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Rounds, otherwise known as "perpetual canons", are no more than the Voice-leading lines of a Melo-harmonic chord pattern. Unfortunately, this has not been the case in their historical development, and a great number of them, including
the much revered but poorly conceived Frère Jacques, do not adequately measure up to this minimal exigency of harmonic structure because they were conceived as being purely
and uniquely melodic. Any of these traditional round canons would be appropriate material for  Analysis.
The M4 Pattern
Let's start by seeing what we can produce with the basic DOMINANT / TONIC pattern
The Orbit Voice-leading Lines are -
Orbit 3/ Orbit 2, the notes F / E,
Orbit 2/ Orbit 1, the notes B / C,
Orbit 1/ Orbit 1, the notes D / C, and
Orbit 0/ Orbit 0, the notes G / G.
Canonic Disposition of the Orbit Lines
These Orbit Voice-leading lines can be distributed in various ways -
(A) 0 / 0 , 2 / 1 , 3 / 2 , 1 / 1 , will be developed below,
and proved to be a great success.
(B) 3 / 2 , 1 / 1 , 0 / 0 , 2 / 1 , has placed the last 2 Orbit Lines at the beginning,
and can serve as a Counter-Melody for the (A) version.
(C) 0 / 0 , 3 / 2 , 1 / 1 , 2 / 1 , has a nice smooth, melodic, descending scale,
the disposition we recommend in SingAlot for learning this chord pattern, and
which is the basis for the ever-popular Chopsticks.
(A) Embelishing Orbit Lines into Canonic Melody
Processes
There are 2 processes of embelishment in this canon : Melo-rhythmic subdivision and Embroideries.
In Canonic Line 1, we find a Feminine Rhyme, with an important superior Embroidery, A,
to improve the sonority with the Masculine Rhyme of Canonic Line 2, C,
followed by a superior and then a (chromatic) inferior Embroidery at the end.
In Canonic Line 2, we find an inferior Embroidery just before the Masculine Rhyme.
The second half of Canonic Line 2 acts as a pick-up to Canonic Line 3,
placing the second half of the canon at a smaller Rhythmic Level.
In this pick-up we find a (chromatic) inferior and then a superior Embroidery
before the Feminine Rhyme of Line 3.
In Canonic Line 3, after the Feminine Rhyme, we repeat the whole process twice,
into the Feminine Rhyme of Line 4
In Canonic Line 4, after the Feminine Rhyme, we repeat the whole process
into the Masculine Rhyme at the end.
It is a good idea to fill in the last 3  s,
to get back to the large level of the beginning and not start the repeat too soon.
One could clap hands or simply say "two, three, four".
The Melo-rhythmic subdivision of Line 1 was repeated in Line 2, and
the second half of the Melo-rhythmic subdivision of Line 1
was used for Lines 3 and 4.
(B) Producing a Counter-Melody Canon
Producing a Counter-Melody is quite similar to producing a Round Canon,
maintaining the same Melo-harmonic Chord Pattern M4, and
distributing the Orbit Voice-leading Lines wisely,
especially the resolutions of the Secondary Notes (Orbit 3 and Orbit 2),
while constantly seeking satisfactory sonorities between the 2 melodies.
The processes of embelishment in this canon are :
Melo-rhythmic subdivision, use of 2 lines, Substitution of Orbit 3, and
Non-Chordal Tones (including a Passing Tone).
In Canonic Line 1, we find a substitution 0(3), GF / E.
In Canonic Line 2, we find double and single Non-Chordal Tones of Orbit 1, FED / EC,
the only Feminine Rhyme.
In Canonic Line 3, there is nothing but Orbit 3, G.
In Canonic Line 4, we find 2 Orbit Lines, 0 / 1, G / C (the Fundamental Bass), and 2 / 1, B / C,
with a Passing Tone between them, GAB.
Orbit 0, which can "resolve" anywhere,
is often used as a supplementary Orbit Line to create more melodic variety.
The Melo-rhythmic subdivision is much simpler in this canon,
 /  for Lines 1 and 3, and
\ / for Lines 2 and 4,
with the Feminine Rhyme in Line 2.
The canon remains at the same (large) Rhythmic Level throughout.
These 2 Counter-Melody Rounds are very popular in Quebec with French words.
We hope to have English words for them shortly,
and include them in the SingAlot repertoire.
They should be sung a little higher, preferably in Eb.
