Getting Started With Writing, Part XIX

(con't from Part XVIII)
We have it on reliable authority from those who personally knew the strongest fugue writer in history that fugue writing is an art (photo shows the cover page of the 1st edition of The Art of Fugue published posthumously in 1751 by the sons of J.S. Bach).
Although it's come down to us in an incomplete form (the composer was overtaken by death before he could finish it), this cycle of fugues and canons is one of the greatest monuments in music history and one of the loftiest achievements of the human mind [See blog, Getting Started With Writing, Part XXI].
There also is indirect evidence to support the idea that it was Bach's intention to use this work not only for study and performance but to embed with in, in numerical symbolism, his various titles connected with his Leipzig post [See blog, subpage, The Art of Fugue].
Fugue writing therefore, being an esoteric art but an art nonetheless, can and absolutely should be explored to expand the boundaries of this art in the interests of furthering its progress.
Every fugue written by this author, in some way or another, can be cited as an example which explores those boundaries in some kind of unexpected or sometimes bold way [See menu bar, Free Stuff].
Every one of these fugues, whether paired or unpaired with another work, took only a few days to compose using the system for fugue writing described on this web site [See blog, Ten Steps].
It will help to download and print a hard copy of the G Major Fugue from Op. 20 as this narrative on how this music was put together proceeds; the writing of the Introduction paired with it is described in a separate posting [See blog, Getting Started With Writing, Part XXIV]:
Longer fugue subjects in 4/4 (common) time like this one can be regularly 2, 4, 6, or 8 bars in length, but this subject, which occupies an odd number (5) of bars, is considered irregular in length; it enters first in the tenor voice in the home key and is answered in the alto in the dominant key.
One notes immediately that the outline of the subject reaches a peak on the 6th scale degree; this is important in that this scale degree will need to remain unaltered in any entry in a minor key.
Here the opening statement of the subject, starting on the 1st scale degree, has a real answer which follows in the dominant on the 5th degree, as expected from the rules of common practice [See blog, Getting Started With Writing, Part XX].
This is followed by a short modulating interlude of 4 bars which brings about a smooth return to the home key in anticipation of the 3rd entry.
Technically, in passages in only 2 parts, we do not have harmony; with the addition of a 3rd note to an interval, or with the addition of a 3rd melodic line to 2 other lines, we have harmony; when there are only 2 notes sounding together, we have an interval, not a chord; when only 2 melodic lines sounding together, the harmony is "implied."
There are several places in this Fugue where it appears that a note a half step below the tonic note of the passage fails to resolve to that tonic note a half step above, when actually, it isn't serving as a leading tone.
The unwary can be lead astray by the term "leading tone."
Usually this term is applied to the 7th scale degree in a major scale or the raised 7th degree in a minor scale: for example, the note C# in a D Major passage or the note G# in an a minor passage.
The note that is just a half step below and away from the tonic can seem to "lead back" to it (in minor keys the 7th degree is raised whenever it needs to function as a leading tone; the natural minor scale has no leading tone at all).
But note this: a note a half step below the tonic isn't always serving as a leading tone; in the key of D Major, for example, we can have a melody descending from D and passing through C# on the way down, either as part of an f# minor harmony or maybe as a dissonant "passing tone," in which case it isn't really functioning as a leading tone.
If that same C# were part of a f# minor chord in the key of D Major, for example, it wouldn't be a leading tone because the f# minor harmony isn't dominant; it's not trying hard to go anywhere in particular and, if it does move, it's more likely to move to the b minor chord rather than the tonic D Major chord.
A true leading tone is a half step away from its destination and is part of a harmony that is headed to that destination.
In other words, we can tell a real leading tone by its harmony, either real harmony such as being part of a dominant 7th chord, or that harmony which is implied by the melody.
In the same way, when the 7th scale degree appears in a moving line, let's say the bass, underneath the harmony of a tonic chord, it isn't functioning as a leading note because it isn't trying to "get somewhere" as part of a dominant harmony; it's merely part of an animated bass figure (See Lied in B Major Op. 15, bar 31, for an example).
If the 7th scale degree appears in an outer voice (soprano or bass) where it's most noticeable, it's functioning as a leading note, and it fails to rise to the tonic note, this is called a "frustrated leading tone."
According to the general rules of part writing, frustrated leading tones are prohibited except when they appear in an inner voice (alto or tenor), where they're allowed.
Returning to the 3rd entry, following this episode the 3rd voice then enters with the subject in the soprano as the alto continues with the 1st countersubject and another line (what will become the 2nd countersubject) enters in the tenor.
The 4th voice is last to enter with the subject in the bass in the dominant key with the additional voice occupying the tenor line, the 1st countersubject entering in the soprano, and the 2nd countersubject entering in the alto, in regular order; because this additional 4th voice is retained in each subsequent entry, it becomes a 3rd countersubject; if all 4 independent moving lines appear in the bass at least once in the course of the fugue, the writing is in "quadruple counterpoint."
