18th century counterpoint

The first two pieces presented here are based on Bach’s 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 Bach’s 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.

1 Quoted from Mattheson, Der vollkommene Capellmeister in Schubert & Neidhöfer, 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 Bach’s 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.

Telemann’s style differs from Bach’s 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.

2 In Versuch einer Anweisung die Flöte 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 Shostakovich’s 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 antecedent-

consequent (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 Shostakovich’s 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.

3 Mazullo, M. Shostakovich’s 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 Shostakovich’s 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 Shostakovich’s 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 ¾ , 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 ¾ 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 ¾ 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 Beethoven’s 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 Shostakovich’s 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 cycle’s audition in Sovetskaya Muzika) is

preceded by a naïf 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 10,11-

etc.).

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