(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 score posted on this web site (Op. 6, 10, 11, 13, 18, 19, 20, 21, 22, 23 ) can be cited as an example which explores those boundaries in some kind of unexpected, bold, or even daring way [See menu bar, Free Stuff].
While this is not the kind of music that's likely to disappear and be replaced by something more up to date, 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]:
Fugue subjects in 4/4 (common) time like this one can be regularly 2, 4, 6, or 8 bars in length, but the length of this subject, which occupies an odd number (5) of bars, is irregular in length; it enters first in the tenor voice in the home key and is answered in the alto in the dominant 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 we have an interval, or there are 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 here's the tricky part: 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 free voice occupying the tenor line, the 1st countersubject entering in the soprano, and the 2nd countersubject entering in the alto, in regular order.
To keep the bass and tenor lines from crossing here the bass line is broken and some of its notes are placed an octave lower.
The next entry in the dominant key immediately follows without an intervening episode; here the subject and both countersubjects are inverted with the inverted subject entering in the soprano line, the inverted 1st countersubject in the tenor, and the inverted 2nd countersubject in the bass; a free voice in the alto completes a 4 voice texture.
Here a few notes in the inverted 1st countersubject in the tenor line have to be "tweaked" or changed to avoid creating harsh dissonances with the other moving lines; at the same time a few notes in the free voice in the alto line must be dropped due to inadequate space between the tenor and soprano lines.
This leads to a cadence in the home key and another 4 bar episode which modulates to the relative minor key (e minor).
Here the subject enters right side up in the bass, the 1st countersubject in the soprano, the 2nd countersubject in the tenor, and a free voice in the alto; this is followed by another 4 bar episode in the mediant key which modulates to the dominant relative key (b minor).
In this 4th entry the subject enters surprisingly in the alto line, the 1st countersubject in the tenor, the 2nd countersubject in the bass, and the free voice occupies the all-important soprano line; this leads to a cadence in the key of the leading note (F#).
Another 4 bar episode modules from this key around the Circle to the subdominant key (C Major), where in this 5th entry the subject enters in the bass line, the 1st countersubject in the soprano, the 2nd countersubject in the alto, and the free voice occupies the tenor line.
Another modulating episode of 4 bars brings about a shift to the subdominant relative key (a minor) as the music undergoes a crescendo.
Here in this 6th entry the subject enters in the soprano, the 1st countersubject in the bass, the 2nd countersubject in the tenor, and the free voice in the alto line;
Here the 1st countersubject in the bass line is broken and some of the notes are moved an octave lower to eliminate crossings with the tenor line; this entry ends in a cadence in the submediant major key (E Major).
From here another 4 bar episode brings about a return of the home key in preparation for the reentry of the subject in stretto.
In this episode the energy level drops off as the 2 moving lines descend in range to meet at a unison on tenor G, which serves to bring about a bigger crescendo as the voices "pile up" afterwards in stretto.
This stretto section leading into the coda adds a 5th voice -- a baritone line -- to the harmony; to separate this closing section in 5 voices from the rest of the fugue the score is marked with a double bar line starting at bar 116.
The subject enters in the bass line here 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.
This stretto section employing imitations is 7 bars long and builds one voice at a time to 5 voices.
A long subdominant pedal point (held low C in the pedals) begins on the 6th bar of this stretto section.
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 brings the work to a close in the same 5 voices.
By saving the subdominant key for the closing section of the Fugue it helps to reestablish the balance of tonalities and reaffirms the original key.
After a brief pause on a diminished 7th chord played against the dominant note in the baritone voice, the work closes employing a held dominant 7th chord with flatted 5th in the pedal over the full power of the instrument before resolving.
These kinds of things are what's exciting about writing our own music; it challenges us to think up new ways of using old materials for arriving at where we want to go with it.
(con't in Part XX)