Fugue (Prout)/Chapter 3
CHAPTER III.
THE ANSWER.
55. In our first chapter (§ 9) we defined the answer as "the transposition of the subject into the key of the perfect fourth or fifth above or below the key of the subject." It is most necessary that the student should know how to find the correct answer to any given subject; unfortunately there is hardly any point on which the rules given in the older text-books differ so widely from the practice of the greatest composers. The rules to be given in the present chapter will therefore not be taken from existing treatises, but deduced from the works of the great masters themselves.
56. In by far the largest number of cases, the keys in which the subject and answer are found are the tonic and dominant. If the subject be in the tonic, the answer will be in the dominant; if the subject be in the dominant, the answer will be in the tonic. If the subject begin in the tonic and modulate to the dominant, the answer will begin in the dominant and modulate to the tonic, and vice versa. Occasionally, however, as will be seen presently, the place of the dominant is taken by the subdominant.
57. The answer of a subject may be either real or tonal. It is said to be real when it is an exact transposition (with one possible exception, to be noticed in its proper place—see § 69) of the subject; it is called tonal when certain alterations, the nature of which we shall explain later, have to be made in transposing it.
In the above examples the subject is marked S and the answer A. At (a) the answer is real; at (b) it is tonal, the interval of a third from G to B being answered by a second from D to E. Let the student also notice that at (a) the last note of the answer is longer than the last note of the subject. We shall meet with other instances of this common procedure as we advance; it is always allowed either to lengthen or shorten the first or last note of the answer.
58. As being the easier, we shall first speak of real answers. The rule for knowing when a subject can have a real answer is very simple, and may be thus stated:—Every subject in which there is no modulation to the dominant, either expressed or implied,[1] may have a real answer, excepting, first, when it begins on the tonic and leaps to the dominant either direct or with the third of the scale as an intermediate note; and secondly, when it begins on the dominant. But even in these two cases a real answer is always possible (§§ 101, 105–107).
59. We shall first give examples of real answers in the dominant key to subjects which are in the tonic throughout. We shall in each case give the counterpoint to the answer, which is, as will be seen, the continuation of the music by the voice which has just had the subject; we shall also extend our quotations beyond the end of the answer, as this will help the student in determining the limits of the subject. Our first example illustrates what was said in § 53—that when the subject commences with an accented note, the answer usually enters on the last note of the subject—
That the subject here ends on the F sharp of the fifth bar (the third of the dominant chord—§ 42) is proved by the fact that the next note, G, is not imitated in the answer. In this example the answer is below the subject.
60. In our next examples
the answer is above the subject. In both, the subject commences on an unaccented note, and ends on the accented note (here at the half bar) immediately preceding the entrance of the answer.
61. The following passage shows some new points—
Here the answer enters shortly before the end of the subject, which terminates at *, the nearest accent to the entry of the answer. In § 53 it was said that the length of the subject could mostly be determined by seeing how much was imitated by the answer. It looks at first sight as if the imitation were here continued for another half bar; but the subject cannot end on the D at the beginning of the third bar; because, in that case, as we shall see later in this chapter, the answer could not possibly end on A. Besides this, the imitation in the half bar is not exact, D sharp being imitated by A natural, not by A sharp. The fact is, we have here a common case, in which part of the continuation of the subject is imitated in the answer—sometimes strictly, at other times (as here) freely.
62. In the example just given, the answer entered before the end of the subject. In our next
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the subject ends (as will be seen by comparing the answer) on the first note of the third bar, and the answer does not enter till the fourth. Such cases are of frequent occurrence. Here it would have been quite possible for Handel to have commenced his answer in the third bar; thus—
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but if the student will remember what was said in the last chapter about the implied harmony of a fugue subject, he will see that at the end of the second bar of this subject there is clearly a chord of the dominant seventh implied; and the continuation we have suggested would have been far less satisfactory from a harmonic point of view. The passage introduced between the end of the subject and the beginning of the answer, which we have marked with a | |, is called a codetta. In many cases some such connecting portion is absolutely necessary.
63. The following example
shows a more chromatic subject than those already given. Here the answer enters on the last note of the subject, because it begins on an accented beat. Our last example was an exception from this rule.
