A Dictionary of Music and Musicians/Fugue

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FUGUE, or FUGA, from the Latin fugare, to put to flight, because one part after another seems as it were to chase the subject or motive throughout the piece. (So Milton, Par. Lost, xi. 563.) It has been technically defined as 'a regular piece of music, developed from given subjects according to strict contrapuntal rules, involving the various artifices of imitation, canon, and double counterpoint, and constructed according to a certain fixed plan.' The necessary parts of a fugue are (1) Subject (or Dux, or Führer), (2) Answer (or Comes, or Gefahrte), (3) Countersubject, and (4) Stretto; to which may usually be added (5) Codetta (or conduit, or copula), (6) Episode, (7) Pedal, and (8) Coda. The Subject is the theme, or chief melody, on which the whole fugue is based. The Answer is the correlative of the subject. The relation of the answer to the subject, in fact, determines the whole character of the fugue. Speaking roughly, the answer is a transposition of the subject from the key of the tonic to that of the dominant. If the answer can be thus simply transposed without modulating out of the key, which often happens, the fugue is called a 'Real fugue,' and the answer a 'Real answer.' But in most cases the answer has to be modified according to certain rules to avoid modulating out of the key. These modifications are called 'mutations,' and an answer so treated is called a 'tonal answer,' and the fugue is called a 'Tonal[1] fugue.' For instance, if the subject were

{ \time 4/4 \relative c'' { c4 d e d8 c g'2 } }
and the answer were a simple transposition
{ \time 4/4 \relative g' { g4 a b a8 g d'2 } }
it is obvious that we should have left the original key of C altogether, and modulated towards the supertonic; to avoid this the answer would have to be modified thus—
{ \time 4/4 \relative g' { g4 a b a8 g c2 } }

so as to keep in the key of C, and the change of the concluding note is called a Mutation. Thus the dominant answers the tonic, and the tonic answers the dominant. Example—

{ \time 3/4 \relative g' { g4^\markup { \smaller \italic Subject. } c b c c,2 \bar "||" c'4^\markup { \smaller \italic Answer. } g' fis g g,2 \bar "||" } }

A few more examples of mutations will exemplify the principle of tonal answers.

{ \time 2/2 \key f \major \clef bass \relative f { f2^\markup { \smaller { 1. \italic Subject. } } c a'2. g4 f e d2 c1 \bar "||" } }
{ \time 2/2 \key f \major \clef bass \relative c' { c2^\markup { \smaller \italic Answer. } f, d'2. c4 bes a g2 f1 \bar "||" } }


{ \time 2/2 \key e \minor \relative e' { e2^\markup { \smaller { 2. \italic Subject. } } g4 fis8 e b'2 c4 b a g a b g4. fis8 e2 \bar "||" } }
{ \time 2/2 \key e \minor \relative b' { b2^\markup { \smaller \italic Answer. } d4 cis8 b e2 g4 fis e d e fis d4. cis8 b2 \bar "||" } }


{ \time 3/2 \key g \minor \relative d'' { d1^\markup { \smaller { 3. \italic Subject. } } ees2 fis,1 g2 bes a d bes2 g1 \bar "||" } }
{ \time 3/2 \key g \minor \relative g'' { g1^\markup { \smaller \italic Answer. } bes2 cis,1 d2 f e g f d2 \bar "||" } }

Rules for the finding of correct tonal answers may be found in all the treatises on the construction of fugues. Sometimes it is no easy matter to find the proper answer; and there are subjects which will admit of more than one correct answer.

Into these details it is impossible to go in such an article as the present. But the following general rules may be useful: (1) Wherever the subject has the tonic, the answer should have the dominant; and vice versa. (2) Wherever the subject has the 3rd of the tonic, the answer should have the 3rd of the dominant; and vice versa. (3) Wherever the subject has the 6th of the tonic, the answer should have the 6th of the dominant; and vice versa. (4) Wherever the subject has the 4th of the tonic, the answer should have the 4th of the dominant; and vice versa. (5) In the minor mode, if the subject has the interval of a diminished 7th, that interval is unaltered in the answer. (6) If the subject, in either mode, goes from the dominant up to the subdominant in the upper octave, the answer constitutes the interval of an octave; thus—

{ \override Score.TimeSignature #'stencil = ##f \time 3/2 \key g \major \relative g' { g2^\markup { \smaller \italic Subject. } d c' b1. \bar "||" d2^\markup { \smaller \italic Answer. } g, g' fis1. \bar "||" } }

(7) Every mutation should be made in approaching or quitting the tonic or dominant.

