Melody/Melo-Rhythm/Procedures

0. Preface

The Generation of Melo-rhythmic Patterns for each melody is quite similar
          to the Generation of Rhythm and to the Generation of Harmony.
     1. One starts from Basic Materials, in this case the Fundamental Melo-rhythmic Cell.
     2. Then one applies various forms of Transformations which we call Procedures
          - Division of large note-values, producing the smaller levels
          - Multiplication (copy, repeat) of the Fundamental Cell, producing the larger levels
          - Fission of a cell, dividing it into two identical parts
          - Fusion of several cells producing a single larger Melo-rhythmic Entity.
     3. The Symmetry produced (or destroyed) by these procedures
          is observed during the generative process
               as proper equilibirium of this symmetry must be maintained.
     In the application of this theory of generation,
          transformations will not necessarily be applied in the order given above (and below).

1. The fundamental Melo-rhythmic Cell (at Level 0)

1.1. Definition
1.1.0. The Basic Materials of this generation will be the Fundamental Melo-rhythmic Cell
     which is indicated KM (a Kinetic Off-beat and a static, Masculine, Beat),
          and placed at the end of the Melo-rhythmic Pattern,
               possibly at the end of Melo-rhythmic Entities grouped within the complete Pattern,
     very much the same way that the Fundamental Melo-harmonic Cell
               (4, DOMINANT-TONIC)
          is placed at the end of a Melo-harmonic Pattern.
1.1.1. The Masculine rhyme on its Beat (an undivided "Whole note"), static (without movement),
     offers a maximum amount of final rest (followed by a breath); and
1.1.2. its completely Kinetic Off-beat, without any breath to interrupt its movement,
     offers a maximum amount of movement before the rest.

1.2. Two variations are already possible at this primitive, basic (0) size
1.2.1. The Off-beat may be preceded by a pick-up of varying length and subdivision -
     1.2.1.1. one note (maximum at -2) "Quarter note", indicated p2, (as in Auld Lang Syne),
          the largest level amount possible at -2 without displacing the position of 0,
     1.2.1.2. three notes (maximum at -3) "Eight noteEight noteEight note", indicated p3, (as in Oh, When The Saints),
          two notes "Eight noteEight note", will be indicated p2, like "Quarter note", (as in She'll Be Coming' Round The Mountain),
          one note "Eight note", will, for the present, be simply indicated p, (as in Oh Where, Oh Where),or
     1.2.1.3.seven notes (maximum at -4Quarter note) "Sixteenth noteSixteenth noteSixteenth note Sixteenth noteSixteenth noteSixteenth noteSixteenth note", indicated p4, (as in Never On Sunday),
          six notes "Sixteenth noteSixteenth note Sixteenth noteSixteenth noteSixteenth noteSixteenth note", will be indicated p3, like "Eight noteEight noteEight note", (as in Quando, Quando)
          five notes "Sixteenth note Sixteenth noteSixteenth noteSixteenth noteSixteenth note", will for the present be indicated like six notes p3,
               (as in The Shadow Of Your Smile),
          four notes "Sixteenth noteSixteenth noteSixteenth noteSixteenth note", will be indicated p2, like "Quarter note",
          three notes "Sixteenth noteSixteenth noteSixteenth note", will be indicated as four notes,
          two notes "Sixteenth noteSixteenth note", and one note "Sixteenth note" will simply be indicated p.
1.2.2. The static quality of the Beat of this fundamental cell M - Whole note ' may be diminished,
          if no Beat of greater static quality precedes it -
     1.2.2.1. by substituting the snapped Feminine rhyme F- - Quarter noteHalf note. ' (as in London Bridge),
          which diminishes the static quality slightly, or, less frequently (mostly in 3/4),
     1.2.2.2. by substituting the full Feminine rhyme F= - Half noteHalf note ' (as in Tannenbaum),
          which diminishes the static quality more.
1.2.3. The fundamental cell may eventually be submitted
     to the procedures of Division, Fission, and Multiplication.

It is almost impossible to find a case where the Fundamental cell, in its basic state (K1M, possibly pK1M, K1F, or pK1F) remains unchanged by some form of Procedure. However, a simple and approximate example might be better than nothing.

Polly Put The Kettle On - Fundamental Cell
We'll have some tea'

In the fourth and last cell of Polly Put The Kettle On
          p2K1M - Quarter note \ Half noteHalf note / Whole note '
     we find the Fundamental Cell in a basic form, without the presence of any procedure.
          However, you will see in the Generations on the next page,
               that the cell is not as pure and virginal as it might seem.

2. Procedures of Generation

2.0. Intro

Transformations
Four processes of Transformation will be applied to this Fundamental Cell,
     gradually working "backward" toward the beginning of the complete pattern,
          (as is the case with the Melo-harmonic patterns).

