, usually lowering it a half step. For example, in the fugue in f# minor Shostakovich uses the b7, and in the fugue in E major the b2 and b3 scale degrees. Apart from this criteria other aspect that I considered relevant was the use of irregular meter (often 5/4; A major, E major, g# minor) or frequent changes of time signature (b minor and D major). For the rest, we find very diverse approaches. From the themes closer to a traditional design, like the ones in a minor and G major, to others with a structure of antecedentconsequent (D major) or sentence (g# minor), more typical of homophonic elaborations. We also find repetition of motifs within the theme (f# minor) and others particularly idiosyncratic, like the b-flat minor, that resembles an ornamented melody, or the b minor fugue, in which the theme consist of two contrasting parts, the first more vocal like and the second more instrumental. For my first fugue I took as a model the fugue in e flat minor, representing the diatonic/vocal qualities. Its theme has irregular length of 13 bars and can be divided in (4+4)+5. The second section (b.9) starts as a repetition of the beginning. The range is one octave and there is emphasis on the fifth degree. It is characteristic the absence of leading tone, using the b7 of the key, which is part of the eolian scale. I wrote the following fugue themes imitating these features.
As the new voice enters they work mostly in complementary rhythm. The form is quite strict. There are two countersubjects that are used every time the subject is heard except for the stretto sections (b. 155-178) and the last entry of the subject in the main key (b. 204). The divertimenti are always based on the same material: a, b (presented in divertimento I) and c (presented in divertimento II), with the usual sequential treatment. Traditional functional harmonic analysis proved unsuccessful to understand the harmonic conception of the piece. Considering the parts with three voices we can see that the harmonic progressions have a modal character. The scales are used only as modes, without strong dominant-tonic tendencies. Thus the modulations are better understood as changes of mode. For instance, the c on the alto in b. 17 changes the eb Eolian into eb Dorian, but the expected bb (eolian) is not really heard us such until b. 26. Sometimes there is ambiguity concerning the actual mode in use (b. 30-46 eb Eolian or Gb Ionian?) Usually the succession of modes is within the near modes (adding one flat or one sharp), going into a direction of a faraway mode in the sharp region (f# eolian b. 145) from where Shostakovich makes a fast transition to go back to the original key of eb, for the entrance in stretto in b. 155. As the functional analysis of the harmony didn't give results I look at the individual vertical sonorities (type of chord and inversion). There is preference for consonant combinations (major and minor triads). The 6/4 chords are used as consonant chords. There is use of passing and neighbor notes, and occasional suspensions. The degree of dissonance is increased towards the stretti sections (b. 148 b flat Against b natural; use of non-dominant seventh chords). Subtle chromaticism is also added (b. 138) Also characteristic is the use of extreme registers (lower register in b. 145). As a preliminary exercise I made a free 3 part exercise.
Finally I took one of the fugue themes I wrote for writing my complete fugue.
For my second fugue, I took two contrasting fugues as models: the fugues in D major and E major, that are representative of the more chromatic style. The D major theme is very characteristic for its use of chromatic scales in contrary motion, in form of compound melody, at the beginning and at the end of the theme. It is also very characteristic the changes of meter, that break any metric regularity. This irregularity is emphasised by the accents of bars 3 and 4. Although this level of chromaticism is unmatched almost in any of the other 23 fugues of the cycle we cannot consider it as an exception within Shostakovichs oeuvre. As M. Mazullo remarks Shostakovich was clearly capable of writing unassuming melodies that employed the twelve tones of a chromatic scale, including themes that could subsequently be used neatly within fugal contexts. The opening theme of the first movement of the String Quartet No.3 (1946) covers the entire chromatic scale. 3 Another thematic element close to this theme can be found on the eighth symphony.Symphony n. 8, 2nd movement
As in the other 4 part fugues Shostakovich makes use of 3 countersubjects. The first is exclusively chromatic, and the second and third ones are almost chromatic, with occasional leaps. The internal divertimento, also often used by Shostakovich, presents augmentation of the head of the subject, and syncopations taken from the first counterpoint, always in complementary rhythms. It is remarkable that the divertimento is not treated sequentially. The fugue in E presents irregular meter (5/4) that seems to alternate 3+2 and 2+3 groupings. The use of non-diatonic pitches in the theme is restricted to 2 and 3. The range is relatively small, a diminished fifth (c-g). Again each voice against the theme will be used as a countersubject. The first countersubject moves chromatically around a central pitch (5) like a chromatic turn. The second counterpoint also uses the chromatic turn, in faster values. For the divertimento Shostakovich uses the head of the subject, inverted, and also the chromatic turn from the countersubjects. According to these principles I tried to make fugal expositions on that style.