64. In our next example
we see a somewhat rare case. The first voice ceases for some time to accompany the answer. The quotation is the commencement of a fugue with independent orchestral accompaniment; and the tenor, therefore, though the bass is silent, is not left entirely alone.[2] Such treatment is, however, exceptional; and the student is not recommended to imitate it.
65. Our last example in a major key
shows the leading-note of the dominant treated as the third of the supertonic chromatic chord, and therefore inducing no modulation. It is consequently answered by C sharp, the third of the supertonic chromatic chord in the key of G. The last note of the subject, also, is here slightly altered in the answer, being delayed by a suspension.
66. We now give some answers to subjects in minor keys. These will always be in the minor of the dominant—never in the major. We have seen already (§ 35) that if a minor subject modulates to the dominant, it is always to the dominant minor; and the same rule holds good when the first modulation that is made is on the entrance of the answer. This will be seen from the two following examples—
67. If the student will examine the various counterpoints accompanying the answers we have given, he will see that (like the answers themselves) they are in the key of the dominant. Were it otherwise, the feeling of tonality would be obscured, for the music would be in two keys at once. Occasionally, however, the harmony of the dominant key is not clearly defined till toward the end of the answer, as in the following passage—
Here the key of D sharp minor, the dominant of G sharp minor, is not reached till the third bar of the answer.
68. Our next example illustrates a point of considerable importance—
Here the last note of the subject is D flat, the minor third of the tonic; but the last note of the answer is not A flat, the minor third of the dominant, but A natural, the major third.
69. That this is by no means an isolated case will be seen by the following examples, taken from a much larger number that might be given—
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Further illustrations of this point will be met with when we come to tonal fugues. The following rule is fully justified by the practice of the great masters:—
Whenever a subject in a minor key ends on the third of the tonic, the answer may end on either the major or minor third of the dominant, as may be preferred.
70. If the subject be throughout in the key of the dominant, the answer will be in the key of the tonic—
It is important to notice that the answer is now a fourth above, or a fifth below, instead of being (as in previous cases) a fifth above, or a fourth below, the subject.
71. By an extension of this relation of subject and answer, we sometimes find that when the subject is in the tonic, the answer is in the subdominant, instead of the dominant—
Here the subject is in C, and the answer is no less clearly in F. The commencement of the answer illustrates what was said in § 57, the initial notes being lengthened—
Here again the answer is in the subdominant. The alteration of the semitone near the end (B natural answering F natural) is frequently to be met with (§ 144)—
Here the answer is in the fourth above, instead of the fifth below. This fugue has an independent organ accompaniment (not quoted), which still more clearly proves the key of the answer to be C.
72. If we examine the three subjects last given, we shall see that in all of them prominence is given to the dominant or to notes of the dominant harmony. The same thing will be found in our examples in a minor key, in which an answer in the subdominant is much more common than in a major key—
Here the subject commences with the arpeggio of the dominant seventh; then comes tonic harmony, and then dominant harmony again. The answer is now in the subdominant, in order to carry out the important principle that dominant harmony should be answered by tonic.
73. As the possibility of a fugal answer being in the key of the subdominant has not, so far as we know, been touched upon in any existing treatise, it will be needful to give a considerable number of examples by the greatest masters—not only to establish the fact, but to enable us to deduce the necessary rules for the student's guidance in deciding when such an answer is advisable. Our next example deserves close examination—
Here the subject does not, like those previously given, begin with a note of the dominant chord; but the diminished fifth immediately following clearly indicates the chord of the dominant seventh. In the next bar is a modulation to the dominant key, the return to the tonic being made in the third bar.
74. Now let us examine the answer. The first note is C. This cannot be regarded as a subdominant, because the tonic at the commencement of a subject cannot be answered by a subdominant. We have already seen that it is almost invariably answered by dominant—that is to say, by the tonic of the key in which the answer appears. The C here must therefore be considered not as the subdominant of G minor, but as the tonic of C minor. This choice of a key for the answer enables Bach to carry out the important general principal already mentioned, and of which we shall have more to say when we come to speak of tonal answers, that dominant harmony in the subject should be replied to by tonic harmony in the answer. Here we have the dominant seventh chord in G at the first bar of the subject, answered by the notes of the tonic seventh of G in the first bar of the answer. It would have been quite possible to give a real answer for this bar, beginning on the dominant; but then the dominant harmony of the subject would have been answered by the supertonic harmony, instead of the tonic.
