counterpoint and fugue...baroque counterpoint is characterized by optimal balance between the amount...

“GHEORGHE DIMA” MUSIC ACADEMY

Cluj-Napoca

T u d o r F e r a r u

C O U N T E R P O I N T

a n d F U G U E

TEXTBOOK FOR THE GENERAL MUSIC STUDIES

IN ENGLISH

2019

CONTENTS

INTRODUCTION 5

EVALUATION 5

1. BAROQUE COUNTERPOINT 7

1.1 The Baroque Musical Style 7

1.2 Baroque Melodic Features 7

1.2.1 Intervallic Idioms 8

1.2.2 Rhythm of Polyphonic Writing 8

1.2.3 Harmonic Content of Melodic Lines 9

1.3 Apparent Polyphony 9

1.4 Techniques of Melodic / Rhythmic Development 10

1.4.1 Inversion. Retrograde Form. Retrograde Inversion 10

1.4.2 Augmentation. Diminution 10

1.5 Baroque Two-Part Writing 11

1.5.1 Dissonances in Two-Part Polyphony 11

1.6 Harmonic Sequence in Contrapuntal Context 17

1.6.1 Sequencing Patterns 18

1.7 Two-Part Invertible Counterpoint / Double Counterpoint 19

1.8 Baroque Three-Part Writing 21

1.8.1 Dissonances in Three-Part Polyphony 21

1.9 Three-Part Invertible Counterpoint / Triple Counterpoint 24

1.10 Baroque Polyphonic Techniques 25

1.10.1 Imitation – General Principles 25

1.10.2 Canon. Canonic Imitation 26

1.10.3 Ground Bass Technique (Basso ostinato) 26

1.10.4 Complementary Voice Motion Technique 27

1.10.5 Parallel Counterpoint Technique (Planing) 27

1.11 Settings of Chorale Melody. Chorale Variations 28

1.11.1 Chorale Partitas 29

3

1.12 Subject - Answer Relationship 29

1.12.1 Real Answer 30

1.12.2 Tonal Answer 30

1.12.3 Cases of Tonal Answer Use 30

2. FUGUE (In the Music of Johann Sebastian Bach) 33

2.1 Fugue – General Presentation 33

2.2 The Fugue Subject – Typical Features 34

2.3 The Fugue Exposition 35

2.4 Counterpoint and Countersubject 36

2.5 False Episode 37

2.6 Episodes Proper 38

2.7 Middle Entries 38

2.8 Final Entry 39

2.9 Coda 40

2.10 Development Techniques in a Fugue 40

2.11 Tonal Outline of Fugues 41

2.12 Double and Triple Fugues 41

2.13 Fugues with Two or Three Subjects 42

3. EVOLUTION OF POLYPHONY FOLLOWING THE BAROQUE ERA 43

READING MATERIAL 44

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INTRODUCTION

The aim of the Counterpoint and Fugue textbook is to introduce concepts and

terminology pertaining to polyphony, and to help students develop their music

analysis abilities. Baroque instrumental and vocal music displays a wealth of

contrapuntal devices, which will represent the focus of this analytical endeavour.

Students will be familiarized with various compositional techniques and stylistic

features as well. The subject requires prior solid knowledge of music theory and tonal

harmony.

EVALUATION

Students will be tested in writing at the end of each semester, as well as

periodically throughout the year. Homework and in-class practice will comprise of

identification of various techniques, as well as contrapuntal writing exercises.

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1. BAROQUE COUNTERPOINT

1.1 The Baroque Musical Style

The Baroque era saw the emergence of functional tonality, and of tonal harmony, as its essential attribute. Functional harmony involves a precise hierarchy

among chords / harmonic degrees, and a preference for certain types of harmonic

progressions, which is equally taken into account in polyphonic contexts. The tonal

system is thus organized around the Major-minor scales, the functional identities of

Tonic, Dominant, Subdominant, and the various relationships that are established

among key centres (relative keys, near-related keys, parallel keys, etc.). The concept

of harmonic cadence represents a reference point in polyphonic music.

Tonality is a complex system, a paradigmatic way of pitch structuring, which

evolved in close relationship with other musical phenomena, such as rhythm, metre

and form. Baroque polyphony showcases all the traits that are typical of the tonal

system.

1.2 Baroque Melodic Features

Baroque melodic lines are intimately related to the harmonic background of

the specific musical context in which they unfold. Sometimes, harmonic content

generates the melodic contour itself. The two principal melodic types are:

- Melodic lines with explicit harmonic content;

- Melodic lines with apparent harmonic content.

The first type includes lines that contain figurations, arpeggiandos – primarily

instrumental in nature. The second type includes lines that originate in Gregorian

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Counterpoint and Fugue Tudor Feraru

chant, or Lutheran chorale phrases – primarily vocal in nature. Stepwise motion is

very common, either directly or ornamentally.

Chromaticism is frequently encountered. In the works of Johann Sebastian

Bach, chromaticism has a few distinct functions:

- Ornamental chromaticism;

- Modulatory chromaticism;

- Passus duriusculus (chromatic tetrachord / pentachord, usually descending).

1.2.1 Intervallic Idioms

Baroque melodic lines enjoy relative freedom with respect to the intervals

used; however, lines are organically constructed, by means of unique motives, cells

and figurations.

Characteristic intervals are the augmented fourth, the diminished fifth, and the

diminished seventh (more rarely, the augmented second as a substitute). Rising,

falling or undulating scale patterns are common, as are changes of register within the

same melodic line.

Among the various means for melodic development are repetition,

transposition, sequencing, intervallic variation, fragmentation, changing harmonic

content, apparent polyphony, etc.

1.2.2 Rhythm of Polyphonic Writing

Rhythm of Baroque polyphony displays consistency (with regard to particular

features and patterns) and fluency. The rhythmical continuum may be achieved by

individual voices, or by complementarity among voices.

