Preface
Definition
A syncopation can best be defined as -
the prolongation of a note
attacked on an Off-beat
to the next Beat.
It is usually anticipated (attacked sooner) ,
but we have left a section open at the end,
for cases where it is retarded (attacked later).
Anticipated Syncopations
One may anticipate by different amounts (note-values)
and we will catalogue these amounts by the corresponding rhythmic level -
a  anticipation at Level -2,
a  anticipation at Level -3, and
a  anticipation at Level -4.
Level -2
In a bar (composed of a  ) with the basic Melo-rhythmic pattern 
the third beat (the first ) can be anticipated by a , producing the pattern
A kind of snap
If there is a breath after the , as is often the case,
we have the same process as when a normal Feminine Rhyme is transformed into a snap.
In other words, a snap is a form of syncopation, but not all syncopations are snaps.
This pattern is frequently used at Level -3 with shorter note-vales, as .
Level -3
In a bar with the basic Melo-rhythmic pattern
the first (on the second beat ) can be anticipated by an , producing the pattern
which we find in Rudolph The Red-Nosed Reindeer
as well as in the Habanera Melo-rhythm (frequently written as a triplet).
In a bar with the basic Melo-rhythmic pattern , a typical tango rhythm,
the first (on the fourth beat ) can be anticipated by a , producing the pattern
less frequently used than the previous example.
However, in the same basic pattern,
the whole (of the third and fourth beats ) can be anticipated by an ,
producing the pattern
the typical Freilach rhythm, which has been used in popular music of all nations,
including the French, in Y'a d'la joie by Charles Trenet.
Let's not forget the basic pattern,
where the whole (of the third and fourth beats ) can also be anticipated by an ,
producing the pattern .
the typical Charleston rhythm, so dear to Gershwin.
These patterns will re-appear with shorter note-values in Level -4.
Level -4
In Caribbean folk-music, one often finds the basic . ' pattern
syncopated into _. '
by anticipating both the second and the . by a
as well as the whole last beat , also by a .
Retarded Syncopations
It took us a long time to elaborate the operation of retarded syncopations.
They seem so much more insidious and uncertain than anticipated syncopations.
Syncopations are a little like Non-chordal tones (which are a displacement in Pitch of a Chordal Tone)
in that they are also displacements but, in this case, in Time.
Since songs are composed in the syncopated state,
we usually have no "unsyncopated" version with which to compare.
We finally found one, originally written without syncopations,
later transformed into a syncopated version.
Comparing the 2 versions enabled us to establish the nature and position of retarded syncopations.
The songs which follow are all quite well known and can be found in most Fake-Books.
La Cucaracha
Analysis of the Melo-Rhythm
The song is composed of -
a Chorus which consists of 4 cells -
a split cell with a pick-up and Feminine Rhyme, followed by
a Kinetic Off-beat with a Masculine Rhyme on the Beat,
these 2 cells are repeated for the second half,
2x(p3F=p3F= K3M),
and a Verse which also consists of 4 cells -
a Kinetic Off-beat with a Feminine Rhyme on the Beat,
which appears 3 times, and
the same Kinetic Off-beat with a Masculine Rhyme on the Beat, for the fourth cell.
3x(K3F=) K3M.
NOTE that the Verse consists uniquely of the second (or fourth) cell of the Chorus,
with fusion (Feminine Rhymes) applied to the first 3 cells.
Original Ternary Version in 3/4
In the original Mexican version in 3/4 at Level -1 without any syncopations
the Melo-rhythm of the 8-bar Chorus is composed of 2x( \ ' / \ / . )
and the Melo-rhythm of the 8-bar Verse is composed of 3x( / ) / ..
Transformation to Binary Version in 4/4
When this is transformed into the Basic Binary 4/4 at Level -1
the Melo-rhythm of the Chorus is now 2x( \ ' / \ / _ )
and the Melo-rhythm of the Verse is now 3x( / ) / .
