====== On Fugue ======
==== On Counter-Subject ====

The melody which accompanies, either the ''Subject'' or the ''Response'', is called the ''Counter-Subject''; as the ''Counter-Subject'' is intended to be introduced above and below the ''Subject'' and the ''Response'', the necessity will be perceived of combining it by double counterpoint in the octave, that it may be susceptible of inversion either from high to low, or from low to high, without incurring the risk of defect or necessity for any change:

{{ :cherubini_counterpoint_and_fugue:ex193-1.png?800 |}}

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It is not, however, absolutely indispensable to preserve the exact identity of the ''Counter-Subject'' in its transpositions and inversions; and some notes of it may be changed, should this be deemed advisable for the sake of purity in the harmony, and strictness in the counterpoint.

In a two-part fugue, there can be only one ''Counter-Subject''; in a three-part fugue, two ''Counter-Subjects'', and in a four-part fugue, three ''Counter-Subjects''. The number of ''Counter-Subjects'' may increase in proportion with the increased number of parts; and it is to be understood, that, there can only be as many counter-subjects as there are parts, exclusive of the part which contains either the ''Subject'' or the ''Response''. When there is only one counter-subject, whatever the number of parts may be, those that accompany the ''Subject'' and the ''Counter-Subject'' jointly, are ''Ad Libitum'' parts, of which the melody may be varied each time they intervene - whether in the lower, the higher, or the middle part:

{{ :cherubini_counterpoint_and_fugue:ex194-1.png?800 |}}

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It is needless to say, that in a fugue in five, six, seven, or eight parts, several ''Ad Libitum'' parts must be had, on account of the difficulty, and even impossibility, of finding a sufficient number of ''Counter-Subjects''; that is to say, of parts in double counterpoint, for so large a number of voices.

The ''Counter-Subjects'' in a fugue, may be placed immediately and simultaneously with the ''Subject''. For my own part, I cannot say that this disposal appears to me to be the best. I think that greater variety in the union of the parts is obtained, by so contriving the ''Counter-Subject'' as that they shall enter successively; and by allowing the subject first to be heard, by itself, or accompanied at the most by a single counter-subject, if the fugue be in three parts, or by two, if it be in four.

Whatever the number of parts may be, when a fugue is commenced by accompanying the ''Subject'' immediately with a ''Counter-Subject'', this disposal gives to the fugue the name of a ''Fugue on Two Subjects''.

Example of what is called a //Fugue on Two Subjects//, whatever be the number of parts:

{{ :cherubini_counterpoint_and_fugue:ex195-1.png?800 |}}

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When a ''Subject'' is accompanied by two ''Counter-Subjects'', the fugue is called a ''Fugue on Three Subjects''.

Example of what is called a //Fugue on Three Subjects//, whatever be the number of parts, beyond three:

{{ :cherubini_counterpoint_and_fugue:ex196-1.png?800 |}}

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When to a ''Subject'' three ''Counter-Subjects'' are opposed, the fugue is said to be on ''Four Subjects'', etc:

Example of what is called //Fugue on Four Subjects//, whatever be the number of parts beyond four:

{{ :cherubini_counterpoint_and_fugue:ex197-1.png?800 |}}

{{ :cherubini_counterpoint_and_fugue:ex197.mp3 | :cherubini_counterpoint_and_fugue:ex197.ogg |}}

**Observation** - Although the denomination of //fugue on two, on three, and on four subjects//, be generally adopted, this denomination (to my thinking) is improper; and I base my opinion respecting this point upon the circumstance that a fugue cannot, nor ought to have more than a single principal subject as its exponent, and cannot nor ought to bear any other name than that of ''Counter-Subject''. Therefore, according to this principle, a fugue, which by habit is called a //fugue on two subjects//, should be named a //fugue on one subject and a counter-subject//; that on //three subjects//, should be called a //fugue on one subject and two counter-subjects//; and lastly, that on //four subjects//, should bear the name of a fugue on //one subject and three counter-subjects//, etc.

