Preface

The "Face to Face Duet" in which two performers read the same sheet of music in opposite directions, is, tecnically speaking, a retrograd inverse canon transposed to the proper key. Although Bach composed a large number of canons, none of them were of this specific type. The only example we are aware of is a duet by Mozart for two violins, presented here as edited and abridged by Livingston Gearhart.

This presentation of the Mozart Face to Face Canon
                   (with the clefs and key signatures at both ends of each line)
         is what is called the "Enigma" from which the two performers read the work.
It is evidently quite difficult to acurately assess the result of the canon from this disposition.
For this reason, we will present most of our examples in the "score" form
                   (with the retrograde line, written in its forward direction, below the first line, the original Enigma)
         and see what we call the "Upside" and the "Downside" at the same time.

Theory

Since Face to Face Canons are both Retrograde (in Time) and Inverse (in Pitch), the all-important aspect of Pivots will be equally important in the Rhythm of the Canon, on one hand, as well as in the Harmony and Melody of the Canon, on the other.

Pivots

The Melo-rhythmic aspects of Face to Face Canons
will be the same whatever pivot is used
for the Melo-harmony and for the Melo-lines.

In Time

In Each Bar
Rhythmic Pivots will exist at different levels of the Canon,
         from the largest level in the very center, around which all must be symmetrical,
                   possibly to intermediate levels in the center of sections,
                             and even to individual bars, which will ensure the same result backward as well as forward,
                                       and which is strongly recommended for the beginner.
                   This is quite similar to starting the Footsies at the smallest possible level.

Bars of 4/4 -
         left intact, with 1 note -
                   would evidently be a , ,
         divided into 2 notes -
                   would evidently be 2 , ,
         divided into 3 notes -
                   would normally be 2 with a between them, ,
                   or possibly 2 tied to the extreme s, __,
                             (a syncopated Latin Melo-rhythm, written with ties because dots are not "retrogradable")
         divided into 4 notes -
                   would normally be 4 s, ,
                   or possibly 2 s tied to the extreme s with 2 other s in the middle, _ _,
                             (the "dot-snap" Melo-rhythm of Comin' Through the Rye)
         divided into 5 notes -
                   could be 2 s on each side of a , ,
                   or 4 s in the middlle of 2 s with the 2 middle s tied, _,
                             (another favorite syncopated Latin Melo-rhythm, also used in the Frailach)
                                       It is preferable not to write the 2 tied s as a syncopated
                                                 to avoid the individual flags of the other 2 s which are not as "retrogradable" as the beams.
                   or possibly 3 s in the middlle of 2 s
                             all syncopated, Latin style (the individual flags are inevitable),
         divided into 6 notes -
                   could be 2 s on each side of 2 s, ,
                   or a on each side of 4 s, ,
         divided into 7 notes -
                   would be 8 s with the middle 2 tied, _.
         More complex Melo-rhythmic patterns could be devised using s (See 3/4).

Bars of 3/4 -
         left intact, with 1 note -
                   would evidently be 3 tied s, __ (remember that dots are not retrogradable),
         divided into 2 notes -
                   would evidently be 2 s in the middle tied to the outside s, __,
         divided into 3 notes -
                   would evidently be 3 s, ,
         divided into 4 notes -
                   would be 2 s between 2 s, ,
                   or possibly 2 s between 2 s, ,
                             all syncopated, Latin style (the individual beams are inevitable),
         divided into 5 notes -
                   could normally be 2 s on each side of a , ,
                   or possibly a on each side of 2 with an between them, .
         We will certainly find other symmetrical possibilities as we go along.

At Larger Levels
We will examine the rhythmic pivots of larger levels
         as we proceed in the practice of writing these Face to Face Canons.

In Pitch

1. TONIC Frame as Pivot

Melo-harmony - Chord Patterns
With the FRAME of the TONIC chord acting as Pivot,
                   this TONIC chord evidently corresponds to itself, and
         the DOMINANT and COUNTER(dominant) chords, on each side of the TONIC,
                   correspond to each other.

The most natural Melo-harmonic chord pattern will obviously be the 74pattern,
         shown here in Diatonic Major, but also possible in the 4 Strong Modes.
NOTE the symmetry between
         the COUNTER (below the TONIC line) and
         the DOMINANT (above the TONIC line).
The most basic Melo-line on this pattern would be the 1-1 Orbit line,
         the notes A,G at the end, on the 4 pattern, and
         the notes D, C at the beginning, on the 7 pattern,
                   producing the Melo-line D, C, A, G, consisting uniquely of Orbit 1.