The following patterns are typical of Baroque contrapuntal writing:

- Syncopated rhythms;

- Repeated patterns (dactyl, anapest, iamb, trochee, triplet, dotted rhythm,

Sicilian rhythm, etc.);

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- Mixed rhythm (virtually free combination of various patterns).

As far as metre is concerned, melodic lines may begin on downbeats, on

upbeats, or within incomplete measure (catalectic). Melodic hemiolas (rhythmic

patterns of syncopated beats, with two beats in the time of three or three beats in the

time of two) are relatively frequent, especially in the music of J.S. Bach.

1.2.3 Harmonic Content of Melodic Lines

Harmonic content refers to the actual harmonies / chords that could be

extracted from polyphonic music. The Baroque style is characterized by strict

periodicity of harmonic progression. Once established, the harmonic rhythm remains

constant over extended segments of music. Melodic lines frequently imply harmonic

content, through intervallic contour, arpeggiation, ornamentation, etc.

1.3 Apparent Polyphony

Apparent polyphony represents the illusion of two (or multiple) voices created

by a single voice. The impression of virtual additional melodic layers may result in

one of the following situations:

- A pivot note + a set of moving notes (usually stepwise motion);

- Two distinct, alternating sets of moving notes (or alternating pivot notes);

- An embellished pivot note + a set of moving notes;

- A melodic cell that replicates in significantly spaced-out registers, giving the

impression of multiple voice entries;

- Two contrasting, alternating, melodic cells or figures (usually in different

registers, as well).

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By means of apparent polyphony, a single voice (usually instrumental in

nature) generates clearer harmonic content, without the need for actual multiple voice

superimposition.

1.4 Techniques of Melodic / Rhythmic Development

1.4.1 Inversion. Retrograde Form. Retrograde Inversion

For purposes of melodic and motivic variation, Baroque music places great

emphasis on several melodic development procedures, such as melodic inversion,

retrograde melodic form, and retrograde inversion.

Inversion consists of reading successive intervals of a melodic segment in the

opposite direction (e.g. a rising third becomes a falling third). Only the quantitative

aspect of intervals is preserved. Melodic inversion may be rigorous or free.

Retrograde form involves reading an already stated melodic segment right-to-

left. This procedure affects rhythmic patterns as well, and sometimes renders the

melody impossible to recognize. For this reason, retrograde form is utilized much less

frequently.

Retrograde inversion combines the two techniques – thus, a line is stated from

its end to its beginning, with each melodic interval going in the opposite direction

compared to the original.

1.4.2 Augmentation. Diminution

Augmentation represents the lengthening of all note values in a melodic part,

by the same rate (doubling, tripling, quadrupling durations).

Diminution is a similar process, consisting in shortening of all note values

(usually halving durations).

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Thus, recurrences of a melodic segment may preserve the initial rhythmic

durations, or have proportionally increased / decreased durations. The melodic

intervals are generally not affected by such a procedure.

1.5 Baroque Two-Part Writing

Two-part polyphony entails a set of norms that govern the relationship

between the two voices, and most of the time generates explicit harmonic content.

In the Baroque style, all harmonic intervals are utilized, with certain

preferences with regard to the strong beat - weak beat relationship, as described

below.

Excepting the initial statement of melodic material, and endings of significant

fragments, all unisons, perfect octaves and perfect fifths are avoided. Therefore,

strong beats prefer the harmonic intervals of thirds, sixths, tenths, or dissonances.

1.5.1 Dissonances in Two-Part Polyphony

In Baroque counterpoint, the concept of dissonance refers to a note that meets

two distinct criteria simultaneously:

- It is a note foreign to the existing harmonic content (a non-harmonic tone);

- It is a note that generates a harmonic interval of a second, seventh, fourth,

ninth or eleventh in combination with the other voice; these intervals are considered

dissonant in the Baroque style.

Whenever either of the two criteria is not met, the respective note is deemed a

semi-dissonance (e.g. the note generating a seventh, as part of a virtual dominant

seventh-chord, or a non-chord tone that creates a sixth in combination with the other

voice).

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Baroque counterpoint is characterized by optimal balance between the amount

of consonance and dissonance. In the case of J.S. Bach’s music, an abundance of

dissonances is typical and expressive, while the harmonic content remains functional.

In music analysis, dissonances will be marked with an x, and semi-dissonances with

an (x).

Types of dissonances:

Passing tone – in terms of melodic contour, it may be ascending or

descending, with any duration, on any beat or part of beat – including relatively strong

beats. The following are a few possible passing tone situations:

1) Passing tone + sustained note in the other voice;

2) Passing tone + octave leap;

3) Passing tone + movement between chord members;

4) Passing tone + arpeggiation;

accented passing tones accented passing tones

5) Passing tones in both voices, in contrary stepwise motion, either with identical

or with different rhythms;

6) Passing tones in both voices, in direct / parallel stepwise motion, usually with

different rhythms;

NOTE: Cases 5) and 6) allow two situations – either beginning and arriving on a

vertical consonance, or simply arriving on a consonance (irrespective of the number

of dissonances along the way):

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7) Passing tone with change of register;

8) Passing tone approached or continued by a skip / leap.

Neighbouring tone – in terms of melodic contour, it may be superior or

inferior, with any duration, on any beat or part of beat – including relatively strong

beats. The following are a few possible neighbouring tone situations:

1) Neighbouring tone + sustained note in the other voice;

2) Neighbouring tone + octave leap;

3) Neighbouring tone + movement between chord members;

4) Neighbouring tone + arpeggiation;

5) Neighbouring tone + stepwise motion (in combination with passing tones);

6) Neighbouring tone + arpeggiation and stepwise motion;

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7) Dual neighbouring tones (simultaneous or slightly delayed).

