Preface

The "Face to Face Duet" in which two performers read the same sheet of music in opposite directions, is, tecnically speaking, aretrograd inversecanon 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 ourexamplesin 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

TheMelo-rhythmicaspects of Face to Face Canons
will be the same whatever pivot is used
for theMelo-harmonyand for theMelo-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 2with abetween them,,
          or possibly 2tied to the extremes,__,
               (a syncopated Latin Melo-rhythm, written with ties because dots are not "retrogradable")
     divided into 4 notes -
          would normally be 4s,,
          or possibly 2s tied to the extremes with 2 others in the middle,_ _,
               (the "dot-snap" Melo-rhythm ofComin' Through the Rye)
     divided into 5 notes -
          could be 2s on each side of a,,
          or 4s in the middlle of 2s with the 2 middles tied,_,
               (another favorite syncopated Latin Melo-rhythm, also used in theFrailach)
                    It is preferable not to write the 2 tieds as a syncopated
                         to avoid the individual flags of the other 2s which are not as "retrogradable" as the beams.
          or possibly 3s in the middlle of 2s
               all syncopated, Latin style (the individual flags are inevitable),
     divided into 6 notes -
          could be 2s on each side of 2s, ,
          or aon each side of 4s, ,
     divided into 7 notes -
          would be 8s with the middle 2 tied,_.
     More complex Melo-rhythmic patterns could be devised usings (See 3/4).

Bars of 3/4 -
     left intact, with 1 note -
          would evidently be 3 tieds,__(remember that dots are not retrogradable),
     divided into 2 notes -
          would evidently be 2s in the middle tied to the outsides,__,
     divided into 3 notes -
          would evidently be 3s,,
     divided into 4 notes -
          would be 2s between 2s,,
          or possibly 2s between 2s,,
               all syncopated, Latin style (the individual beams are inevitable),
     divided into 5 notes -
          could normally be 2s on each side of a,,
          or possibly aon each side of 2with anbetween 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 thepracticeof writing these Face to Face Canons.

In Pitch

1. TONIC Frame as Pivot

Melo-harmony - Chord Patterns
With theFRAMEof 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 the74 pattern,
     shown here inDiatonic Major, but also possible in the4 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 the1-1Orbit line,
     the notes A,G at the end, on the4pattern, and
     the notes D, C at the beginning, on the7pattern,
          producing the Melo-line D, C, A, G, consisting uniquely ofOrbit 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 the64 chord patternon the last 4 notes.

The rhythmic symmetry of this64chord 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 the74chord 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 theFRAMEof the TONIC chord placed in the center,
     theMEDIANof 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.
     InPractice, 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 TONICFRAME.

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.

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 theHarmonyVolume, all examples are given in theDiatonic MajorMode.
     They can subsequently be tranformed into the otherStrong Modes.

Diatonic Minor
Transposition from Diatonic Major toDiatonic Minoris simply one of Inversion
     around the melodic Pivot of the canon.

We have here the 3examplespresented 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 andChromatic Minormodes,
          in this situation using the convenient Keys ofG majorandG minor,
     we see that -
          thenucleus FRAMEnotes, C, G, D, A, are common to both keys, but that
          theMEDIANs 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 thedominantizedTONIC) are in the Key of G major.
          The dominantized TONIC at the beginning of them74pattern is obligatory
               to preserve the harmonic symmetry ofmajor,minor,major,minor(G, Cm, D, Gm).
The main task here will be to "spread theMEDIANs around" between the 2 lines.

The secondexamplepresented 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 theMEDIANs first (here ins) -
          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 2FRAMEnotes of each chord will now be placed (ins) in the appropriate available spots,
          in such a way as to always surround eachMEDIANby conjunct motion withPROPER 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 ofCounter-melodywhich we will see shortly.

Chromatic Major
Transposition from Chromatic Minor toChromatic Majoris 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 3examplespresented 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) thefivenotes 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 theexample 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 inChromatic 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 theNatural Canon SwingwithVoice-leading A.
In the Intra-frame Winner we have the Soprano and Tenor Voices, at the same octave,
          with the G at the end aSubstitutionofOrbit 0byOrbit 1, and
     in the Inter-frame we have the Alto and Bass Voices, in the required octaves.
               More on this later (In 5.).