Faà di Bruno, Giovanni Matteo [Horatio, Orazio] 83

1. A classic fugue analysed.

The fugue in C minor from book 1 of Bach’s ‘48’ (ex.1) is now generally described by English speakers as follows.

The fugue is for three voices, which may be labelled soprano, alto and bass, and the independence and integrity of each are strictly maintained until the last two bars, when chords are introduced to lend fullness and finality. A single voice, the alto, begins the fugue by stating the ‘subject’. The subject is in the tonic key: it begins on the tonic note C, emphasizes the dominant note G (downbeat of bar 2) and ends on the mediant note (downbeat of bar 3). Once the subject has been stated in its entirety, the second voice (the soprano) enters with the same subject, but transposed to the key of the dominant. This second statement is termed the ‘answer’. Such a transposition often requires, as here, that the original intervals of the subject be altered in order to keep the answer close to the tonic key. More specifically, whereas tonic note is answered by dominant note (i.e. transposed up a 5th or down a 4th), dominant note is answered by tonic rather than by supertonic. In this particular answer, the second note is an exact intervallic reproduction, producing F and signalling the key of the dominant, G minor, but the fourth note is changed from D (supertonic) to C (tonic). All other intervals from the fifth note to the end of the answer are exact renderings of the subject’s intervals. An answer of this sort, in which intervals are altered to remain close to the tonic key, is called a ‘tonal answer’. Any answer in which no intervals of the subject are altered is called a ‘real answer’.

While voice 2 states the answer, voice 1 continues with counterpoint against it. This counterpoint may, as here, be material that returns frequently during the course of the piece, usually as counterpoint to the subject, or it may present material that never returns. Especially in the former case, this thematic material is called a ‘countersubject’. Both answer and countersubject conclude on the downbeat of bar 5, at which point both continue in counterpoint for two bars without stating either the subject or the countersubject in complete form. These two bars constitute what is often called a ‘codetta’. Although neither thematic unit is present in its entirety, the material in voice 2 is a melodic sequence based on the opening motif of the subject, and voice 1 contains scalar passages reminiscent (although in contrary motion) of the countersubject. The final voice enters with the subject (in its original, not its answer, form) at the beginning of bar 7, accompanied by voice 2 with the countersubject. Voice 1 states yet another countersubject, though one that is treated rather freely during the course of the fugue. All three – subject, countersubject 1 and countersubject 2 – end with the downbeat of bar 9.

The opening eight bars make up the fugue’s ‘exposition’. Standard requirements of a fugal exposition are that (1) the voices enter one by one with the subject, each waiting until the preceding voice has completed its statement before entering; (2) each voice enter with the subject, in either subject or answer form, only once (occasionally the first voice to enter may restate the subject at the end of the exposition); and (3) the entries alternate between subject and answer statements. Additional options are that (1) the first statement of the answer may be accompanied by a countersubject, which is then stated in turn by all voices (except the last) as accompaniment to the next statement of the subject; and (2) there may be a codetta between statements 1 and 2 and statement(s) 3 (and 4).

An exposition is the most strictly regulated portion of a fugue. The remainder is understood to be an alternation between sections in which the subject is stated in its complete form by one or more voices and sections in which it is not present in its complete form. The latter, called ‘episodes’, may or may not take any of their motivic material from the subject or countersubject. Complete statements of the subject may take place in keys other than the tonic, in which case episodes serve to modulate to and from those keys. Statements may also incorporate some learned contrapuntal device that alters the subject in some way but leaves it complete and recognizable. These devices include augmentation (the slowing down, generally by a factor of two, of the original note values), diminution (halving or quartering the note values), inversion (stating the subject upside down) and stretto (introducing a second statement before the first has finished). It is generally understood that the fugue will end with some sort of statement of the subject in the tonic key. Any material following that statement is termed a coda.

Beginning with bar 9, Bach’s C minor fugue proceeds as follows: there are four episodes (bars 9–10, 13–14, 17–19 and 22–6). Each takes its thematic material from the opening five-note motif of the subject and the scalar passages of quavers and semiquavers in the two countersubjects. These motifs are generally treated in melodic sequence. In addition, the first two episodes modulate to and from the key of the relative major, E. The complete statements of the subject that appear in between involve in each case subject and two countersubjects distributed among the three voices. In bars 11–12 (in E) the soprano carries the subject, in 15–16 the alto, in 20–21 the soprano again, and in 26–8 the bass. After a brief connecting passage the final statement of the subject, in its original form and at its original pitch, is stated by the soprano over a C pedal point in the bass and accompanied by a few full chords in the alto. The entire fugue appears in ex.1. Most elements of a ‘textbook’ fugue are present in Bach’s C minor fugue. One of its most attractive features is its thematic tightness, that is, the presence of material from the subject or one of the countersubjects in virtually any voice at any point in the fugue. Also present is a modulation to a related key with the subject stated in that key. What this particular fugue lacks is the use of any of the contrapuntal devices enumerated above.

Fugue