As a farther-convincing proof that this should be so, suppose that these different //subjects//, instead of being all at once and simultaneously employed with the principal //subject//, should be so only successively by the parts which enter in turn; these different accompaniments of the //subject// or of the response, which were named subjects when employed at the outset, would in this case be called //counter-subjects//; now, because all these //counter-subjects// might be introduced at the same time that the //principal subject// is first proposed, it does not follow, that they must therefore change their denomination.

It should, however, be observed, that in case a fugue be so disposed, as that several //counter-subjects// are employed only afterwards, either during the //subject//, or with the response, and that they have not been introduced at the beginning, with the //subject// itself, there is free leave then, either to preserve their identity each time they recur, or to alter them a little, by changing some few notes, according to the exigency and situation of the parts.

In every case, it is important and indispensable, always to combine these //counter-subjects// according to the laws of //double counterpoint//, so as to be able to use them under all circumstances, and in rder that they may afford scope for the different devices in which it may be desirable to employ them.

==== On Stretto ====

''Stretto'' is an Italian word, signifying //close//; it has been adopted into our language, and is employed to indicate a device which consists in approaching, as closely as possible, the entrance of the response to that of the subject.

Example of the //response// entering after the period of the subject is terminated.

{{ :cherubini_counterpoint_and_fugue:ex198a-1.png?800 |}}

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Example of the //response// entering during the period of the subject, forming the //stretto//.

{{ :cherubini_counterpoint_and_fugue:ex198b-1.png?800 |}}

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The //stretto// is - as has been already observed - one of the essential requisites of a fugue; the place which it should occupy will be indicated when the entire context of a fugue comes in question. The art of judiciously employing the //stretto//, consists in the manner of varying its aspects, and in inventing means, each time the stretto is introduced, of approaching the entrance of the response more and more closely to the commencement of the subject. The effect which this produces is extremely attractive, and tat the same time very appealing.

It is sometimes permitted, when impossible to do otherwise, in order that the entrances of the response and subject may be brought closely together, to change some notes of either the one or the other; or, if not to change the notes, to change their value: but these alterations can take place in the ''Subject'' only after the entrance of the ''Response''; and in this latter, only after the re-entrance of the ''Subject'', and so on. All this admits of many exceptions, which are allowed, according to the existing dilemma, as will be seen, in studying fugue.

It is also permitted - when the ''Subject'', by its nature, is not well suited for combining the ''Stretto'' in a manner quite natural - to commence the ''Stretto'' by the ''Response''; but if neither the one nor the other be adapted for obtaining all the aspects desired in the ''Stretto'', we must content ourselves with making the ''Response'' enter after the ''Subject'', or this after the other, at any place we can; and, as a last resource, employ the permitted changes either in the notes, or in their value. Moreover, practice will indicate better still, the means of successfully eluding difficult cases of this kind.

A good fugal subject should always give scope for an easy and harmonious ''Stretto''; in composing a subject, therefore, the difficult combinations of ''Stretto'' ought to be carefully pre-considered.

==== On Pedal ====

The ''Pedal'' is a note prolonged and sustained during several bars. It may be placed either in the highest part, in one of the middle parts, or in the lowest part; it can be made - whatever its position - only upon the ''Tonic'', or upon the ''Dominant''; but the best pedal - the one from which the most-advantageous effect may be drawn, and the one most generally used in fugue - is that of the ''Dominant'' placed in the lowest part. The property of the ''Pedal'' is to emancipate the composer from the rigour of the rules; that is to say, he can, while the period of its duration continues, introduce unprepared discords ((dissonances)), and even modulate, provided the parts which effect this operation are combined each with each according to the rules, and as if the ''Pedal'' did not exist, save in the first and in the last bar, which ought always to be in harmony with the ''Pedal'' note. In accordance with what has just been stated, the composer should cause to be heard upon the ''Pedal'': the ''Subject'', the ''Response'' in ''Stretto'', the ''Counter-Subjects'', and, if possible, some of those ingenious devices that may have been introduced in the course of the fugue.

{{ :cherubini_counterpoint_and_fugue:ex199-1.png?800 |}}

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As there are ordinarily requisite, at least two parts to execute work upon the ''Pedal'' which shall fulfil all the prescribed conditions, it follows that the ''Pedal'' is not necessarily in a two-part fugue. This is why the ''Pedal'' does not form one of the indispensable attributes of a fugue.