If we add the missing, central, note B in this D, C, A, G Melo-line,
                   we have the D, C, B, A, G line (which we affectionately call "the winner"),
         and the "cadential 64 chord" would normally be placed on the new note B,
                   producing the 64 chord pattern on the last 4 notes.

The rhythmic symmetry of this 64 chord pattern will be achieved
         by shortening the final TONIC chord and
         placing the second half as a pick-up at the beginning (shown here in black),
                   (TONIC for a , COUNTER for a , TONIC for a , DOMINANT for a , and TONIC for a ),
                             with the "cadential 64 chord" in the center.
         Remember that the 74 chord pattern consists of
                   (TONIC for a , COUNTER for a , DOMINANT for a , and TONIC for a ).
         We will see how useful both of these patterns can be when creating Melo-lines.

Melo-lines - Clefs and Keys
With the FRAME of the TONIC chord placed in the center,
         the MEDIAN of the TONIC chord will be placed on the center line of the staff -
                   the note B in Treble Clef, placing us in the Key of G (major or minor),
                   the note D in Bass Clef, placing us in the Key of B or Bb (major or minor),
                   the note G in C Clef first line, placing us in the Key of E or Eb (major or minor),
                   the note E in C Clef second line, placing us in the Key of C (major or minor),
                   the note C in C Clef third line, placing us in the Key of A (major or minor),
                   the note A in C Clef fourth line, placing us in the Key of F or F# (major or minor),
                   the note F in C Clef fifth line, placing us in the Key of D (major or minor).
         We have listed the 7 possibilities
                   despite the fact that few of the C Clefs are still in use.
         In Practice, we will see that the Retrograde (Downside)
                   need not necessarily be in the same Clef as the Forward (Upside),
                             and the mean between the two acts as pivot for the canon.
                   Example - with Treble Clef at one end of each line (center B), and Bass Clef at the other (center D),
                             the note C (as in the C Clef third line) would act as melodic pivot.
NOTE that the choice of Clef(s) (and Key) in no way affects the Chord Pattern of the Harmonic Symmetry,
         which is determined solely by the Harmonic Pivot, in this case the TONIC FRAME.

We have here 3 examples -
                   the first a descending scale from D to G (our "winner"),
                   the second a descending arpeggio through the COUNTER and DOMINANT triads, and
                   the third an ascending scale from D to G which covers the whole staff.
         These 3 examples sound exactly the same in both voices (directions), producing unison passages
                   (the Upside and the Downside being identical).
         The first 4 notes of the third example (as well as the last 4 notes, in each case, D, E, F#, G)
                   would have the Downside at the octave of the Upside, on each side of the center of the staff,
                             as we will later see.
These examples are written in the simplest possible note-values, all .
         More complex and interesting Melo-rhythm could eventually be contrived.

2. TONIC-DOMINANT Swing as Pivot

3. DOMINANT Frame as Pivot

4. DOMINANT-ANTE-1 Swing as Pivot

Pitch Specifics

The following variables of Modes, Intervals, and Counter-melodies,
         evidently apply only to Pitch and not to Time.

Modes

Diatonic Major
As we did in the Harmony Volume, all examples are given in the Diatonic Major Mode.
         They can subsequently be tranformed into the other Strong Modes.

Diatonic Minor
Transposition from Diatonic Major to Diatonic Minor is simply one of Inversion
         around the melodic Pivot of the canon.

We have here the 3 examples presented in the "Tonic Frame as Pivot", with
         the Key Signature changed to Gm (2 flats), and
         all the notes inverted around the center of the Treble Clef staff (the note B, in this case Bb).
All previous comments (in the Diatonic Major Mode) also apply here.

Chromatic Minor
If we compare the Diatonic Major and Chromatic Minor modes,
                   in this situation using the convenient Keys of G major and G minor,
         we see that -
                   the nucleusFRAME notes, C, G, D, A, are common to both keys, but that
                   the MEDIANs are divided -
                             Eb (of the COUNTER) and Bb (of the TONIC) are in the Key of G minor, and
                             F# (of the DOMINANT)) and B (of the dominantized TONIC) are in the Key of G major.
                   The dominantized TONIC at the beginning of the m74 pattern is obligatory
                             to preserve the harmonic symmetry of major, minor, major, minor (G, Cm, D, Gm).
The main task here will be to "spread the MEDIANs around" between the 2 lines.