American Syncopated Version in 4/4
In the American Syncopated Version in 4/4 at Level -1
the Melo-rhythm of the 8-bar Chorus is now
2x( \ ._' / ._ \  / _ )
where represents an rest,
and the Melo-rhythm of the 8-bar Verse is now
3x( / ._ ) / .
By comparing the syncopated version with the unsyncopated 4/4 version, we see that -
(a) the at the beginning of bars 3 and 7 of the Chorus and bars 1, 3, 5, and 7 of the Verse
are Retarded Syncopations,
(b) the ._ in bars 1, 2, 5, and 6 of the Chorus and the ._ in bars 2, 4, and 6 of the Verse
are Anticipated Syncopations.
The Rule
Syncopations are placed so as to enlarge the breath between phrases.
1. Retarded syncopations are placed after a breath (at the beginning of a phrase).
2. Anticipated syncopations are placed before a breath (at the end of a phrase).
3. Retarded syncopations seem to apply only to the very first note(s) of a phrase
but not to the anacrusis, as we will later see (in Jamaica Farewell).
4. Anticipated syncopations apply to any of the other notes of a phrase, especially the last one(s).
Other Examples
Jamaica Farewell
This song is written in 4/4 at Level -1 and is composed of -
A Verse which consists of 4 cells (8 bars), all K3F=
where cells 2 and 4 have pick-ups, p2K3F=
which prevent any possibility of Retarded Syncopations at the beginning of bars 3 and 5.
However, cells 1 and 3 do not have pick-ups, which allows them the same
which we found in La Cucaracha.
A Chorus which also consists of 4 cells (8 bars, 9-16) also all K3F=
where cells 3 and 4 have pick-ups, p and p3
which prevent any possibility of Retarded Syncopations at the beginning of bars 13 and 15.
However, cells 1 and 2 do not have pick-ups, which allows them the same .
NOTE that, in the whole song, we have 8 F=s, not a single M.
The pick-up between the Verse and the Chorus, at the end of bar 8,
should normally be but is anticipated to
to permit the Retarded Syncopation at the beginning of bar 9
which would not, otherwise, have the required breath preceding it.
This breath between the Verse and the Chorus is now staggered -
the breath in the Melo-rhythm is at the very end of bar 8, and
the breath in the lyrics is before the last 2 notes of bar 8, before the words "But I'm".
There are many variations (both notes and note-values) in the different versions of this song.
In the 2 versions which we examined, we found (with a tie indicated underscored, as _)
In bar 2, _ and _
In bar 3 (Verse 3), and
In bar 4, _ and _
In bar 5, and
In bar 7, _ and
In bar 10, scale degrees 224 and 234
In bar 12, scale degrees 113 5 and 123 5
In bar 16, _ and _
The first version is blatantly inconsistent in its syncopation of the 8 F=s
3 anticipations of only 1 note, _, in bars 2, 4, and 16,
3 anticipations of 2 notes _ in bars 6, 8, and 10, as well as.
3 anticipations of 3 notes (imposed by the words) _, in bars 12 and 14.
The other version is more consistent in its syncopation of the 8 F=s
6 anticipations of 2 notes _ in bars 2, 4, 6, 8, 10, and 16, as well as
the 2 inevitable anticipations of 3 notes _, in bars 12 and 14.
A good candidate for Analysis
Food for thought
Might it be possible that -
if 2 notes are retarded in the opening ,
2 notes should be anticipated in the closing _, and
if only 1 note is retarded in the opening ,
only 1 note should be anticipated in the closing _ ?
There is certainly more work to do.
The Basic Un-syncopated Version -
Verse 1 consists of
/ ' \ / ' \ / ' \ / ' .
The Chorus consists of
/ ' \ / ' \ / ' \ / ' .
The Basic Melo-rhythm of Cell 1 of the Chorus
is the same as that of Aura Lee, Mary Had A Little Lamb, Polly Put The Kettle On, London Bridge.
One could easily syncopate these songs in a Calypso style.
From This Moment On
This song is written in 2/2 at Level -2.
For present purposes of examining Retarded Syncopations,
we will only examine Cell 1, composed of bars 1-4, K3M, which is syncopated at both ends,
2 Retarded notes at the beginning and 1 Anticipated note at the end , _ /
written here  \ _ / _\ .
