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Specifics
Form AAAA BBAA - Chord Pattern M34 - Subject line 3-2 - Counter-subject line 2-1
The length of the Subject being 2 bars, at Level -1, Chord Pattern M3,
the Exposition AAAA will be 8 bars, Chord Pattern M3434,
the Divertimento BB will be 4 bars, Chord Pattern M4s1,
a half-circle, ending on the DOMINANT, and
the Exposition AA will also be 4 bars, Chord Pattern M34.
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The complete fugue will be 16 bars long.
The Expositions
The Fugue-lines
Since the S1 and the S2 are placed on harmonies which resolve in opposite directions,
the S1 on the TONIC / DOMINANT progression and
the S2 on the DOMINANT / TONIC progression,
it is normal and logical that the Fugue-lines will also be in opposite directions,
symmetrically disposed around the COMMON TONE, Orbit 0 (the note G).
NOTE that each Orbit 3 has been replaced by 0(3), 3
to facilitate the entrance by attacking on a more fundamental note, the COMMON TONE, and
to "improve" the Sonorities between the Subject and the Counter-subject (see below).
In each Fugue-line (except the last), a CS2 will follow the S1, or a CS1 will follow the S2.
The same symmetry will exist between CS1 and CS2 as between S1 and S2.
The fill sections ("X" in lines 1 and 2) will offer the choice between the remaining Orbit lines,
in this case, 1-1 and 0-0,
with advantageous use of the Fundamental Bass for cadences.
Decisions will be taken in the Choral Dispositions.
Sonorities
When only 2 Lines are heard
(at the second A of an Exposition AAAA and in a 2-part Divertimento),
one should take care of the Sonorities between them.
Since this question of Sonorities pertains to cultural habit and usage
far more than to technical structure,
we will use the classical, academic norms as our starting point.
The first choice will be the triadic Sonority of the third (sixth),
major or minor.
We will then eventually progress to both
more pure, fundamental sonorites (octave and fifth), as well to the
more discordant, pungent sonorities of the second (seventh), major or minor.
In the Subject of this fugue, Orbit 3 is replaced by 0(3), 3
not only to facilitate its entry,
but also to produce the triadic Sonority of the third (sixth)
with Orbit 2 of the Counter-subject.
The Choral Dispositions The last Exposition (AA)
The last Exposition, being a consequent, must come to a full close (cadence),
for which 2 criteria must apply -
1. the Bass Voice must have the Fundamental Bass, and
2. the Soprano Voice must have the 1-1 Orbit line,
thus placing the static fundamental harmonic Primary Notes of the FRAME
exposed in the outer voices (S and B) and
the kinetic polyphonic Secondary Notes (3-2 and 2-1)
concealed in the inner voices (A and T).
In this case, which Fugue-lines meet these criteria ?
- only lines 1 and 2 could offer the FB, and
- only lines 1 and 2 could offer the 1-1 Orbit line in the Soprano.
We have 2 possible dispositions with lines 1 and 2 alternating in the outer voices,
with the preceding Divertimento BB between these two voices.
The first disposition -
If Fugue-line 1 is placed in the Bass Voice, with the FB for the last 2 cells (in XX),
Fugue-line 2, with its 1-1 Orbit line option (in X), must be in the Soprano Voice,
Fugue-line 3, in the same direction as Fugue-line 1, must be in the Alto Voice,
Fugue-line 4 in the Tenor Voice,
entries in descending, clockwise order.
Placing this in the Key of F, gives us a good Choral Disposition.
The first Exposition (AAAA) of this disposition will be seen later.
The second disposition -
If Fugue-line 2 is placed in the Bass Voice, with the FB for the last cell (in X),
Fugue-line 1, with its 1-1 Orbit line option (in X), must be in the Soprano Voice,
Fugue-line 4, in the same direction as Fugue-line 2, must be in the Alto Voice,
Fugue-line 3 in the Tenor Voice,
entries in ascending, counter-clockwise order.
Placing this in the Key of C, gives us a good Choral Disposition.
The first Exposition (AAAA) of this disposition will also be seen later.
NOTE -
Only the second half of the last Exposition will be used,
because it is only an AA,
the first AA being replaced by the BB, in the outer voices.
The first Exposition (AAAA)
To avoid the full close (cadence) in the first Exposition, an antecedent,
and remain in the same key, with the same range of voices,
one must invert -
1. the high Voices (Soprano and Tenor) and
2. the low Voices (Alto and Bass)
The kinetic polyphonic Secondary Notes (3-2 and 2-1)
are now exposed in the outer voices (S and B) and
the static fundamental harmonic Primary Notes of the FRAME (without the FB)
are now concealed in the inner voices (A and T).
The first disposition, in F
NOTE the choice of Orbit-lines for the "X"s -
in the Alto Voice, at the first "X", it is preferable to choose the 0-0-0-0 line,
and avoid FRAME Inversion
(by not hearing the root above the fifth in the Bass Voice entrance).
in the Tenor Voice, one places the only Orbit-line left, 1-1.
The second disposition, in C
NOTE the choice of Orbit-line for the "X" in the Alto Voice,
one places the only Orbit-line left, 0-0.
Ornaments
The use of repeated notes (subdivision of the  ) adds interest to the important elements
(especially the Subject and the Counter-subject).
Since the Subject is already subdivided (in  s),
it would be interesting to subdivide the Counter-subject (in  s).