NOTE: Sometimes, two simultaneous neighbouring tones, in contrary motion,

may generate the harmonic interval of a diminished octave (dissalteration).

8) Neighbouring tone approached or / and continued by a skip / leap (called

escape tone).

Anticipation – is a non-accented, dissonant, non-chord tone that becomes a

chord member on the immediately following beat. It may be falling or rising, and

always involves note repetition (or syncopation). Anticipations may be approached by

step or by skip / leap. They are commonly associated with dotted rhythms and

cadential gestures:

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falling anticipation rising anticipation anticipation approached by leap

The passing tone, neighbouring tone and anticipation are collectively referred

to as ornamental dissonances.

Suspension / Retardation – is a dissonant note that is approached from and

resolved to a consonance, by a falling or a rising step (either whole-tone or half-tone).

Suspensions are evident dissonances that occur on strong beats or parts of beats. Any

chord member may be delayed by means of a suspension, and any of the polyphonic

voices may contain suspensions / retardations. Suspensions may be prepared – by the

same note, in the same voice, that is usually a consonance in the context of the

preceding harmony. Preparation involves either note repetition or a tie.

NOTE: The preparation itself may be a dissonant note – such a situation is called a

self-prepared dissonance.

Sometimes, the suspension is not followed directly by its resolution, but rather

by a foreign note, or a group of foreign notes that precede the consonant resolution.

Such a case represents an ornamentally resolved suspension (figured resolution). The

interpolated foreign note(s) will be called the suspension’s figuration.

Possible situations of ordinary suspension:

1) Suspension + sustained note in the other voice;

2) Suspension + octave leap;

3) Suspension + arpeggiation;

4) Suspension + ornamental dissonances;

5) Suspension + ornamental dissonances at the time of resolution;

6) Suspension + combination of stepwise and arpeggiated motion.

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The following are some of the possible cases of ornamentally resolved

(figured) suspensions (all situations listed for ordinary suspensions are relevant, too):

1) Figuration by dissonance repetition;

2) Figuration by interpolation of a consonant note (by leap);

3) Figuration by interpolation of a note group in stepwise motion;

4) Figuration by interpolation of an arpeggio;

5) Figuration by interpolation of both arpeggiated and stepwise motion;

6) Retardation that resolves in a different voice;

7) Retardation that eludes resolution altogether (or continues to another

dissonance, rather than a consonance).

usually consonant

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NOTE: A suspension / retardation that lacks preparation is also named

appoggiatura. In the case of figured suspensions, the figuration itself may include one

or more appoggiaturas.

1.6 Harmonic Sequence in Contrapuntal Context

Harmonic sequence is the direct recurrence of a musical idea, on a different

pitch level. It consists of an immediate, transposed, strict or free repetition of a

melodic segment and its supporting harmonies. The repetition may occur once or

more times. The starting point of each sequence is called a model (pattern), while the

transposed recurrences represent the sequences proper.

Harmonic sequence can be:

- Strict or free;

- Tonally stable (usually diatonic, but chromatic sequencing is to a

certain degree possible), or modulatory;

- Ascending or descending;

- Authentic or plagal;

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- Stepwise or non-stepwise (involving skips from one recurrence to

another).

The Baroque style utilizes mostly strict, authentic sequencing.

1.6.1 Sequencing Patterns

Descending stepwise sequencing conforms to the following possible patterns:

- The “circle of fifths” pattern (chord roots move by intervals 5↓-5↓, 4↑-4↑, or

4↑-5↓):

//

- The 3↓-2↑ pattern:

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- The 2↑-3↓ pattern:

Ascending stepwise sequencing involves three possible patterns, as well. They

are classified according to the chord root movement:

- The 3↓-4↑ pattern;

- The 4↑-3↓ pattern;

- The 2↑ pattern – where the harmonic model contains only one chord.

Ascending sequencing is less typical of the Baroque style.

Harmonic sequence may be modulatory or non-modulatory. When modulation

is involved, the target key is usually that of the dominant or relative. It is possible to

encounter continually modulatory sequences (especially following the circle of fifths

pattern).

Sequencing, as a melodic / harmonic development device, is characteristic to

the entire Baroque repertoire. In the music of J.S. Bach, the process consists of two to

three sequences the most, in order to prevent it from becoming cliché.

Free (non-rigorous) sequence may involve changes in the sequencing interval,

the sequencing direction, or the harmonic model.

1.7 Two-Part Invertible Counterpoint / Double Counterpoint

Invertible counterpoint is a technique of writing two (or more) voices so that

their registral positions can be reversed. Thus, the higher voice can become the lower

and vice versa, while conforming to conventions of dissonance treatment. Sometimes,

the technique is called “double” counterpoint because each of the two voices serves a

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dual role, either as upper or as lower part. The procedure was known during the vocal

polyphony era; however, it became prevalent only in the Baroque style.

A B

B A

Invertible counterpoint involves three main possibilities, with regard to the

permutation interval: at the octave (most frequent), at the tenth, and at the twelfth.

In the familiar case of inversion at the 8ve, where one of the two voices is

transferred above or below the other voice by transposing it up or down an octave, a

third inverts into a sixth, unison into an octave, second into a seventh, augmented

fourth into a diminished fifth. In those cases, consonance inverts into consonance,

dissonance into dissonance. However, the interval of fifth inverts into a fourth, which

is a dissonance in two-voice counterpoint. Fifths in two-voice invertible counterpoint

must therefore be written as though they were dissonances.

Invertible counterpoint at the 12th and at the 10th is much less common, due

to the technical difficulties and the harmonic transformations it would involve. For

example, in the infrequent case of invertible counterpoint at the 10th, parallel thirds

and sixths need to be avoided, because they would result in parallel octaves and fifths,

respectively.