This is, so far, the only song we found where a K3M is syncopated at both ends -
In La Cucaracha, the K3M is not syncopated at the end, and
In Jamaica Farewell, we have no Ms, only F=s.
The As, of a complete AABA
are composed of K3M K1F= K2F= K2M,
with an added cell at the end of the last A.
a most unusual combination.
Another good candidate for Analysis
The Basic Un-syncopated Version -
Cell 1 consists of / .
the same as Cell 2 of Aura Lee.
Desafinado
This song is also written in 4/4 at Level -2.
For present purposes of examining Retarded Syncopations,
we will examine mostly Cells 1 and 2, each composed of 4 bars (1-4 and 5-8), K4F-,
which only have 2 Retarded notes at the beginning,  . / ._
written here \ . / ._\ .
These 2 cells are only the first half of the first A (of a complete AABA)
which consists of 16 bars, K4F- K4F- K4F= K4F-.
Our "Food for thought" in Jamaica Farewell (above),
leads us to wonder if the last 2 notes of Cells 1 and 2 should not be Anticipated
so as to correspond to the 2 Retarded notes at the beginning, . / _.
all the more so that the dotted rhythm in bar 3 corresponds to that in bar 2
with which it has no real rhythmic alliance.
Another good candidate for Analysis
The Basic Un-syncopated Version -
Cells 1 and 2 each consist of \ / _\ , at Level -2,
which we would prefer to write / _ at Level -1,
a very simple and basic Melo-rhythmic pattern,
quite similar to that found in From This Moment On.
Bernie's Tune
Another song written in 4/4 at Level -2.
Here, we will examine only Cell 1, K4F=,
each A of the complete AABA being composed of 2 such cells,
which have 2 Retarded notes at the beginning and 1 at the end,
/ .__
written here _\ / .__\ .
NOTICE -
the ternary grouping of notes 1-4 and 5-8 in s (or s), and
the repeat of the opening (the second indicated _)
at the very beginning of the cell, an interesting and unusual innovation.
The Basic Un-syncopated Version -
Cell 1 consists of \ / \ , at Level -2,
which we would prefer to write / at Level -1,
the basic Rumba Melo-rhythmic pattern.
Button Up Your Overcoat
Another song written in 4/4 at Level -2.
Here, we will examine mostly Cell 1, F+F=,
Cell 2 being K4F-, each A of the complete AABA being composed these 2 cells.
Cell 1 has -
2 Retarded notes at the beginning and 1 Anticipated note at the end of the Off-beat,
_, written here \ _, and
2 Retarded notes at the beginning of the Beat,
/ .__, written here \ .
NOTICE the auspicious use of Feminine Rhymes in the complete F+F= K4F-, with
F+ and F= on Split and Fused Cell 1, and
K4 and F- on Kinetic Cell 2.
The Basic Un-syncopated Version at Level -2 -
Cell 1 consists of \ / \ ,
which we would prefer to write / at Level -1, and
Cell 2 consists of \ / _\ ,
which we would prefer to write / _ at Level -1.
Suggestions for Cell 1 -
The first note seems a little over-retarded, by a rather than by an .
Reducing this Retarded Syncopation to an would give us for Bar 1.
Anticipating the last 2 notes of Bar 2, _ would balance the beginning.
It might be interesting to check recordings to see how singers interpret these syncopations.
Spread (and Dot) Syncopations
Some forms of syncopation have left us baffled for a long time. The most refractory case was the principal theme of the Chopin Waltz in B minor, Op. 69 No. 2 posthm. This waltz opened a door to a new Spread Syncopation concept, as was the case for La Cucaracha concerning Retarded Syncopations.
The Chopin Waltz in B minor
The piece opens with this Melo-rhythm - _ / _ /
with the Pick-up tied to the following across the first bar-line.
This tied Pick-up reappears regularly during the first 16 bars of the waltz.