One could find simple, explanatory words to fit this Melo-rhythm, such as -
for the Subject : "Subject first,"
for the Counter-subject : "Counter-subject next,"
for the first "X" : "Fill in"
for the second "X" : "the rest."
for the solitary "X" : "Fill in the rest.",
in shorter note values.
The Divertimento
The Fugue-lines
We could use either the Subject or the Counter-subject as a motif for this canon
on the half circle - ANTE-3 / ANTE-2 \ ANTE-1 / DOMINANT,
with the ANTE-1 dominantized (possibly also the ANTE-3).
We will limit ourselves, for now, to a 2-part canon,
using the Orbit Chain 3-2 (or 2-3) and Voice-leading C.
The Subject as canon motif -
In the Key of C, using S2 as motif, with the words "Subject first,"
the canon starts in Fugue-line 1 with 0(3), 3-2 on the Ante-3, (E)D-C
and is answered in Fugue-line 2, also with 0(3), 3-2 on the Ante-2, (A)G-F#.
At the end of the Divertimento, we see (in parentheses) the resolutions,
which we will need to tie in the lines of this Divertimento with the next (and last) AA.
Fugue-line 1 resolving to Orbit 1 ties in with an "X", and
Fugue-line 2 resolving to Orbit 2 ties in with CS1.
The Counter-subject as canon motif -
In the Key of F, using CS2 as motif, with the words "Counter-subject next."
the canon starts in Fugue-line 1 with 2-10(3) on the Ante-3, C-D(C)
and is answered in Fugue-line 2, also with 2-10(3) on the Ante-2, F-G(F).
NOTE that the CS2 is subdivided into s as suggested in the "Ornaments".
At the end of the Divertimento, we see (in parentheses) the resolutions,
which we will need to tie in the lines of this Divertimento with the next (and last) AA.
Fugue-line 1 resolving to Orbit 2 ties in with CS1, and
Fugue-line 2 resolving to Orbit 1 ties in with an "X".
The Complete Fugue
General Instructions
For either of the 2 dispositions, the one in F or the one in C,
1. Place the Expositions -
The AAAA at the beginning, and the AA at the end (leaving 4 bars empty for the BB).
2. Insert the BB Divertimento in the 2 Voices which do not present the Subject in the AA,
making sure that the resolutions at the end of the Divertimento,
tie in perfectly with the lines at the beginning of the AA.
3. It is elegant to have some voice tie in the AAAA with the BB,
preferably one of the Voices performing in the BB,
but possibly one of the other 2 voices
which would rebound after the AAAA.
4. There will be adjustments required in the words at a few places.
The fugue in F - Version 1 with a Counter-subject canon
The first Exposition AAAA is the inversion of version 1 of the last disposition.
The last Exposition AA is the second half of version 1 of the last disposition.
NOTE (in the Soprano Voice) the subdivision in s
to place the words of the 2 "X"s into 1 "X".
The 2 Divertimento Counter-subject lines have been disposed
in the Soprano and Bass Voices,
replacing the 2 first entries in the original version 1 of the last disposition,
to tie in to the second half of version 1 of the last Exposition,
Fugue-line 1 tying in to the CS1 in the Soprano Voice, and
Fugue-line 2 tying in to the 2 "X"s the Bass Voice.
NOTE, in the Tenor Voice,
a rebound from the preceding AAAA Exposition, with the words "the rest",
NOTE, in the Bass Voice,
the word "next" is shortened (to a ) to fit in the word "Fill" of the 2 "X"s.
The fugue in C - Version 2 with a Subject canon
The first Exposition AAAA is the inversion of version 2 of the last disposition.
NOTE (in the Alto Voice) the subdivision in s to place the words of the 2 "X"s into 1 "X".
The last Exposition AA is the first half of version 2 of the last disposition.
NOTE (in the Bass Voice) the subdivision in s to place the words of the 2 "X"s into 1 "X".
The 2 Divertimento Subject lines have been disposed in the Soprano and Bass Voices,
replacing the 2 first entries in the original version 2 of the last disposition,
to tie in to the second half of version 2 of the last Exposition,
Fugue-line 1 tying in to the 2 "X"s in the Soprano Voice, and
Fugue-line 2 tying in to the CS1 the Bass Voice.
NOTE, in the Bass Voice,
the added note at the beginning of the Divertimento with the word "The",
the word "first" missing in Bar 4 of the Divertimento for lack of space.
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Exercise
Write your own fugue
Keeping the same Specifics-
Form AAAA BBAA,
Chord Pattern M34, for the AAAA
with a half circle to the DOMINANT for the BB, M4s1
Subject line 3-2, and
Counter-subject line 2-1,
but freely choosing-
disposition 1 or disposition 2 of the last Exposition,
the Subject or the Counter-subject, as motif, for the canon of the Divertimento,
and freely changing-
the Melo-rhythm time signature (6/8, 3/4 ... at Level -1)
the Substitution "formula" for the Subject,
the repeated note "formula" for the Counter-subject,
the words (or possibly scat singing) for the Subject, the Counter-subject, and the "X"s.
Check each Voice carefully (Soprano, Alto, Tenor, and Bass) from beginning to end,
making sure that the melodic movements are easy and natural, and
that the words are coherent.
Correction is in the performance -
Get some friends together, at least 4, preferably 8 (for a double quartet),
and evaluate the results -
1. How quickly, and easily, was it performed ?
2. How did the performers evaluate it, both singing it and hearing it ?
3. What did you, the composer, think of it ?
Don't spend too much time correcting it, move on to the next one.
All the performers should ideally be writing their own fugues.
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On to Class 2
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