The counter-subject is primarily to be regarded as an accompaniment to the subject or answer. But it is more than this, for it ought to be made so melodious as to be an available foil to the subject when used in alternation with it, or with the answer. It should also be, in most cases, so constructed as to work in double counterpoint with the subject. It usually makes its first appearance as an accompaniment to the first entry of the answer, after the subject has been duly announced by itself. We now proceed to give an example of the commencement of a fugue, containing subject, answer, and counter-subject. Such a commencement is called 'the Exposition.'

{ \time 4/2 \key f \major << \relative f' { r\breve r << { r r r \[ f1 g2. a4^"Subject." bes f bes1 a2| g1 \] } \\ { r1 \[ c, d2. e4 f^"Answer" c f2 ~ f e d1 ~ \] d2 c4 d e c f e d2. e4 f c f2 ~ c e_"etc." } >> }
\new Staff { \clef bass \key f \major \relative f { \[ f1 g2. a4^"Subject." bes f bes1 a2 g1 \] \[ a2 g4 a bes g c^"Countersubject." bes a2. b4 c g c1 \] bes2 ~ bes a g f g f4 g a2. bes4 c1 } } >> }

When the countersubject is introduced simultaneously with the subject at the beginning of a fugue, it should be looked on rather as a second subject, and treated strictly as such throughout the fugue. In such a case the piece would be properly described as a Double fugue, or Fugue with two subjects. Similarly there are fugues with three or more subjects; the only limitation being that there should always be fewer subjects than parts; though there are exceptions to this rule, as e.g. 'Let old Timotheus' in Handel's 'Alexander's Feast,' where there are four subjects and only four voice-parts.

It is very often desirable to interpose a few notes to connect the subject and answer, and to facilitate the necessary modulations from tonic to dominant, and back again. Such connecting notes are named the Codetta, conduit, or copula, and are very useful in rendering the fugue less dry and cramped.

The following is the exposition of a two-part fugue, including a codetta:—

{ \time 2/2 \key d \major << \relative d' { d1 a'2._"Subject." fis4 g a8 b a4 g fis a d2 ~ d4 cis cis b8 a b1\trill a4 c_"Codetta." e d c d b c a r a2_"Countersubject." fis gis a2. a4 b cis d2 ~ d cis d_"etc." }
\new Staff { \clef bass \key d \major \relative a, { r1 r r r r r r a_"Answer." d2. cis4 d e8 fis e4 d | cis e a2 ~ a4 g fis e8 d e1\trill d2 } } >> }

After the exposition is completed by the successive and regular entry of every part, it is well to make use of fragments of the materials already announced, working them up contrapuntally into passages of imitation, and modulating into nearly related keys for a few bars, before returning again to the subject and answer. These may then be introduced in various kindred keys, according to the taste of the composer, so as to secure variety and contrast, without wandering too far from the original key of the piece. As the fugue goes on, it is important to keep the interest of it from flagging by the introduction of new imitations, formed of fragments of the original materials. These passages are termed Episodes. With the same object in view it is customary to bring the subject and answer nearer to one another as the fugue draws towards its conclusion. The way to effect this is to make the entries overlap; and this is called the Stretto (from stringere, 'to bind'). Thus the above subject would furnish a stretto as follows:—

{ \override Score.TimeSignature #'stencil = ##f \time 4/4 \key d \major << \relative d' { d1 a'2. fis4 g a8 b a4 g fis a d2 ~ | d4 cis cis b8 a b2 cis d r a1 e'2. cis4 d e8 fis e4 d cis e a2( | s4)_"etc." }
\new Staff { \clef bass \key d \major \relative a, { r1 a e'2. cis4 d e8 fis e4 d cis e a2 ~ a4 g g fis8 e d1 a'2. fis4 g a8 b a4 g fis a d2 ~ d4 cis cis b8 a s4 } } >> }

Some subjects will furnish more than one stretto. In such cases the closest should be reserved for the last. [Stretto.]