Although this tied note complies with the usual definition of a syncopation as
"the prolongation of a note attacked on an Off-beat to the next Beat",
it does not comply with the exigencies of either Retarded or Anticipated Syncopations.
The first note being in reality a . and the second note an ,
it seemed natural to suspect that the un-syncopated state might be /
even if the first was on the Off-beat and the second on the Beat.
The Melo-rhythm _ / _ / would thus have been
/ / before applying the Spread performance practice.
In the original Spread performance practice,
the 2 original s were in the same
and the resulting . did not produce a Syncopation, as the snapped . did.
However, in this Chopin Waltz,
the 2 original s were NOT in the same
and the resulting . DID produce a Syncopation.
For future reference, we will note that this Spread Syncopation was over a Level -1 Bar-line.
This extension of the Spread process,
(which includes a reversal of the rhythmic positions of the 2 original values involved),
seemed sufficiently daring to deserve further examination and, especially, further application.
The Bach Fugue in Eb minor
In Rhythm/Preface/The Unknown Container/1995,
we examined the Rhythmic nature of the subject of Bach's Eb Minor Fugue, First Book of the Clavier,
to conclude that it was in 3/2 time and not in 4/4 time as written by the author.
However, we did not mention its binary origins before the ablation into ternary form,
nor did we mention the nature of its syncopation,
even if we were convinced, at the time, that there was truly a normal syncopation involved.
We now suspect that there might rather be a Spread Syncopation involved here,
and we will now examine both possibilities, the Anticipated and the Spread Syncopations.
The Anticipated Syncopation
The Melo-rhythm of the subject of this fugue being . / . / ,
if the . is an Anticipated Syncopation, it should have been the first in the next ,
producing / / ,
with the next 2 notes also "pushed back" at the end,
and a White Christmas-style Melo-rhythm at the beginning,
a fairly complex fundamental (pre-syncopation) version.
The Spread Syncopation
With the same Melo-rhythm . / . / ,
if the first after the . should be given full value,
the basic Melo-rhythm would have been / / ,
a much more fundamental version, with all its even s.
The Fundamental Binary and the Spread Syncopation
With the binary Melo-rhythm (in 4/4 bars) . / \ . /
and application of the Spread Syncopation,
the basic Melo-rhythm would have been / \ /
with even more even s.
The Beethoven Symphony No. 8, First Movement
The third theme of the First Movment of the Beethoven Symphony No. 8 in F major, Opus 93
seems dangerously close to producing a Dot Syncopation across a bar-line
which would correspond to the Spread Syncopation of the Chopin Waltz in B minor.
The Melo-rhythm of this theme consists of -
in 3/4 _\_'_/_'_\_ / _
with the at the end of each Pick-up (bar) tied over the Bar-line.
The reason we said "dangerously close" is that, technically, to be a Dot Syncopation,
this should be tied to a and not to another ,
as is the case here, with, across the Bar-line, , Rudolph style.
This is a most interesting borderline case which certainly deserves mention.
Other Examples
There will certainly be more to say on the application of Spread (and Dot) Syncopations.
The 3/4-6/8 Performance Shift
Performing in 6/8 a song originally conceived and generated in 3/4 (see Red River Valley)
often produces an interesting syncopation.
Where and why does this happen ?
1. If we examine the six s in 3/4 and in 6/8, we see that -
the first and second (as well as the fifth and sixth) s are placed Beat, Off-beat in BOTH cases, but
the third and fourth s (in the middle) are placed Beat, Off-beat in 3/4 and Off-beat, Beat in 6/8.
2. If the third and fourth s are tied (by a or by a .),
there will be a syncopation in the 6/8 (not in the 3/4), as the hemioles in Dark Eyes.
3. If the second and third (or, more probably, the fourth and fifth) s are tied (by a or by a .)
there will be a syncopation in the 3/4 (not in the 6/8), as in the Bach Fugue in Eb minor of Book 1.
4. If the bar is disposed
(with any further subdivision whatever of these values, but no ties between them)
there will no syncopations in either the 3/4 or the 6/8.
The association between syncopations and the 3/4-6/8 Performance Shift seems a promising one.
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