(C) Chopsticks
Canonic possibilities
The well-known Chopsticks, which very young children play with their two index fingers,
makes a very ingenious use of these 4 Orbit Voice-leading Lines -
Orbit 0/ Orbit 0, G / G, and Orbit 3 / Orbit 2, F / E, are presented together, then
Orbit 2/ Orbit 1, B / C, and Orbit 1 / Orbit 1, D / C, are presented together.
It is surprising that no one seems to have realized that the 2 phrases could be played simutaneously,
and that a second child, playing an octave lower, could start when the first reaches the second phrase,
the 2 phrases complementing each other perfectly
to give a complete DOMINANT / TONIC progression.
It is also possible to organize the middle section of Chopsticks to form another canon,
but we will see this in the Evolving Canons.
(D) Answering Machine
A new invertible 4-voice round canon
Here is another ingenious use of the 4 Orbit Voice-leading Lines in the M44 chord pattern -
Orbit 0/ Orbit 0, G / G, Orbit 3 / Orbit 2, F / E, Orbit 2 / Orbit 1, B / C, and Orbit 1 / Orbit 1, D / C.
The 4 lines all start on Orbit 0, G -
Line 1 remains there for all of its 8 s.
Line 2 leaves it at the second DOMINANT chord for Orbit 3, F, (the Procuration of Voice-leading A),
which resolves to Orbit 2, F / E.
Line 3 leaves it at the first TONIC chord for Orbit 3, A, (also the Procuration of Voice-leading A),
and closes with the Orbit 2 / Orbit 1 line, B / C,
(the small notes are for the ending only).
Line 4 leaves it in the first DOMINANT chord for Orbit 3, G-F, ( Substitution 0(3)),
and closes with the Orbit 1 / Orbit 1 line, D / C.
The lines spread out in a fan-like pattern, with Line 3 ascending and with Lines 2 and 4 descending.
In other modes
WITHOUT the optional Eb (indicated "(b)" in Lines 2 and 4) and singing the original E natural,
this version is in the Diatonic Major Mode in the Key of C major.
WITH the optional Eb (indicated "(b)" in Lines 2 and 4)
this version is in the Chromatic Minor Mode in the Key of C minor.
The inversion
The inversion is not around the central note D of the Window but rather around the FRAME C-G
and uses the corresponding w44 chord pattern in C minor (Fm6 / Cm, Fm6 / Cm)
rather than in A minor (Dm6 / Am, Dm6 / Am),
with the 4 Orbit Voice-leading Lines -
Orbit 0/ Orbit 0, C / C, Orbit 3 / Orbit 2, D / Eb, Orbit 2 / Orbit 1, Ab / G, and Orbit 1 / Orbit 1, F / G.
Here again, the 4 lines all start on Orbit 0, C -
Line 1 remains there for all of its 8 s.
Line 2 leaves it at the second DOMINANT chord for Orbit 3, D, (the Procuration of Voice-leading A),
which resolves to Orbit 2, D / Eb.
Line 3 leaves it at the first TONIC chord for Orbit 3, Bb, (also the Procuration of Voice-leading A),
is placed an octave higher to remain within the C-C octave range,
and closes with the Orbit 2 / Orbit 1 line, Ab / G,
(the small notes are for the ending only).
Line 4 leaves it in the first DOMINANT chord for Orbit 3, C-D, ( Substitution 0(3)),
and closes with the Orbit 1 / Orbit 1 line, F / G.
With Line 3 placed an octave higher we no longer have a fan-like pattern,
but we still have 1 line descending (Line 3) and 2 lines ascending (Lines 2 and 4).
In other modes
WITHOUT the optional E natural (in Lines 2 and 4) and singing the original Eb,
this version is in the Diatonic Minor Mode in the Key of C minor.
WITH the optional E natural (in Lines 2 and 4)
this version is in the Chromatic Major Mode in the Key of C major.
Traveling between the modes
With the inversion around the FRAME C-G rather than around the central note D of the Window,
the 4 versions of this canon are all in the Key of C, either C major or C minor,
making it very convenient to travel from one mode to another,
all combinations being possible.
For combining the 4 versions, we recommend the following order to get the best possible balance -
The Diatonic Minor Mode, version II, singing the original Eb,
The Chromatic Minor Mode, version I, singing the optional Eb,
The Chromatic Major Mode, version II, singing the optional E natural, and
The Diatonic Major Mode, version I, singing the original E natural.
The 2 minor modes are placed first, the 2 major modes last.
The sharpening (ascending) modes alternate with the flattening (descending) modes.
The diatonic modes are placed first and last, the chromatic modes in the middle.
Performance
1. For a mixed-voice choir it is preferable to have M-F-F-M entries
to have the best disposition at the end of the first entry.