The principle of inverting voices is not affected by actual transposition of the

entire polyphonic structure on a different pitch level.

The concept of rhythmic double counterpoint refers to a situation in which the

technique is not applied to the melodic intervals of the two voices, but rather to their

rhythmic makeup.

Sometimes, an entire polyphonic work is designed according to invertible

counterpoint principles; in such a case, the technique generates the form of the piece

itself. The double counterpoint relationship may be applied to individual musical

phrases, or be relevant to entire sections of the piece. The example below illustrates

the use of invertible counterpoint over entire phrases, along with a modulation to the

dominant key:

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J.S. Bach – Two-Part Invention no. 14, in Bb major:

measures 1-2

measures 6-7

1.8 Baroque Three-Part Writing

Three-part counterpoint is characterized by the existence of explicit harmonic

content, resulting from functional chord progressions. The consonance-dissonance

relationships follow the same norms as in the case of two-part writing.

In the case of three-part polyphony, chord doublings are treated more freely

than in conventional harmony; in principle, any chord member may be doubled, as

long as voice-leading is correct. From the superimposition of three distinct lines, the

possible resulting vertical structures are as follows: complete triads, incomplete triads

involving doublings, incomplete seventh-chords, as well as multiple unisons.

1.8.1 Dissonances in Three-Part Polyphony

The dissonance types are the same as in two-part polyphony: passing tone,

neighbouring tone, anticipation, suspension (or appoggiatura), and various

combinations of these.

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Passing tone – may occur in all forms already described. The following

situations are typical of three-part counterpoint:

dual passing tones, by parallel or contrary motion:

single and dual passing tones, by parallel or contrary motion (in context):

triple passing tones, in identical rhythm, by contrary motion:

passing tone approached by leap:

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Neighbouring tone – may occur in all forms already described. The following

situations are typical of three-part counterpoint:

dual neighbouring tones, by parallel or contrary motion:

neighbouring tone chromatic approached by leap: neighbouring tones:

Anticipation – may occur in all forms already described. A few particular

cases are the dual anticipation (with both voices approached by step, with one by step

and the other one by leap, or both by leap), and anticipation followed by a suspension:

single anticipation: dual anticipations (by step and by leap, followed by suspensions):

Suspensions / retardations (appoggiaturas) occurring in three-part polyphony

are even more evident dissonances, due to the explicit harmonic content. They may be

assigned to any of the voices, and behave much like their two-voice counterparts.

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Thus, dual suspensions / retardations, various figuration patterns, atypical resolutions,

as well as combinations with other ornamental dissonances are possible. The

following situations are typical of three-part counterpoint:

dual suspensions, dual suspensions, dual suspensions dual suspensions identical rhythm: different rhythm: + other dissonances: with figuration:

1.9 Three-Part Invertible Counterpoint / Triple Counterpoint

Triple counterpoint, similarly to double counterpoint, is a technique of writing

three voices so that their registral positions can be exchanged. There are six

permutation options, of which usually three or four are utilized (some permutations

raise harmonic problems, related to consonance-dissonance conventions, or produce

incorrect six-four chords).

A B C A

B A B C

C C A B

The most frequently used type of triple counterpoint is at the octave. Invertible

counterpoint in three or more parts is easier to achieve when there is an abundance of

dissonances.

In order to avoid six-four chords, fragment beginnings and endings will have

to contain incomplete chords (omitting the fifths). Al precautions with regard to voice

leading that were mentioned in the case of double counterpoint apply here too.

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There are particular cases of triple counterpoint, in which the permutation

process is applied only to two of the three voices, while the third retains its constant

registral position (usually, the bass line).

Invertible counterpoint (double, triple or multiple) is essentially a musical

development device, which allows for increased exploitation of melodic material. The

technique is used extensively in J.S. Bach’s Fugues (in Fugues with Countersubjects,

or Fugues with more than one Subject).1

1.10 Baroque Polyphonic Techniques

1.10.1 Imitation – General Principles

Imitation is the identical or slightly modified restatement of a melodic

segment, in a different voice of the polyphonic texture. Exact repetition is called strict

(rigorous) imitation, while modified repetition is called free imitation.

Imitation may begin on the same pitch level, or on a different pitch than the

original material. In Baroque polyphony, the imitation interval is variable (most

common are the unison, perfect octave, perfect fifth or fourth, either up or down).

The original melodic segment may be followed by its imitation immediately,

or after a short transition material. It is also possible to have a closely followed

imitation (involving partial superimposition of the original with its imitating material).

Such a case is called stretto. This is usually realized by successive melodic entries, a

measure or less apart. The stretto technique may involve two or more voices entering

in cascading imitations.

Imitations may preserve the original rhythm, or may occur with proportionally

lengthened or shortened durations (in augmentation or diminution, respectively).

Successive melodic intervals of the original melody usually remain

unchanged. However, in the case of imitation at common intervals (perfect fifth and

1 See Chapter 2, dedicated to the Fugue.

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perfect fourth), it is possible to encounter changes in the intervallic makeup (strict

versus free imitation). Such changes will be described in detail later on.

1.10.2 Canon. Canonic Imitation

Canonic imitation is the very strict imitation of an extended melodic segment,

occurring in two-part, three-part, or multiple-part counterpoint. The consecutive

imitating entries are usually close together.

A musical work based exclusively on this technique is called a canon. Canons

may include imitations at different intervals, augmentations, diminutions, as well as

inverse or retrograde forms of the melodic material. When the melodic material of

each voice arriving at its end loops back to its beginning, the piece becomes a round,

or perpetual canon.

More rarely encountered cases are those of the double canon – a multi-voice

composition that unfolds two different canons simultaneously, and the mirror canon –

in which voices imitate one another in inversion, by contrary motion.