75. It will also be seen that at the second bar of the subject there is a modulation to the dominant key. Such a modulation is almost invariably answered by a return to the tonic key. Here, however, the tonic harmony in the answer is really the harmony of the dominant key of C minor. Had the answer not been in the key of the subdominant, a tonal answer would have been necessary.
76. Our next illustrations, containing no modulation,
further show the answering of dominant harmony at the commencement of the subject by tonic harmony at the beginning of the answer. The two subjects are somewhat similar in character.
77. The same point is exemplified in the following—
The subject here begins on the leading note. We shall see when we come to tonal answers that the leading note, excepting when it is merely an auxiliary note of the tonic, is almost invariably considered as the third of the dominant, and answered accordingly by the major third of the tonic (§ 131). This is the case here, and any other answer than that which Bach has given in the subdominant key, will either sacrifice this reply of tonic to dominant, or (if a tonal answer) distort the subject almost beyond recognition. It should be specially noticed that the 'Art of Fugue' from which this example is taken, was expressly written by Bach for the purpose of showing the possibilities of fugal composition; his giving an example of an answer in the subdominant key may therefore be fairly taken as proving, apart from all the other examples we have given, that he considered such an answer correct.
78. The last example we shall give from Bach
is similar in character, and even more pronounced. The subject, except the last note, is formed entirely of dominant harmony, which is therefore answered by corresponding tonic harmony. The counterpoint accompanying the answer conclusively proves the key of the answer to be G.
79. We now add a few examples, by other composers, of real answers in the subdominant key—
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After what has been said, these examples require no further remark.
80. We shall find a few more examples of answers in the subdominant when we come to treat of tonal answers, but we have already given enough to enable us to generalize from. The rule to be deduced from an examination of these and similar passages is the following:—
Whenever, in a subject which ends in the key of the tonic, particular prominence is given to dominant harmony, especially near the beginning of the subject, the answer may be in the subdominant key, in order to conform to the important general principle that dominant harmony in the subject should be replied to by tonic harmony in the answer.
81. If the whole subject be in the key of the subdominant, the answer will be in the key of the tonic—
In this case the relationship of the two keys is evidently the same as that of tonic and dominant.
82. If the subject begin in the key of the subdominant and modulate to the tonic, the answer will begin in the key of the tonic and modulate to the dominant—
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The subject here ends on the first crotchet of the third bar. It begins in G minor and modulates in the second bar to D minor. The answer begins in D minor and modulates to A minor. The proof that the subject commences in G minor is found in the first note of the answer. If Handel had regarded A as the dominant of D minor, instead of the supertonic of G minor, he would have answered it, according to the laws of tonal fugue, by D and not E.
83. Intermediate modulations (except to the key of the dominant) should be imitated exactly in the answer—
In the second bar of the major subject at (a) is seen a modulation to the subdominant, imitated at the same point of the answer; and in the third bar of the minor subject at (b) a modulation to the relative major, replied to by a similar modulation to the relative major (G major) of the dominant.
84. In order to understand what is meant by a tonal answer, we must remember that each of the old Ecclesiastical scales, out of which our modern scales were developed, had two "modes," one of which was a fourth below the other, but contained the same notes. If the scale was from final to final (or, as we should now say, from tonic to tonic), and the dominant was in the middle, the mode was said to be authentic; if, on the other hand, the scale was from dominant to dominant, with the final in the middle, the mode was called plagal. Each scale was divided into two unequal halves by the dominant or the final. Let us take, for example, the old Dorian mode—
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The dominant in the authentic mode and the final in the plagal are marked in this example. It will be seen that the lower half of the authentic scale has the compass of a fifth, and the upper half the compass of a fourth; while the plagal scale has a fourth for the lower half, and a fifth for the upper.
85. The old rule for fugal answer was that a subject made in either half of the authentic scale should be answered in the corresponding half of the plagal scale, and vice versâ. For instance, if the subject began with the leap between tonic and dominant, in the lower half of the authentic scale,
the answer would begin with the leap between dominant and tonic,
these being the corresponding lowest and highest notes of the lower half of the plagal scale; and conversely, if the subject began in the lower half of the plagal scale, with the leap up from dominant to tonic, or down from tonic to dominant, the answer would begin in the lower half of the authentic scale with the leap up from tonic to dominant, or down from dominant to tonic.