2. It's a good idea to sing the canon through in unison before the canonic performance.
3. A satisfactory, short performance could consist of 8 bars of unison and 8 bars of canon,
with a fermata at the end.
4. Don't hesitate to travel between different modes and try out all the combinations.
5. You will probably prefer to sing it a tone higher, in D (minor and major).
Lyrics
The words are, of course, pure nonsense,
what you might hear on the answering machine of a loan-shark,
based on the old "beg, borrow, or steal" saying.
In the French version, the lyrics are far more poetic and sentimental,
praising the joys of friendship, as in Auld Lang Syne.
You might feel like writing some lyrics of your own.
The M34 Pattern
Let's look at this 2-cell TONIC / DOMINANT , DOMINANT / TONIC pattern
The Orbit Voice-leading Lines are -
Orbit 3/ Orbit 2, Orbit 2 / Orbit 1, the notes A / B, B / C,
Orbit 2/ Orbit 1, Orbit 3 / Orbit 2, the notes E / D, F / E,
Orbit 1/ Orbit 1, Orbit 1 / Orbit 1, the notes C / D, D / C, and
Orbit 0/ Orbit 0, Orbit 0 / Orbit 0, the notes G / G, G / G.
Canonic Disposition of the Orbit Lines
Since this chord pattern consists of 2 cells, with a breath between the two (at the dashed bar-line),
the Canonic Lines can jump from one Orbit Voice-leading line to another -
(A) 3 / 2 , 2 / 1 // 2 / 1 , 3 / 2 // 1 / 1 , 1 / 1 // 0 / 0 , 0 / 0
are the 4 "normal" lines exposed above with the same Orbit on both DOMINANT chords.
(B) 2 / 1 , 2 / 1 // 1 / 1 , 3 / 2 // 0 / 0 , 0 / 1, with a Fundamental Bass in the third line,
are the choice of Orbit Lines made for a first 3-voice canon.
(C) 0 / 3 , 3 / 2 // 2 / 1 , 1 / 1 // 3 / 2 , 2 / 1
are the choice of Orbit Lines made for a second 3-voice canon
which can serve as a Counter-Melody for the (B) version.
(B) Embelishing Orbit Lines into Canonic Melody
The processes of embelishment in this 3-voice canon are :
Melo-rhythmic subdivision, use of 2 Orbit Lines, and Non-chordal Tones (Embroideries and Passing Tones),
The 3 Canonic Lines have Masculine Rhymes,
and the first two have the same Melo-rhythmic subdivision.
In Canonic Line 1, we find 2 Orbit Lines, 0 / 1, G / D and 2 / 1, E / D,
with a superior Embroidery , F, which is also a Passing Tone from the G.
There is also a Passing Tone, C, as we change Orbit Line.
In Canonic Line 2, we find 2 Orbit Lines, 0 / 1, G / D and 1 / 1, C / D,
with 2 Passing Tones, A and B, between G and C.
There is also a Passing Tone, E, as we change Orbit Line.
Here again, Orbit 0, which can "resolve" anywhere,
is used as a supplementary Orbit Line to create more melodic variety.
In Canonic Line 3, we have a different Melo-rhythmic subdivision,
without any Foreign Tones whatsoever.
A series of 5 octave "sneezes" with the FB at the end, GG, GG, GGGGGC.
(C) Producing a Counter-Melody Canon
Here again, for this Counter-Melody, we will
maintain the same Melo-harmonic Chord Pattern M34, and
distribute the Orbit Voice-leading Lines wisely,
especially the resolutions of the Secondary Notes (Orbit 3 and Orbit 2),
while constantly seeking satisfactory sonorities between the 2 melodies.
The processes of embelishment in this canon are :
Melo-rhythmic subdivision, use of 2 Orbit Lines, Substitution of Orbit 3,
and a variety of Non-Chordal Tones.
In Canonic Line 1, we find the Voice-Leading A procuration, G / F,
Substitutions 1(3) and 0(3), DGG / E.
In Canonic Line 2, we find :
unprepared Non-Chordal Tones of Orbit 2 and Orbit 1, FE / D and ED / C
as well as the insertion of Orbit 0, G, with the Passing Tones E and F.
the only Feminine Rhyme, with another Orbit 0, the low G.
In Canonic Line 3, we find Substitution 1(3) with Passing Tone B,
insertion of Orbit 0, G, with Passing Tone A.
These 2 Counter-Melody Rounds are very popular in Quebec with 5- and 6-yearolds.
We hope to have English words for them shortly,
and include them in the SingAlot repertoire.
They should be sung lower, preferably in G.
The M54 Pattern
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