Writing a canon involves step-by-step imitation, so that each segment of the

leader is repeated rigorously and immediately by the follower, while each new

melodic segment becomes the very counterpoint to its preceding segment. Masterful

examples of canons can be found throughout the works of J.S. Bach, such as in his

Musical Offering.

1.10.3 Ground Bass Technique (Basso ostinato)

Basso ostinato is a contrapuntal technique in which a short, recurring melodic

pattern (usually in the bass part) serves as the principal structural element. The pattern

is concise and emblematic, and is repeated identically or slightly modified throughout

the entire musical work.

In addition to the ground bass, a variable number of contrapuntal voices

contribute to a freely, yet organically, polyphonic unfolding. The technique generally

26


involves evolution from simple to complex textures (with regard to rhythmic

intricacy, harmonic content, registral spacing, etc.). Musical works based chiefly on

the ground bass technique are the Passacaglia and the Ciaccona. In J.S. Bach’s

output, the best-known examples are his Passacaglia for organ in C minor, and

Ciaccona for solo violin in D minor.

The ostinato pattern may migrate to other parts, including the discant. It may

also be subjected to transformations, variations (ornamentation, rhythmic alteration,

fragmentation, etc.). The number of contrapuntal voices varies from section to section.

The ostinato technique is sometimes combined with imitation and its various forms.

A universally valid distinction between Ciaccona and Passacaglia is

impossible to operate. In J.S. Bach’s case, Passacaglia involves changes to the

harmonic background from one recurrence of the pattern to another, while Ciaccona

preserves the same harmonic background throughout.

1.10.4 Complementary Voice Motion Technique

This technique derives its basic principles from the concept of complementary

rhythm. Complementary rhythm refers to a situation in which two or more voices

achieve continuous motion by complementing each other’s pulse. Complementary

voice motion usually opposes a significant melodic line to one or more supporting

contrapuntal parts, which then reverse roles. The supporting parts may contain

sustained notes, repeated rhythmic patterns, or various combinations of these. They

can themselves move in- or out- of sync. Such an approach insures textural interest,

while highlighting each of the polyphonic voices.

1.10.5 Parallel Counterpoint Technique (Planing)

Parallel voice-leading (German: Mixturen) is a technique in which a leading

voice is shadowed by one or more supporting, secondary lines that move by parallel

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intervals (usually parallel thirds, sixths, or six-chords). Most frequently, the main line

and its parallel melodies have the same rhythmic structure.

The technique is sometimes called planing. The role of the supporting lines is

to emphasize melodic contour. They may also move by contrary or oscillating motion,

producing densely textured polyphony. This phenomenon is more frequently

encountered in instrumental or vocal-instrumental contexts (e.g. the orchestral

introduction to Saint Matthew’s Passion, or Sanctus from the Great Mass in B minor,

both by J.S. Bach).

1.11 Settings of Chorale Melody. Chorale Variations

Protestant chorale tunes made their way into Baroque art music in various

forms and contexts, from simple four-voice harmonizations, to sophisticated

polyphonic works (organ pieces, cantatas, etc.). J.S. Bach exploited the chorale

repertoire extensively, in a few distinct types of settings / arrangements.

Chorale variations are a species of polyphonic compositions based on the

contrapuntal treatment of chorale melodies, usually involving two to five voices. The

characteristic features of such arrangements are complementary rhythm (with constant

duration ratio of 1:2, 1:3, 1:4, 1:6, 1:8), and independence of lines. Ostinato patterns

are sometimes utilized. In other cases, contrapuntal lines are highly complex, to the

point they overshadow the chorale melody itself.

Chorale melodies are usually assigned to the highest voice, but they can

appear in any of the other voices, as well. They may be arranged ad literam, with

proportionally lengthened durations, or in a fragmentary manner (with individual

phrases spaced out by interludes), or even in ornamental forms (from elementary to

very rich ornamentation).

Contrapuntal lines may involve imitation (even canonic imitation), and various

melodic development techniques (augmentation, diminution, inverse or retrograde

forms). Monumental chorale variations incorporate full-scale preludes, interludes and

postludes alternating with the actual chorale phrases.

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NOTE: Chorale variations of the Baroque period should not be mistaken for

variation forms (theme and variations), or for Fugues with Subjects derived from

chorale melodies!

1.11.1 Chorale Partitas

A chorale variation may be continued with other polyphonic settings of the

same chorale tune. Such a multi-movement composition based on the same chorale is

called a chorale partita. It is usually written for a keyboard instrument (mainly

organ). Chorale partitas share similar traits with conventional variation cycles, as

stipulated by musical forms.

Sometimes, contrapuntal techniques utilized in chorale variations and chorale

partitas infiltrate other polyphonic genres. Chorale arrangements that incorporate

ample preludes, interludes, postludes, and sophisticated polyphony render the chorale

melody itself a mere pretext for a monumental composition.

1.12 Subject - Answer Relationship

Polyphony may be divided into two main categories: imitative and non-

imitative. In imitative polyphony, the two main members of the polyphonic texture –

the original and its imitation – are commonly called Subject and Answer (Dux and

Comes in Latin, or Leader and Follower in English). A number of correspondences

are established between the Subject and its Answer(s), generally depending on their

degree of similarity.

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1.12.1 Real Answer

Real Answer results from an imitation with no modifications except for the

diatonic adjustment of half and whole steps. It may represent an exact transposition of

the original material to a different pitch level.

1.12.2 Tonal Answer

There are situations in which, for tonal stability reasons, the Answer is

subjected to slight intervallic changes. Such a case is called Tonal Answer. A Tonal

Answer is usually called for when the Subject contains a prominent dominant note

very close to its beginning, and prevents the undermining of the sense of key. The

usual perfect fifth or perfect fourth relationship between the initial pitches of the

Subject and Answer place the music in a Tonic key - Dominant key paradigm. The

very role of the Tonal Answer is to prevent the music from migrating to other key

centres (such as the Subdominant, for example).