86. The rule to be found in nearly every work on fugue respecting tonal answer is, that if a subject leaps from tonic to dominant, either direct or through the third of the tonic, the answer must be tonal—that is to say, the tonic must be answered by the dominant, and the dominant by the tonic. This is a good rule enough, if it were only observed; but, as we shall proceed to show, the great masters, from Bach and Handel downwards, "drive a coach and four through it" continually. If we wish to conform to their practice, we shall have to modify this rule very considerably.
87. Evidently the first thing to be done is, to find out what the practice of the great masters really was in this respect. For this purpose a large number of quotations will be necessary. It may be at once admitted that in the majority of instances they conformed to the old rule; but quite enough examples will be found in which it is broken to show that they did not regard it as one of the laws of the Medes and Persians. In the examples now to be given, we shall no longer add the counterpoint that accompanies the subject, because the student will by this time have learnt how to find out where the subject ends; instead of this, we shall put the answer under the subject, in order that the two may be more easily compared.
88. We first give examples in which the old rule is strictly followed. Of these there are plenty.
This specimen of a simple tonal answer illustrates more than one point of some importance. The subject is here in the tonic; the answer will therefore be in the key of the dominant; and, except the first note of the second bar, every note of the subject belonging to the key of E flat must be answered by the corresponding note of the key of B flat. It must be especially noticed that though the note B flat (the dominant of E flat) is used four times in the course of the subject, it is answered every time except the first by F, and not by the tonic, E flat. The rule of answering tonic by dominant, and dominant by tonic, applies only to the beginning of a subject and to passages where a modulation to the dominant occurs. In the present case the claims of the law are satisfied as soon as E–B at the beginning of a subject has been answered by B–E; after this, the rest of the subject is transposed, as if the answer were real, into the key of the dominant. The following notes of the subject are respectively the subdominant, mediant, submediant, and dominant of E flat; and they are answered by the subdominant, mediant, submediant, and dominant of B flat—and so on, to the end of the answer. There is no mistake which students are more apt to make in beginning to write tonal answers than to answer dominant by tonic every time these notes occur. This is almost invariably wrong.
89. If we look at the second bar of the above example, we shall find that an interval of a second in the subject has become a unison in the answer. Whenever a subject begins with the leap from tonic to dominant, it always, if answered tonally, causes a change in the following interval. Here the first and third notes of the subject are the tonic and subdominant of the tonic key; the first and third notes of the answer are the tonic and subdominant of the dominant key: but the difference in the size of the first leap of the subject (a fifth), as compared with the leap of a fourth in the answer, makes a difference also in the interval between the second and third notes. We give two more illustrations of the same point—
J. S. Bach.
Wohltemperirtes Clavier, Fugue 17.
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At (a) a third in the subject becomes a second in the answer; at (b) a second in the subject becomes a third in the answer. Note, in passing, the shortening of the last note of the answer at (b)—(§ 57).
90. That the answering of tonic by dominant, and dominant by tonic, applies only to the beginning of the subject is clearly shown by the examples of real answers quoted in § 59 and § 83 (b), both of which contain the leap from tonic to dominant in the second bar, not answered by the leap from dominant to tonic.
91. Though the general practice of the great masters is, as has been already said, to answer the leap between tonic and dominant tonally, a real answer under such circumstances is not infrequent, especially when the leap is downwards—
In not one of these examples (and more could be given) is dominant answered by tonic, but in each instance by the dominant of the dominant key.
92. When the tonic goes to the dominant through the third of the scale, the rule of the old text-books is that the answer should be tonal. We give two examples by Bach—
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J. S. Bach.
Cantata, "Ich hatte viel Bekümmerniss."
In both these cases the dominant is answered by the tonic. But these subjects belong to a large class—those that begin with the notes of the tonic chord taken in succession. In such cases the great masters give a real answer nearly, if not quite, as often as a tonal one. We give specimens of both: one example of a tonal answer to a subject of this kind has been already seen at § 89 (a). Where the subjects are long we shall quote only the commencement, as the rule is never intended to apply to the middle of an answer, but only to its beginning.
93. We give first some tonal answers—
J. S. Bach.
Organ Toccata and Fugue in C.