Mazullo, M. Shostakovichs preludes and fugues, Yale University Press, 2010.
Finally, the theme that I used for the fugue was the following:
It combines most of the features we find in the Shostakovich examples: the irregular meter, the flattened degrees (4 and 2), and also the chromatic sekundgang, taken from the fugue in Db major. My theme takes the head from that fugue, but changing the accentuation, by starting with an upbeat instead of starting on the beat. Description of the fugue. In spite of the chromaticism, the theme is clearly heard in c minor. Once the rest of the voices are added it will be more difficult to find stable tonal centres due to the chromaticism of all voices. The second entrance is as usual a fifth higher (the fifth relationship between subject and answer is only changed in the fugue in B-flat major, where the answer enters on the relative minor key, g minor). The countersubject is mainly moving in half steps and presents two characteristic elements: the chromatic turn in sixteenth notes in bar 9 and the alternation of the chromatic pitches e and e flat, that causes a great tonal instability. After the second entrance of the theme there is an internal divertimento, often found in Shostakovichs fugues, that employs the chromatic turn from the countersubject. Two bars are repeated sequentially one tone higher. The chromaticism makes possible going fast to very distant tonal centres: for example in bars 14-15 we go from the flat side (g minor) to the sharp side (E major). This kind of connexions will be often used. The third entrance of the subject is in bar 19, where a second countersubject is added in the alto. Again it is based on chromatic movement and includes the chromatic turn (b. 22). A new divertimento comes in bar 25. It reuses the material from the internal divertimento, adding a third voice. This repetition of the thematic material of the divertimentos is also characteristic of Shostakovichs fugues. After a fake entrance of the subject in the alto in bar 30, the subject appears again in the soprano in the next bar and once more in bar 38 on the bass. In bar 46 starts a new divertimento, with same material as the previous ones, but in two parts, with the difference that this time the sequence is going downwards. In bar 48 starts the major version of the theme in the soprano that is followed by a new major version in the tenor in bar 45. Another divertimento, again in three parts comes next. This time it is slightly extended to give place to the introduction of a new texture. Similarly to what Shostakovich does in his fugue in D, here the strict polyphonic texture is abandoned and changed into a two-fold texture: the left hand plays the complete theme in octaves, while the right hand plays chords, making complementary rhythms with the theme. Besides the upper voice of the chords (also doubled at the octave) plays the first part of the theme. From bar 75 the roles of the hands are exchanged, but the relationships between the two elements are the same. After the excitement of the octaves and the chords, there is a subito pp, that will be the departing point for a new building up of the tension that will go to the end of the piece.
The section starting in 81 employs a deformation of the theme, that consists of breaking the irregular change of meter characteristic of the theme, to enclose it in a fixed , that will give an impression of rush, that will be enhanced by the use of shorter note values and the shortening of the motifs. The bass in bar 91 introduces an important element, taken from the subject, that establishes a steady 5/4 for a while, underneath the two upper voices that play a game based on the chromatic turn. The first beat of the bass in every bar from 91 will move a half step, again back and forward, dubitative until it continues to the f#, a tritone apart from the main key of c, that is emphasized by repeating it three times, leading to the stretto section. There is a first stretto starting in bar 99, with both themes complete, the second entering at the fifth, one bar later. There is a new stretto between the soprano and the bass, this time at tritone, while a third voice is added. We achieve a point of no return in the building up of the tension. The texture is thickened in bar 112, by doubling in octaves both subjects taking part on the new stretto, plus a third voice also based on the head of the subject. The octaves section is later repeated and transposed upwards. From here the tension is increased again by shortening of the motifs and shorter note values from bar 127, but also by the superposition of two different rhythmic layers: the of the written time signature on the right hand and at the same time a 5/4 on the left hand (from bar 124). The tension finally collapses into an accented dissonant chord in fortissimo, that wildly breaks both the and 5/4 patterns. (The chord is actually a major seventh in first inversion, with the half step on top, as the famous spot in the development of the first movement of Beethovens Eroica bar 276-). In bar 134 there is a last statement of the theme in octaves in the main key of c minor in the right hand. The left hand plays at the same time the inverted version of the head of the theme, continued by a chromatic counterpoint to the theme. A codetta closes the fugue, with the two voices in complementary rhythms, emphasizing distant tonal centres (c minor-e ) and finally resolving the 3-4 ambiguity of the theme, by respelling the 4 as 3 at the very last moment. For this fugue I also wrote a prelude. The character of the prelude contrasts with that of the fugue. Although this is a common fact in Shostakovichs cycle, we can see examples in which the prelude and fugue share not only the character, but also the thematic elements, as it happens in the prelude and fugue in C minor.