1.12.3 Cases of Tonal Answer Use

A Tonal Answer closely resembles its Subject, but does not replicate it

exactly. Here is a classification of such cases:

1) When the Subject begins with scale degrees 1-5 – the Answer will begin

with scale degrees 5-1, or vice versa;

NOTE: If 1-5 or 5-1 is the predominant interval, elementary ornamentation will

not affect the need for a Tonal Answer.

2) When the Subject begins on scale degree 5 (regardless of what the next degree

is) – the Answer will begin on scale degree 1, and one of the initial melodic

intervals will be modified;

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3) When the head of the Subject contains the 1-7 or 7-1 scale degrees – the

Answer may be Tonal or Real, depending on each particular situation;

NOTE: In the first three cases, intervallic changes always occur at the beginning

of the Answer.

4) When the Subject modulates (usually to the Dominant key) – the Answer will

either avoid further modulation, or will re-modulate to the Tonic key; in this

case, intervallic changes will occur toward the end of the Answer (in very rare

cases, a modulating Subject is followed by a Real Answer – an Answer

beginning in the Subdominant key is normally employed for this reason);

5) This case is a combination between one of the first three cases and case

number 4; therefore, two modifications will be necessary – one at the

beginning and one at the end of the Answer (such a situation is commonly, yet

improperly, called a “Double-Tonal” Answer).

NOTE: In certain (yet rare) situations, J.S. Bach employs Real Answers to

Subjects that would normally call for Tonal Answers.

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2. FUGUE (In the Music of Johann Sebastian Bach)

2.1 Fugue – General Presentation

The Fugue is a type of polyphonic composition (a musical genre), and

represents at the same time a structural model, and a contrapuntal technique that was

perfected during the Baroque era. Its origins are complex and are rooted in several

genres of the past, such as:

- The vocal Motet, and later the instrumental Ricercar (in terms of the imitative

technique);

- Toccatas of the early Baroque, as well as improvisatory Fantasias and

Capriccios (in terms of instrumental / keyboard style writing).

From a contrapuntal point of view, the Fugue is built on successive imitative

statements of a prominent melodic material, called Subject. The imitative entries,

called Answers, usually occur at intervals of perfect fifths or fourths. A tonal

exposition centered on the Tonic and Dominant keys is followed by additional

restatements, in other keys. These “thematic” statements may alternate with sections

of non-thematic material.

Structurally, a Fugue is made up of an Exposition, a Development section

alternating Middle Entries and Episodes, and a Final Entry (possibly a Coda, as well).

Baroque Fugues display highly individualized thematic material, which is

subsequently imitated, developed, transposed, etc. The tonal itinerary is also of

paramount importance, with the Subject centering on the Tonic, and the first Answer

on the Dominant. A modulating Subject will call for a re-modulating Answer, or for a

transition segment that returns to the home key prior to the beginning of the Answer.

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2.2 The Fugue Subject – Typical Features

It is important to note that the Fugue’s theme includes all statements of both

the Subject and the Answer.

Fugue Subjects may be categorized as follows (in accordance to their origin

and melodic nature):

- Subject type derived from Gregorian chant (e.g. WTC2 I / C#m);

- Subject type derived from Protestant chorale tunes (e.g. WTC I / F#);

- Subject type derived from instrumental technique (e.g. WTC II / G).

Subjects usually begin with scale degree 1, 5, or 3 (more rarely, with scale

degree 2 – WTC II / Bb, or scale degree 7 – WTC II / F#). Baroque Fugues

(especially those written by J.S. Bach) are based on particularly unique Subjects,

which feature certain melodic idioms. Some of these features derive from individual

motivic gestures, stepwise motion, figurations, the use of arpeggiation, of pivot notes,

of “wedging” melodic contour, etc. Subjects may also involve intense chromaticism,

or striking diatonic-chromatic oppositions.

The overall melodic span of a Subject may range from a third (as in the

unfinished B-A-C-H Fugue) to a ninth / tenth (as in WTC I / Bbm). Note repetition is

very frequent, especially at the beginning of the Subject (WTC II / D#m), but can also

occur toward the end (WTC II / Gm).

Apparent polyphony is common to longer Subjects, as is harmonic

sequencing. Fugues from The Well-Tempered Clavier contain small-scale sequencing,

while organ Fugues feature ample use of this technique.

As far as rhythm is concerned, Fugue Subjects are usually based on a few

distinctive patterns, such as:

- Constant / flowing rhythm (WTC I / Em);

- Constant rhythm interrupted by rests (organ Fugue in Dm);

- Ostinato / repeated rhythmic patterns (WTC I / Cm);

- Patterns derived from dance music (WTC II / Fm);

2 The Well-Tempered Clavier, Books I and II, by Johann Sebastian Bach

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- Juxtaposition of contrasting patterns (WTC II / Dm);

- Relatively free rhythm / various pattern combinations (WTC II / Em).

The Answer is not always introduced immediately following the initial Subject

statement. A short melodic segment may separate the two initial entries – this is called

a codetta.

From a tonal point of view, there are stable (non-modulating) and modulating

Subjects. Therefore, the Answer itself may be stable or re-modulating. Codetta may

involve modulation or re-modulation, as well.

NOTE: A modulating Subject should not be mistaken for a tonally stable Subject

that is followed by a modulating codetta.

Fugue Subjects are quite diverse in terms of their internal structure. The

following are a few possible cases of Subject makeup:

- Indivisible melodic segment (WTC I / Ab);

- Individual opening gesture + melodic follow-up (WTC I / E);

- Two related melodic segments – by variation or sequencing (WTC II / G#m);

- Two contrasting melodic segments (WTC II / Bb, F, Eb);

- Sequenced opening + contrasting melodic material (WTC II / Gm);

- Three melodic segments – less frequent (organ Fugue in Cm);

- Fragmented structure / combination of various materials (WTC II / F#m).