But there are many other devices by which variety can be secured in the construction of a fugue. For the subject can sometimes be inverted, augmented, or diminished. Or recourse may be had to counterpoint at the 10th or 12th. The inversion of the above subject would be as follows—

{ \override Score.TimeSignature #'stencil = ##f \time 4/4 \key d \major \relative a' { a1 d,2. fis4 e d8 cis d4 e fis d a2 ~ a4 } }
etc. and this might be treated with its appropriate answer and countersubject, if desired. Some subjects will furnish a stretto in strict canon, and this should be always reserved for the concluding portion of the fugue, by way of climax. If the fugue ends with an episode, such concluding episode is called the Coda (or tail-piece). It is also customary, in fugues of more than two parts, to introduce a Pedal, or point d'orgue, towards the end, which is a long note held out, almost always in the bass part, on which many imitations and strettos can be built which would often be otherwise impracticable. The only notes which can be thus held out as pedals are the dominant and the tonic. The tonic pedal can only be used as a close to the whole piece. The dominant pedal should occur just before the close. It is not necessary to use a tonic pedal in every fugue, but a dominant pedal is almost indispensable.

Fugues for instruments may be written with more freedom than those for voices, but in all kinds the above rules and principles should be maintained. The fugue-form is one of the most important of all musical forms, and all the great classical composers have left us samples of their skill in this department of the art of music. At the same time it must be observed that in the early days of contrapuntal writing the idea of a fugue was very different from that which we now understand by that term. In Morley's 'Plaine and easie Introduction to practicall Musicke,' published in 1597, at p. 76, we find the following definition:—'We call that a fugue, when one part beginneth, and the other singeth the same, for some number of notes (which the first did sing), as thus for example:

{ \override Score.TimeSignature #'stencil = ##f \time 4/2 \clef soprano << \relative g' { r\breve g1 c | b a g fis | g d' ~ d c b \bar "||" }
\new Staff { \clef alto \relative g { g1 c b a g fis g d' c b a a g } } >> }

This we should now-a-days call a specimen of simple imitation at the octave, in two parts; yet it is from such a small germ as this that the sublime structure of a modern fugue has been gradually developed. Orazio Benevoli (d. 1672) was probably the first of the Italian composers who wrote fugues containing anything like formal development. Later, in the 17th century, however, every Italian composer of church music produced more or less elaborated fugues, those of Leo, Clari, Alessandro Scarlatti, Colonna, Durante, and Pergolesi being among the best.

But it was in Germany that fugue-writing, both vocal and instrumental, reached the highest development and attained the greatest perfection. It would fill a volume to enumerate all the great fuguists of that wonderfully musical nation during the 17th and 18th centuries. Two or three names, however, stand out in bright relief, and cannot be passed over. Sebastian Bach occupies the very pinnacle among fugue-composers, and Handel should be ranked next him. The student should diligently study the fugal works of these great masters, and make them his model. Bach has even devoted a special work to the subject, which is indispensable to the student. [See Art of Fugue.] The treatises of Mattheson, Marpurg, Fux, Albrechtsberger, and André, are also valuable. Among more modern writers may be mentioned Cherubini, Fétis, and Reicha. We abstain from mentioning the works of living authors who have contributed much valuable matter to the literature of this subject. Mozart should be quoted as the first who combined the forms of the sonata and the fugue, as in the overture to 'Die Zauberflöte,' and in the last movement of his 'Jupiter Symphony.'

It is perhaps difficult for a composer at the present day to find a great variety of original fugue-subjects. But the possible ways of treating them are so inexhaustible that a fugue can always be made to appear quite new even though the theme on which it is based be trite and hackneyed. And here we have one of the great advantages of this form of composition—namely, that it does not so absolutely require the origination of really new melodies as every other form necessarily does. But, on the other hand, it does require a command of all the resources of harmony and counterpoint to produce fugues which shall not be mere imitations of what has been done by previous composers; and it also needs genius of a high order to apply those resources so as to avoid the reproach of dryness and lack of interest so often cast upon the fugal style of composition.
  1. This is the modern meaning. In the early days of counterpoint a Tonal fugue was one in which the relations of the subject and answer were governed by the old Church modes, in which each Authentic mode had its related Plagal mode. [See Real Fugue.]