Notice here that, in this fugue, the 2nd countersubject never enters in the soprano; this is to illustrate that a countersubject does not have to appear in every voice, however, to have quadruple counterpoint; what IS required, is that the subject and each countersubject enter in the bass at least once.
Two adjacent moving voices may form a unison momentarily, but to keep them from crossing sometimes one or more adjacent notes must be shifted an octave higher or lower on the staff; such an action is never applied to the subject, however, as this would do violence to its melodic outline and alter its character.
The exposition here undergoes a deceptive cadence to b minor and then quickly from there to the relative minor (e minor) key; this is followed by a 4-bar episode where the texture reduces to 2 parts and the music is bent back to the back to the tonic key for the counterexposition.
NOTE: A counterexposition in a fugue is a 2nd exposition, however, there are only 2 entries, and they occur in different order; the counterexposition is separated from the exposition by an episode and is in the same key as the original exposition.
So, here, the subject, still in the home key, enters in the bass with the 1st countersubject appearing in the soprano in a 2-part texture; halfway through this entry the 3rd countersubject enters enters in the tenor to create a 3-part texture; the music then shifts to the dominant key where the subject enters again in the alto, the 1st countersubject moves to the soprano, and the 2nd and countersubjects move to the tenor the bass, respectively; this counterexposition then concludes in the home key by means of a full cadence.
In the examples of fugue counterexpositions left to us by J.S. Bach the texture does not abruptly thin down to just one voice with an abrupt falling off of energy level only to build up all over again, one voice at a time; instead he presents the subject along with at least one other moving line (very often ALL of them) to maintain the energy level of the music and avoid robbing it of the richness of chordal harmony initially delivered to the listener by the exposition proper.
The purpose for inserting this counterexposition was 2-fold: a) to present the subject with the 1st and 3rd countersubjects in a 3-part texture without the 2nd countersubject taking part, and b) to create the effect of just the 2 outer voices sounding and gradually merging this into a 4-part texture.
After this, the music modulates back to the relative key (e minor) via a short episode; in this e minor entry the subject enters in the tenor, the 1st countersubject remains in the soprano, the 2nd countersubject enters in the bass, and the 3rd countersubject enters in the alto.
Le us stop right here and take note of something very instructive:
Here, in the minor key, some important decisions are needed to get the countersubjects all to sound in consonant harmony with the subject, as the subject should govern any chromatic inflections needed in the other moving lines, not the other way around; so, in the score the ascending moving lines of the 2nd and 3rd countersubjects were adjusted to follow the harmonic minor scale rather than the melodic minor, and the descending moving line line of the 1st countersubject follows the melodic minor scale in one place and the natural minor in another.
This entry is followed by another 4 bar episode which modulates to b minor, the dominant of the relative key.
In this entry the subject return to the alto, the 1st countersubject in the tenor, the 2nd countersubject in the soprano, and the 3rd countersubject in the bass; again, the same chromatic inflections needed in the minor key are applied here.
Another 4 bar episode modulates from this key around the Circle to the subdominant key (C Major), where in this entry the subject enters in the bass, the 1st countersubject in the soprano, the 2nd countersubject in the alto, and the 3rd countersubject in the tenor.
Another modulating episode of 4 bars brings about a shift to the subdominant relative key (a minor) as the music undergoes a crescendo.
In this entry the subject enters in the soprano, the 1st countersubject in the bass, the 2nd countersubject in the tenor, and the 3rd countersubject in the alto.
After this entry cadences in the submediant major key (E Major) another 4 bar episode brings about a return of the home key in preparation for the reentry of the subject in stretto.
Here the music undergoes a decrescendo as the texture unravels to 2 voices which gradually build in stretto to 5 voices, all over a subdominant pedal point on low C.
The 5th voice added in this stretto section is a low tenor (baritone) -- here the subject enters in the bass and is imitated 2 bars later in the tenor, then 2 bars later in the soprano, in pyramid fashion; while these imitations are going on a free counterpoint based upon the "head" of the 1st countersubject is intertwined with them to keep at least 2 lines always sounding at the same time.
The subdominant pedal point (held low C in the pedals) begins on the 6th bar of this stretto section as the tonality in the hands shifts to C Major; halfway through this stretto section the music modulates back to the home key, still over a held low C in the pedal.
The last bar of this stretto section shares itself with the 1st bar of an additional 5 bar section where the subject is inverted in the tenor line at the same time that the 1st countersubject is reiterated in the soprano.
A short coda built upon the melodic curve of the subject brings the work to a close with a crescendo leading into a momentary pause on a big held diminished 7th penultimate chord; the final chord has an added 6th and double pedal, and the work ends in 7 voices with the full power of the instrument.
By saving the subdominant key for the closing section it helps to reestablish the balance of tonalities and reaffirms the original key.
(con't in Part XX)