2.3 The Fugue Exposition

The Fugue Exposition lasts from the initial note of the Subject to the final note

of the last thematic statement centered on the home or dominant key. Depending on

the number of constitutive voices, the Exposition may comprise of 2, 3, 4 or 5

successive entries (Baroque Fugues are typically written for three or four voices).

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The first Answer may occur:

- Immediately following the Subject (WTC I / Em);

- After a short delay – which involves a connecting melodic material between

the end of the Subject and the beginning of the Answer (a codetta);

- Before the end of the Subject – which involves partial superimposition of the

two segments, in stretto (WTC I / A);

Codetta may contain material that is derived from the Subject itself (possibly

in the form of a sequence – WTC II / Em), or completely new material (WTC II / G).

2.4 Counterpoint and Countersubject

The melodic material that accompanies (in a different voice) a theme

statement (either Subject or Answer) falls into one of the following two categories:

- Free Counterpoint (FC) – when it is used incidentally as a companion for the

Fugue theme;

- Countersubject (CS) – when it accompanies all (or almost all) theme

statements (a constant companion for both the Subject and the Answer).

The Countersubject usually contrasts with the shape and character of the

Subject / Answer. The Countersubject / Free Counterpoint may begin at different

times, in relation to the initial Answer:

- At the same time as the Answer (WTC II / G#m);

- Later than the Answer – frequently (WTC II / Dm);

- Ahead of the Answer – rarely.

The Countersubject’s melodic material may derive from the Subject, from the

codetta, or may be completely new (providing contrasting elements).

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Following statements of the theme in all constitutive voices of the Fugue,

additional entries are possible. This group of additional statements forms the Counter-

exposition. The Counter-exposition is sometimes separated from the Exposition by a

transition, and is in the same key as the original Exposition. The Counter-exposition is

then continued with the first Episode of the Fugue.

2.5 False Episode

The False Episode in a Fugue is a transition segment that separates two theme

statements within the Exposition. The most frequent placement for the False Episode

is between the first Answer and the following theme statement. It should never be

confused with a Codetta, which is merely a connecting melodic material at the end of

the Subject!

A False Episode may be placed:

- After two theme statements – in a 3-voice Fugue, with one remaining

statement following it;

- After two theme statements – in a 4-voice Fugue, with two remaining

statements following it;

- After three theme statements (rarely) – in 4-voice or 5-voice Fugues;

- In a Fugue with Counter-exposition, there may be even two False Episodes

(sometimes containing related material) – alternating with additional theme

entries; this case is typical to Fugues with modulating Subjects.

From a tonal perspective, False Episodes may be:

- Re-modulating (D ~ T), in the case of modulating Subjects;

- Non-modulating (T – T), in the case of modulating Subjects followed by re-

modulating Answers (a tonally stable False episode may, however, include

weak tonicizations).

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A False Episode may be very concise or quite extensive (usually between one

measure and five measures long). Its melodic material may be derived from the

Subject, from the Countersubject (or Free Counterpoint), may be totally new

(contrasting), or may even be related to the Codetta – in which case it is called a

“Real” False Episode.

2.6 Episodes Proper

The Episodes in a Fugue are neutral segments that separate further entries of

the Subject / Answer. Episodic material is most of the time contrasting to the theme

and modulatory. An Episode has the primary role of transitioning for the next theme

entry in a new key. It also provides release from the strictness of the Fugue form.

Sequencing is very typical of Episodes, as is free counterpoint. More often than not,

Episodes feature variation in texture density, by temporary voice dropouts and

subsequent build-ups.

2.7 Middle Entries

The Middle Entries in Fugue are thematic segments outside the Exposition /

Counter-exposition. They are usually framed by Episodes. These segments may

contain a single statement of the Subject / Answer, or more (sometimes as many as six

statements). In Fugues from The Well-Tempered Clavier, Middle Entries are centered

on near-related keys, while in organ Fugues they can migrate to distant keys as well.

Regardless of the key in which a Middle Entry occurs, its theme statement is usually

rigorous.

Ricercar-type Fugues do not contain Episodes, and therefore they do not have

any Middle Entries per se. Such Fugues comprise solely of successive theme

statements, in a variety of keys, with no contrasting / episodic sections.

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The size of a Middle Entry section depends on:

- The Subject’s length;

- The number of theme statements it contains;

- The amount of stretto it contains, and its degree of complexity.

Middle Entries may involve a change of mode (Major → minor or minor →

Major). Sometimes, the first Middle Entry in a Fugue does not follow after an

Episode, but rather immediately after the Exposition (or Counter-exposition),

evidently with statements in a key other than the Tonic or the Dominant.

Throughout the developing section of a Fugue, there may be “false entries” of

the theme, which include the head of the Subject / Answer, but are not given in full.

Such a procedure is usually associated with stretto. False entries often anticipate a

“true” entry of the Subject / Answer, heightening its impact.

2.8 Final Entry

The Final Entry in a Fugue represents the last theme statement (or group of

statements), in the home key. When the segment involves more statements, these may

center on the Tonic and Dominant keys. In the case of Fugues with a modulating

Subject, the last statement may begin in the Subdominant key, and eventually reach

the Tonic.

Sometimes, Final Entry segments contain a pedal point, which gives them a

more evident concluding character. At the end of the Final Entry segment, the

following situations are possible:

- A final cadence;

- A concluding extension, and then a final cadence;

- Additional entries, in stretto;

- A climactic conclusion, by means of parallel voicing (voice build-up);

- A rhetorical interruption / a fermata (frequently on a dominant, or an altered

chord), followed by a final cadence.