In both these cases the D is only an auxiliary or passing-note; and it is quite evident that the subject commences with tonic harmony. In our next examples no passing-notes are introduced; both begin with the notes of the tonic chord. Observe at (d) another instance of the lengthening of the last note of the answer.
94. We now give a number of examples where the leap between tonic and dominant has a real answer, because the subject begins with the notes of the tonic chord—
In all these instances, taken from the works of Bach, the answers are real. After what has been said, no further explanation will be required.
95. In the works of Handel we find a real answer in such cases even more frequently than in the works of Bach. We give five examples—
96. In the following answer we see that J. Christian Bach, the youngest son of the great John Sebastian, adopted the same plan as his father—
97. Our next examples are more modern—
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It is only needful to remark that in the latter part of example (a) there is a modulation. The principle by which this part of the answer is regulated will be explained in the next chapter.
98. In Cherubini's Treatise on Fugue we find the following example of a real answer to a subject going to the dominant through the third of the scale—
Cherubini gives this without a word of explanation; it is clear, therefore, that he did not regard it as an irregularity.
99. Two more passages will complete our illustrations of this point—
100. If we examine and compare all the examples we have given of subjects founded upon the notes of the tonic chord, and taking real answers, we shall find that there is an important principle involved in all of them. We have already shown that the tonal answer is the result of the old modal systems (§§ 84, 85), which prevailed before modern tonality, as now understood, was fixed. In all these cases, however, the old rule gives way to a higher and more important law, to which reference has already been made, and which has a wider application. This is the broad principle which is the very basis of fugal answer—that tonic harmony should be answered by dominant, and dominant by tonic. If we look at the tonal answers already given—for instance, § 93 (c), (d)—we shall find that the strong suggestion of tonic harmony in the first three notes of the subject is not replied to by an equally strong suggestion of dominant harmony in the first three notes of the answer. In both these examples the second note destroys the feeling of the dominant at once. When the dominant as the second note of the subject is not followed by another note of the tonic chord, the feeling of the tonic harmony is not so pronounced; and here a tonal answer may frequently be employed with advantage. In this case, however, adherence to the old rule will sometimes injure the form of the answer. This will be seen in the following example—
Here the character of the subject is entirely ruined by the monotonous repetition of the F's in the answer. A real answer here would have been far more effective. In example (d) of § 91, where Handel has given a real answer, the effect of a tonal answer would have been even worse—
101. The rule for the guidance of the student to be deduced from the examples given is as follows:—
If a subject commence with the leap from tonic to dominant, and the following note is not a note of the tonic chord, a tonal answer is generally, though not invariably, preferable; but if at least the first three notes of the subject are all notes of the tonic chord, the answer, provided that no modulation takes place to the key of the dominant, may be either real or tonal.
102. We now have to consider an important class of subjects—those that commence on the dominant. The old rule again was here absolute—that when the subject began on the dominant the answer must begin on the tonic.[3] This rule, like that discussed in §§ 86, 87, is observed by the great masters in the large majority of instances; but numerous exceptions are to be found to it. A few examples of its observance will first be given—
In these answers, which contain no modulation, the first note is the only one which differs from a real answer. The dominant in the third bar of (b) is not answered by the tonic. Sometimes, however (though much more rarely), the dominant is answered by the tonic on its later appearances, as in the following answers—
103. Our next examples give further illustrations in the last note of their answers of the rule given in § 69—
At the second and third bars of (a) we also see an incidental modulation into the key of the subdominant, already referred to in § 41. It will be observed that the answer here modulates to the tonic (the subdominant of the dominant key).
104. When the subject begins on the dominant and leaps to the tonic, the answer usually begins on the tonic and leaps to the dominant—
This example illustrates some other points besides that just mentioned. It will be seen that after the first note, the whole subject is in the key of the dominant. It is therefore answered in the key of the tonic (§ 70). The final C sharp of the subject cannot be considered as the leading note of D minor, for if it were it would be answered by G sharp, the leading note of A minor. It is the major third of A, and is answered by F, the minor third of D, a rare instance of the converse of our examples in §§ 68, 69, 103.