In the D-flat couple however the contrast is big. The highly chromatic, dissonant and anguished mooded fugue (it was described as intolerably cacophonic and nervously spasmatic in the official report on the cycles audition in Sovetskaya Muzika) is preceded by a naf prelude, a kind of scherzo, with a near constant two measure grouping of strong and weak measures, with a very carefree character. It is also true that in spite of the different character, there are connections and references to the prelude in the fugue, being the clearest one the introduction of the steady ternary rhythm of the prelude just before the Stretti section of the fugue. Being my fugue close in character and style to the D-flat fugue, I also chose for a contrasting prelude, but more in a slow, contemplative mood, like the prelude in C minor or the prelude in F-major, the slowest piece in the whole cycle.
Both these preludes share another attribute, they are not very pianistic but rather reflect an idea of orchestral sound. In fact the c minor prelude starts in a very similar way to the beginning of his Symphony n. 11 in g minor (1956-57).
I borrowed from the F-major prelude the big spacing, and the octave doubling of both the upper and lower voices. The bass is related to the shape of the fugue theme, that goes in sekundgang from 1 to 4 (the fugue theme finally reaches the dominant). In this
case the way from 1 to is diatonic, as opposed to the chromaticism of the fugue. Against this bass a descending melody establishes an important thematic element. The choice for starting in the third comes also in contraposition to the end of the fugue, which finishes also on the third, in that case the major third. The e natural on the bass in bar 7, is also connected with the f-flat ambiguity of the theme of the fugue, but here together with the b-natural in the upper voice starts a modulatory progression that leads to the modified repetition of the theme in a minor (bar 11). As it happens in the fugue the chromatic steps in both voices (bar 6-7; 9-10) give place to modulations to distant keys. This section ends with a half cadence on bar 15. From bar 17 starts a contrasting section with two voices in counterpoint against a bass that moves chromatically. The chromaticism is also gradually increasing in the upper voices, especially in the middle voice: from bar 28 ascends chromatically from c# to g# and at this point there is a alternation between g and g# that anticipates similar chromatic alternations that will appear in the fugue (e/f in the theme, e/e in the first countersubject bar 10,11etc.). The long pedal on b resolves by a half step to c, and so do the other two voices (e to e and g# to g), again juxtaposing to distant harmonies (e major/c minor). Here starts a reprise of the first theme, now with a new counterpoint. From bar 42 the theme starts to develop as the bass descends chromatically to the b, from where it will start an ascending scale that will cover an octave with an octatonic scale that results from the harmonization of the different entrances of the theme, that outline a diminished seventh chord (b minor in bar 44, f minor in bar 48 and a minor in bar 50). The sequential pattern is suddenly broken in bar 52 and the expected b minor chord is substituted by a G major chord. This harmonic brake will be enhanced by a melodic break, with three interruptions on bars 55, 57, 59. Harmonically there is an alternance of a G major chord and an E major chord over the same bass note, b. If in the end of the middle section of the prelude the e major chord resolved chromatically to the c minor of the reprise, here the G chord will prevail and function finally as the real dominant of c minor. From bar 63 a short coda combines elements from the initial theme of the piece with elements from the middle section. Besides the chromatic bass anticipates the head of the subject of the fugue (bar 65-66) as Shostakovich sometimes does, like in the g # minor couple.
Last measures of the prelude and beginning of the fugue in g# minor