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2.9 Coda

The closing section of a Fugue may include additional material that follows

the Final Entry. This is normally considered a Coda, and is cadential in nature. It is

usually made up of new material (sometimes related to the Subject’s counterpoint).

The Coda itself may involve a supporting pedal tone (“organ point”). The

conventional number of voices is sometimes amplified during the Coda (five, six or

more voices in the case of keyboard Fugues).

The final chord of a Fugue commonly contains multiple doublings. It can also

be incomplete (without a fifth, sometimes without a third, even multiple unisons of

the Tonic root). In the case of minor key Fugues, the final chord often introduces a

Picardy third (a major triad).

2.10 Development Techniques in a Fugue

Many Fugues utilize stretto as a polyphonic tool, sometimes right from the

Exposition. Stretto may occur during the Middle Entries, as well as in the closing

section of a Fugue.

Inversion of thematic material is also frequent, sometimes inside the

development section, or even generating an entirely separate, inverse Exposition (e.g.

in The Art of Fugue by J.S. Bach).

Fugue Subjects often appear in rhythmic augmentation or diminution.

Sometimes, two or more forms of the same thematic material are superimposed (e.g.

the original theme with its own augmentation).

Obviously, all these techniques may be combined, to create countless possible

development and variation situations.

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2.11 Tonal Outline of Fugues

A Fugue’s Exposition and Counter-exposition always revolve around the

Tonic and Dominant keys. The Final Entry is also directed toward the Tonic / home

key.

The first notable key centre change occurs after the end of the Exposition, and

usually involves a modulation to the relative key, to the relative of the Dominant, or

even to the Dominant itself, which is consolidated this time.

Besides this typical tonal itinerary, there is no precise set of rules governing

the tonal outline of a Fugue. In the case of J.S. Bach, each individual Fugue reveals

unique features regarding its key relationships (especially in the developing section).

In monumental Fugues (like those written for the organ), modulations to distant keys

are not unusual.

2.12 Double and Triple Fugues

There are cases of Fugues that introduce two distinct melodic materials as

their theme. These are often presented simultaneously (or loosely simultaneously), in

contrapuntal relationship. Such a relationship is stronger and more egalitarian than a

simple Subject-Countersubject pairing, which works by subordination. Restatements

of the dual theme are normally treated in invertible counterpoint. Such a composition

is called a Double Fugue.

Similarly, a Fugue that interweaves three distinct melodic materials as its

theme is called a Triple Fugue (e.g. WTC I / Bb).

NOTE: A Double or a Triple Fugue should not be mistaken for a Fugue with two

or three Subjects, respectively. The distinction will be explained below.

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2.13 Fugues with Two or Three Subjects

In rare cases, a Fugue may introduce, successively, two or even three distinct

Subjects. Each of these generates its own Exposition, usually followed by Episodes

and further theme entries. The closing section of such a Fugue consists of a synthesis

of previously stated thematic material – Final Entries that involve partial or total

superposition of the distinct Subjects / Answers. These superpositions may be also

treated in invertible counterpoint (an illustrative example of a Fugue with three

Subjects is WTC II / F#m).

J.S. Bach – Fugue no. 14, in F# minor, The Well-Tempered Clavier, Book II (final measures):

S u b j e c t 1

S u b j e c t 3

S u b j e c t 2

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3. EVOLUTION OF POLYPHONY FOLLOWING THE BAROQUE ERA

Polyphonic writing will be rather sporadic, and will see dramatic variation

from one composer to another during the musical eras following the Baroque.

Nevertheless, even in the context of primarily homophonic music, traces of polyphony

can be identified. The basic contrapuntal principles are the same as those found in the

works of J.S. Bach.

In the music of Haydn, Mozart, Beethoven, Mendelssohn, Schumann and

Brahms, for example, polyphonic textures are frequent, displaying a few particular

features, such as:

- First and foremost, all types of counterpoint utilized in the Baroque repertoire

are present; they are simply adapted to the new stylistic environment;

- The novelty factor is represented by the original mixture of homophony and

polyphony; contrapuntal techniques provide elements of contrast, and serve

development purposes;

- A new technique emerges, especially in instrumental / orchestral music:

textural polyphony (or layered polyphony), in which melodic lines are

absorbed into denser contrapuntal textures, and individual voices / parts are

grouped together to form distinct layers.

Some polyphonic stand-alone compositions, such as the Fugue, are

occasionally revived during the Classical and Romantic eras, with their basic structure

virtually unchanged, while being adapted harmonically and rhythmically to the new

musical style.

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READING MATERIAL

ALDWELL, Edward, Carl SCHACHTER, Allen CADWALLADER. Harmony &

Voice Leading. Cengage Learning, 2018.

BACH, Johann Sebastian. Two-Part Inventions (any edition).

BACH, Johann Sebastian. Three-Part Inventions / Sinfonias (any edition).

BACH, Johann Sebastian. The Well-Tempered Clavier, Books I / II (any edition).

EISIKOVITS, Max. Polifonia barocului: Stilul bachian. Editura Muzicală, București,

1973.

GREEN, Douglass, Evan JONES. The Principles and Practice of Tonal Counterpoint.

Routledge Publishing, 2015 or later.

KOSTKA, Stefan, Dorothy PAYNE, Byron ALMÉN. Tonal Harmony - With An

Introduction To Post-Tonal Music. McGraw-Hill, 2017.

VOICULESCU, Dan. Polifonia barocului în lucrările lui J.S. Bach, vol. I, Scriitura la

două voci. Conservatorul de Muzică “G. Dima”, Cluj-Napoca, 1975.

VOICULESCU, Dan. Polifonia barocului în lucrările lui J.S. Bach, vol. II, Fuga.

Conservatorul de Muzică “G. Dima”, Cluj-Napoca, 1986.

counterpoint and fugue...baroque counterpoint is characterized by optimal balance between the amount...

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