Introduction

         The fugue is a contrapuntal work, consisting of several simultaneous Orbit Melo-lines, and performed by the same number of Voices. Its principal melodic motif, the "Subject", is first presented alone in the first line and then accompanied by its counter-melodic motif, the "Counter-subject", (also in the first line) when it reappears in the second line.

         The fugue is traditionally taught as a melodic structure, its harmonic structure not being planned but the result of the simultaneous melodic lines, and its rhythmic structure not being planned either but the result of a pasting of the various sections of the work.

A new approach is proposed here.

The 4-part Fugue (with 4 Lines performed by 4 Voices) will be considered the Basic Fugue structure,
                   the 3-part Fugue being considered a reduction of the basic 4-part Fugue.
         The large level rhythmical structure
                   is conceived first in its most natural form.
         The harmonic structure, in this case the chord patterns
                             appropriate to the different sections (Expositions and Divertimenti),
                   is placed in the rhythmic framework.
         Finally, the melodic motifs (Subject, Counter-subject, and free motifs)
                   evolve from this harmonic-rhythmic base.
This procedure guarantees a simple, solid, regular rhythmic structure,
         with natural and pleasant harmonies,
                   as well as melodic lines which respect Orbit Voice-leading.
With this method, a student can compose short simple fugues at the very first class.
         Complexity and size will come later.
In this new approach, we will respect the greatest possible number of traditions,
         unless logic dictates a simpler and more natural path.
The writing in this course will use the four orbit lines,
         with the F undamental Bass only at cadences.

Form

The largest rhythmical levels
         The fugue is essentially an alternation of large-level canons (called "Expositions", which act as a kind of chorus because they reappear relatively unchanged) and small-level canons (called "Divertimenti" which act as verses because they constantly change their appearance). The first Exposition consists of a presentation of the Subject in each line. As the fugues in this course will be fundamentally in 4 Lines (eventually presented in the 4 vocal Voices, Soprano, Alto, Tenor, Bass), the first Exposition will consist of 4 presentations of the Subject. If each presentation is represented by the letter "A", the first Exposition will have the form AAAA. The other Expositions will be shorter, of the simplest length AA. Between Expositions AAAA and AA, the Divertimento (represented by the letter "B") will have the ideal length of BB, the same length as Exposition AA. This alternation of BBAA will continue for the rest of the fugue. We will see fugues of 2 sections (AAAA BBAA), 3 sections (AAAA, BBAA, BBAA), 4 sections (AAAA, BBAA, BBAA, BBAA), and 6 sections (AAAA, BBAA, BBAA, BBAA, BBAA, BBAA). In the 3-section Fugue, the opening AAAA will be a consequent, but in all the others it will be an antecedent.

Expositions

Structure of the Fugue-lines
The fugue's first Exposition (AAAA) presents the Subject successively in each Fugue-line.
After having presented the Subject ("S"),
         each Line (except Line 4) presents the Counter-subject ("CS")
                             on a different Orbit-line from that of the Subject,
                   which serves as counter-melody to the Subject.
         There is no Counter-subject at the beginning of the AAAA,
                   but there will be one at the beginning of each AA.
Lines 1 and 3 (as well as lines 2 and 4) will be placed in corresponding Choral Voices,
                   (low, Alto and Bass, or high, Soprano and Tenor)
         and will present the same Subject and Counter-subject
                   which are thus numbered "1" or "2".
After having presented the Subject and the Counter-subject,
         a Fugue-line is melodically free (indicated "X")
                   and can choose from the remaining Orbit-lines of the Harmony.
         Only Lines 1 and 2 have the available space for these "X"s.

Disposition in the Voices
The Fugue-lines will eventually be disposed in the Choral Voices - Soprano, Alto, Tenor, Bass.
         The first entry may be made by any voice,
                   but the other entries must follow a "circular path",
                             either in one direction or in the other,
                                       (clockwise or counter-clockwise)
                             alternating high (Soprano and Tenor) and low (Alto and Bass) Voices.
         Example - If Line 1 is in the Tenor Voice,
                   Line 2 may be in either the Bass Voice or in the Alto Voice,
                   Line 3 will be in the Soprano Voice, and
                   Line 4 in the remaining voice (Bass or Alto).

Chord Patterns
Providentially, the M34 chord pattern,
                   the Basic Materials of Melo-harmony,
         answers most eloquently the exigencies of the classical fugue -
                   that TONIC be anwered by DOMINANT, and DOMINANT by TONIC.
         The chord progression M3, TONIC-DOMINANT (the antecedent),
                   which would be used for the S1 (and the CS1), would be answered by
         the chord progression M4, DOMINANT-TONIC (the consequent),
                   which would be used for the S2 (and the CS2).

Traditionally, the exigency that TONIC be answered by DOMINANT, and DOMINANT by TONIC,
                   was applied on a melodic level,
         but we will apply it on a harmonic level, which is far more fundamental.

There will evidently be more complex and interesting patterns available as we progress,
         but the M34 will be our point of departure.

Fugue-lines
In any chord pattern, we will always find the 4 Orbit Fugue-lines : 3-2, 2-1, 1-1, 0-0,
         and we will consider them in this order of decreasing tension,
                   when making choices of a polyphonic, contrapuntal nature.
Each of these lines can be used as a Subject.
The Counter-subject will preferably use the 3-2 line,
         if it has not been used by the Subject,
                   in which case, it will use the 2-1 line.
The "X" sections will use the lines left over (possibly the F undamental Bass for cadences).

Divertimenti

Chord Patterns
Contrary to the Exposition which basically uses the Swing M34 chord pattern
         so fundamental to Melody itself,
the Divertimento will basically use the Circle (or half-circle) chord pattern,
         so fundamental to the development of Melody.
These Circles (or half-circles) may end on either the DOMINANT or the TONIC,
         depending on the nature of a possible Pick-up,
                   or possibly of the chord pattern itself, like the M64
                             which starts on the COUNTER(DOMINANT) chord.

Fugue-lines
These Divertimento Circles (or half-circles) will produce natural canons,
                   using the different Orbit chains -
         3-2, for a 2-part canon, with Voice-leading C,
         3-2-10 for a 3-part canon, with Voice-leading A,
         10(3)-2-10-01 for a 4-part canon, with Voice-leading B (without the "V" jump).

Disposition in the Voices
The Divertimento lines must be placed so as to tie in with the following Exposition,
         there being a breath between the preceding Exposition and the Divertimento.
                   This process of disposition will be detailed in each "class lesson".

To Class 1