105. The student will have no difficulty in finding any number of answers in which the general rule we have given is adhered to; we now proceed to give examples in which it is not observed. Our first group will be answers to subjects which commence with the notes of the tonic chord—
These are parallel cases to those given in §§ 94–99. In all of them the subject begins with tonic harmony and the answer replies with dominant harmony. Notice in example (f) an incidental modulation to the key of the supertonic minor. The imitation is here exact (§ 83).
106. We next give instances in which the leap from dominant to tonic is not followed by another note of the tonic chord—
The answer at (e) looks irregular; but there is here an implied modulation (§ 118). The subject after the second note is regarded as being in the dominant key, and therefore answered by the corresponding notes of the tonic key.
107. Lastly we give examples in which the dominant is followed by some other note than the tonic—
Handel.
Anthem, "Have mercy upon me, O God."
We have only to note with regard to these examples that in the first bar of (b) is a not uncommon case, G sharp being answered not by D sharp but by D natural. Such disregard of the exact quality of intervals is not infrequent; we shall meet with more instances later. At the end of (f) the subject modulates to the dominant; the answer here is exceptional, and will be discussed in our next chapter.
108. We have given quite enough examples to prove that the rule as to answering dominant by tonic at the commencement of a subject is by no means so "absolute" as it is declared to be by many theorists. For this there are two reasons. First there is the general principle already referred to in § 100, that tonic harmony in the subject should be replied to by dominant harmony in the answer. This is illustrated by the examples in §§ 105, 106. Besides this, the melodic form of the subject should be kept unchanged as far as possible; and it is quite evident that in many cases the great composers felt this to be of much more importance than the keeping of an old rule which was made before modern tonality was established.
109. A further proof that but little weight was attached to the necessity for a tonal answer is found in the fact that sometimes in the first exposition of a fugue the first answer will be tonal and the second real, as in the following case—
Here the first answer is tonal, the first note being shortened (§ 57); but the second answer (still forming part of the exposition, in which strictness is expected) is real. In the later entries of a subject, we continually meet with real answers where tonal have been given at first.
110. We saw in § 104 a subject which, except the first note, was in the key of the dominant, the answer being in the key of the tonic. We have also seen, in discussing real answers, how an extension of the same relation of subject and answer rendered an answer sometimes possible in the subdominant key (§ 71). A similar answer is also possible where the first note of the subject is answered tonally, as in the following examples—
In example (a) we have quoted the counterpoint accompanying the answer, to prove more clearly that the latter is in the subdominant key. The two examples by Buxtehude are very similar in the character of their subjects. In all these subjects the prominence given to dominant harmony, which we have already mentioned as a feature of all subjects which are answered in the subdominant, will again be noticed.
111. Sometimes in the exposition of a fugue the first answer is in the key of the dominant, and the second in that of the subdominant, as in the following passages—
112. The proper method of answering subjects that modulate into the key of the dominant will be treated in the next chapter. We now sum up our conclusions with regard to the subjects we have already dealt with. From a careful investigation of the practice of the greatest composers, we deduce the following principle:—
Though frequently expedient, and even preferable, a tonal answer is never absolutely necessary for any subject which does not fnodulate between the keys of the tonic and dominant.[4]
113. In concluding this chapter it is needful to give the student a most urgent warning with regard to the use of this book. It is not written as a "cram" for examinations; and although all the rules given in the present chapter are founded upon the practice of the great masters and enforced by their example, yet in the present condition of musical examinations, any student who attempts to carry into practice the principles here given will almost inevitably be "ploughed." The old theorists mostly follow one another blindly, like a flock of sheep through a hedge; and examiners in general adhere to the musty rules of two hundred years ago, taking little or no account of the progress made by music since that time. The old rules have therefore been in all cases given in this chapter, and those who are going up for examination had better adhere to them until examiners become more enlightened and liberal. Our object in this, as in the other volumes of this series, has been to found our teaching on the practice of the great composers who have brought our art to its present state of advancement; but Bach himself breaks far too many of the antiquated rules to have had much chance of passing, had he gone up for a Doctor's degree at one of our universities.
- ↑ What is meant by an implied modulation will be seen when we come to speak of tonal answers (§ 118).
- ↑ See § 441, where the complete exposition of this fugue is quoted.
- ↑ If, however, the dominant was an unaccented note of small value, a real answer was sometimes allowed even by the old theorists.
- ↑ A merely incidental modulation to the dominant (as in the example to § 73) does not necessitate a tonal answer.