|
In the serious, sedate, forlorn field of Music Theory, it will probably seem unforgivably misplaced to inject a touch of humor,
especially if it has the slightest erotic connotation. If this lapse into frivolity seems unduly offensive, it will immediately
be retracted and removed.
Sextending the Basic Orbit Chain
The birth of Natural Canons is to be found in the 3-2-1-0 Orbit Chain,
resulting from the use of Voice-Leading A,
which evidently produces a 4-voice canon, usually presented as
0-3-2-1, so as to end on Orbit 1.
However, in the DOMINANT/TONIC resolution in the Diatonic Major Mode,
we had found 2 other Voice-Leading Lines, as we resolved fron Tetrad to Triad of rest,
1-1 (PROPER TONE to PROPER TONE), and 0-0 (COMMON TONE to COMMON TONE),
which can be incorporated into our original 3-2-1-0 line,
extending it into a 6-voice Orbit line composed of 3-2-1-1-0-0,
suggesting our choice of title.
For the most appropriate canonic entries, the orbit chain has been set to
1-0-0-3-2-1, so as to start, and end, on Orbit 1.
Performance
The examples have been scored for a 6-voice choir, composed of -
Soprano 1 and Soprano 2 (S1, S2) in treble clef on the first staff,
Alto (A) in treble clef on the second staff,
Tenor (T) in bass clef on the third staff, and
Bass 1 and Bass 2 (B1, B2) in bass clef on the fourth staff.
Swing Examples
These swing examples are all on the chromatic swing (with chords Fm6 and C7)
but could just as well be on any other swing.
Basic Canon
The canonic entries (B2, S1, T, B1, S2, A) were chosen
to produce the most satisfactory disposition for the final cadence, with -
S1 and S2 sharing the top octave,
A and T sharing the central octave, and
B1 and B2 sharing the bottom octave,
B2, T, and S2 using the lower section of each octave, which rises and descends,
alternating entries with
B1, A, and S1 using the higher section of each octave, which descends and rises.
The 4-part canon required a 2 octave range
and this 6-part canon requires a 3 octave range.
The 6 entries occur in bars 1 and 2, and
the complete 6-voice canon evolves in bars 3 and 4.
2 Voices Rising
This example is in 2 voices only, with entries at a 3-note interval,
at the beginning of each 3/4 bar,
evolving from the lower to the upper voices, B2, B1, T, A, S2, S1.
2 Voices Descending
This is the inversion of the preceding example
evolving from the upper to the lower voices, S1, S2, A, T, B1, B2.
2 Voices Tutti
This is a tutti version of the preceding examples,
with B2, T and S2 together, answered by B1, A, S1.
The inverse order would, evidently, also be possible.
Bach Fugue Theme
Using the disposition of the first example,
we see how easily it can be transformed into the subject of Bach's Fugue in Ebm -
by dotting note 2,
by embroidering Orbit 0 with a superior (or inferior) semi-tone on the following  (ighth-note),
by placing a partial () substitution 0(3) by Orbit 0 on note 4 (Orbit 3).
Once this gets going, there will be constant friction on the Off-Beat s,
between B and Bb, and between D and Db,
with impeccable Voice-Leading in both cases.
Inversus
This is the inversion of the previous example.
Once again, the order of the canonic entries was chosen
to achieve the best possible disposition at the final cadence.
Circle Examples
Sextending the Basic Orbit Chain
The operation is not as simple in the Circle as it was in the Swing
because each 1 is transformed into 10
and each 0 is transformed into 01
by Metamorphosis 1,
producing the 6-Voice Orbit Chain 3-2-10-01-01-10,
with the Voice-Leading (3-2), (2-1), (0-0), (1-0), (1-1), and the procuration (0-3),
rather than the original (3-2), (2-1), (1-1), (1-0), (0-0), and the procuration (0-3),
of the Swing.
Basic Lines
Chord Pattern - C+7 - F+7 - Bm7-5 - Em7 - Am7 - Dm7 - G7 - C
The S1 keeps the original 3-2-10-01-01-10 Orbit Line
with 3-2 added at the end to complete the 8-chord circle.
The S2 uses the next 2-10-01-01-10-3 Orbit Line
with 2-10 added at the end.
The A uses the next 10-01-01-10-3-2 Orbit Line
with 10-01 added at the end.
The T uses the next 01-01-10-3-2-10 Orbit Line
with 01-01 added at the end.
The B1 uses the next 01-10-3-2-10-01 Orbit Line
with 01-10 added at the end.
The B2 uses the next 10-3-2-10-01-01 Orbit Line
with, theoretically, 10-3 added at the end,
preferably changed to the Fundamental Bass in order to cadence.
NOTE the striking similarity of this Circle Sextension,
with the 3-voice Circle with Voice-Leading A, Orbit Chain 3-2-10.
In the 3-voice circle, we had
an Orbit Chain of 3-2-10-3-2-10-3-2, with notes B, A, B, D, C, D, F, E.
In the 6-voice circle, we had
an Orbit Chain of 3-2-10-01-01-10-3-2, with notes B, A, B, B, E, D, F, E.
Only the fourth and fifth notes were changed,
but that was enough to produce 3 more canonic lines.
Dominantized
This is the same as the previous example with each chord Dominantized -
on chord 1 with Orbit 3 Bb in the S1,
on chord 2 with Orbit 3 Eb in the B2,
chord 3, the BUCKLE chord, is left diatonic because it already has a Dominant sound,
on chord 4 with Orbit 2 G# in the B1,
on chord 5 with Orbit 2 C# in the T,
on chord 6 with Orbit 2 F# in the A,
chord 7, is left diatonic because it is the original DOMINANT.
NOTE that this process of Dominantization could be applied to
any of these forms of circles, with 2-, 3-, 4-, or 6-voice canons.
These basic lines could be used for various canonic variations,
as was the case with the swing which was previously seen.
|