The second example presented in "Tonic Frame as Pivot" could easily be transposed to Chromatic Minor
         by cutting the phrase in 2 and giving each player half of it.
                   This is achieved by simply placing rests at the end -
                             The Upside (Gm) player plays the first half (with the Eb) while the other player counts rests,
                             the Downside (G) player plays the second half (with the F#), and
                             they both play the 2 notes in the middle (C and A) for rhythmic stability.

It is also possible to write complete, independant Melo-lines
         by placing the MEDIANs first (here in s) -
                   Eb and Bb in the Upside (Gm) line (in bars 2 and 4), and
                   B and F# in the Downside (G) line (in bars 1 and 3).
                             NOTE that the B and the Bb conveniently correspond to each other (as do the Eb and the F#) .
         The 2 FRAME notes of each chord will now be placed (in s) in the appropriate available spots,
                   in such a way as to always surround each MEDIAN by conjunct motion with PROPER TONEs
                                       (a D on each side of the Eb, and a G on each side of the F#)
                             to assure Retrograde resolution.
NOTE that we are encroaching on the concept of Counter-melody which we will see shortly.

Chromatic Major
Transposition from Chromatic Minor to Chromatic Major is also one of Inversion
                   around the melodic Pivot of the canon, as it was for the Diatonic Modes.
         The Upside line will now be in G major (1 sharp), and
         the Downside line will now be in G minor (2 flats).
         The Downside line is now higher than the Upside line.

Here is the first example, with the 2 lines sharing the melody.

Here is the second example with complete, independant Melo-lines.

Intervals

Unisons - Octaves
The 3 examples presented in the Tonic Frame as Pivot,
         all produced unisons, because they were all symmetrical around the center of the staff.
In this specific form of Pivot, the Tonic Frame (in this case, a fifth from D down to G) is right in the center
         but the "Inter-Frame" (a fourth from D up to G) is off-center and
                   by itself, produces octaves.

We have here, in the Upside, the four notes D, E, F#, G in the lower half of the staff, and
         they will be answered, in the Downside, by the same four notes in the upper half of the staff,
                   an octave higher.

Thirds - Sixths
To produce thirds, we must shift the Pivot of the Upside from the central B to the neighboring C,
         thus shifting the Pivot of the Downside to the corresponding A,
                   and automatically (almost magically) producing thirds.

We have here (in the complete central bar of the Upside) the five notes E, D, C, B, A, centered on the C,
         which will be answered in the Downside by the notes C, B, A, G, F#, centered on the A,
                   a third lower than the original Upside.

Counter-melodies

To produce canonic counter-melodies, we must place them end-to-end,
                   (either on the same line, or on 2 different lines)
         and they will automatically sound together..

We have here (in the Upside) -
         first the notes D, E, F#, G,
                   which we already saw in the example on octaves,
         followed by notes B, C, A, B,
                   which not only answer at the unison,
                   but also act as a suitable Counter-melody to the original Melody.
The Downside will
         first present the Counter-melody (while the original Melody is in the Upside),
         then the original Melody, an octave higher, (while the Counter-melody is in the Upside).
Both the original Melody and the Counter-melody are presented here on the same line,
         but it would be necessary to place them on individual lines
                   if we wanted to insert additional material between them.
NOTE that this is not exactly the same process as the one we had in Chromatic Minor,
         where the Counter-melody evolved directly, almost miraculously, from the original Melody.

Practice

Exercise 1
Pivot 1, only 1 Line, Unisons and Octaves,
in the 2 Diatonic Modes, in Treble and Bass Clefs

Let's start with somerthing simple.

Exercise 2
Pivot 1, only 1 Line in canon, Unisons and Octaves,
in the 2 Diatonic Modes, in Treble and Bass Clefs

This shouldn't be too difficult either.

Exercise 3
Pivot 1, only 1 Line in 2 canons, Unisons and Octaves,
in the 4 Modes, in Treble and Bass Clefs

Let's see if we can arrange the 2 preceding Round-Face Canons to make a complete 4-part canon.
         They are both part of the Natural Canon Swing with Voice-leading A.
In the Intra-frame Winner we have the Soprano and Tenor Voices, at the same octave,
                   with the G at the end a Substitution of Orbit 0 by Orbit 1, and
         in the Inter-frame we have the Alto and Bass Voices, in the required octaves.
                             More on this later (In 5.).