2.1. Division

Definition
2.1.0. The first transformation is the division of the large note-values,
     especially those of the Off-beat of a cell,
          and which creates a smaller level with each subdivision.
2.1.1. at -1 in two parts "Half noteHalf note", indicated "K1" (as in Twinkle, Twinkle),
     (this seems the minimal subdivision possible for the Off-beat to possess the required movement)
2.1.2. at -2 in four parts "Quarter noteQuarter noteQuarter noteQuarter note", indicated "K2" (as in Aura Lee),
2.1.3. at -3 in eight parts "Eight noteEight noteEight noteEight note Eight noteEight noteEight noteEight note" , indicated "K3"
     (as in She'll Be Coming ' Round The Mountain), and even
2.1.4. at -4 in sixteen parts "Sixteenth noteSixteenth noteSixteenth noteSixteenth note Sixteenth noteSixteenth noteSixteenth noteSixteenth note Sixteenth noteSixteenth noteSixteenth noteSixteenth note Sixteenth noteSixteenth noteSixteenth noteSixteenth note", indicated "K4"
     (as in the verse of Never On Sunday).
Here is an excellent example of a song
     whose Melo-rhythm consists uniquely of the Fundamental Cell with Division.

Never On Sunday (verse) - Fundamental Cell
Or you can kiss me on a
Tues- day a Tues- day a Tues- day in fact I wish you
would '

In the second and last cell of the verse of Never On Sunday
     which takes two complete rows of the Box (spread out over three rows),
          p4K4M - Sixteenth noteSixteenth noteSixteenth note Sixteenth noteSixteenth noteSixteenth noteSixteenth note \ Eight noteSixteenth noteSixteenth note Eight noteSixteenth noteSixteenth note Eight noteSixteenth noteSixteenth note Sixteenth noteSixteenth noteSixteenth noteSixteenth note / Half note_Sixteenth note '
     we find the Fundamental Cell in a basic form,
          a seven-note pickup, on the first line,
          a thirteen-note Off-beat, on the second line
          a masculine rhyme Beat, on the third line.
     Division was the only procedure applied.
          Multiplication will evidently be needed to repeat the Fundamental Cell without the slightest changes.
               This is one of the rare songs where neither Fission nor Fusion are applied.

2.2. Multiplication

2.2.1. Definition
The second (simplest and most common) of these transformations, is that of Multiplication,
     which consists of copying or repeating,
     which may be applied once or several times, and
     which creates the larger levels as it doubles the length of the pattern each time.
This is the only obligatory procedure.

2.2.2. Number of Repeats
2.2.2.1. Applied once to the Fundamental Cell, producing a two-cell result at +1,
     This is what must happen to Never On Sunday in order to complete the verse.
2.2.2.2. Applied twice to the Fundamental Cell, producing a four-cell result at +2.
2.2.2.3. It may also be applied after the procedures of Division and Fission
     have been applied to the Fundamental Cell.

Never On Sunday (verse)
Oh you can kiss me on a
Mon- day a Mon- day a Mon- day is ver- y ver- y
good ' Or you can kiss me on a
Tues- day a Tues- day a Tues- day in fact I wish you
would '

Here is the complete 2-cell verse of Never On Sunday
     2x (p4K4M) - 2x (Sixteenth noteSixteenth noteSixteenth note Sixteenth noteSixteenth noteSixteenth noteSixteenth note \ Eight noteSixteenth noteSixteenth note Eight noteSixteenth noteSixteenth note Eight noteSixteenth noteSixteenth note Sixteenth noteSixteenth noteSixteenth noteSixteenth note / Half note_Sixteenth note ')
          with two rows for each cell (four complete rows in all),
     All that was needed was to Multiply (repeat) the Fundamental Cell once.
          Still no Fission or Fusion.

2.3. Fission

Definition
2.3.0. The third transformation is that of Fission,
     where a cell is split into two (usually identical) parts,
          forming smaller Melo-rhythmic Entities.
2.3.1. This fission usually occurs at the beginning of the Melo-rhythmic Pattern by
     replacing the Off-beat by a copy of the Beat, but
     maintaining its pick-up (if there is one), and adding it to the Beat,
          thus placing a breath in the middle of the cell, between the Off-beat and the Beat, and
     making the Off-beat and Beat (with their possible pick-ups) of identical Melo-rhythm.

Application
2.3.2. This fission may be applied with any of the possibilities of the fundamental cell -
     the length and subdivision of pick-up , and
     any form of rhyme -
          a masculine rhyme, an MM cell
               (ex: Eight noteEight noteEight note \ Half note_Eight note ' Eight noteEight noteEight note / Half note_Eight note ' as in Oh, When The Saints) or
          a feminine rhyme, an FF cell
          (ex:Quarter noteQuarter noteHalf note ' / Quarter noteQuarter noteHalf note ' as in Mary Had A Little Lamb or Jingle Bells).

The Off-beat
The subdivision of the Off-beat (see 2.1.0.) is not involved here
     since the pattern of the Off-beat disappears and is replaced by that of the Beat.

Variations of the MM cell
There are several variations of the MM cell (see 2.3.2), always with sufficient pick-up (three to six notes) -
2.3.3. p3F=p3M as in The Old Refrain
2.3.4. p3Mp3F- p3Mp3M as in Quando, Quando with the feminine fusion on the Beat of the first cell
2.3.5. p3Mp3F- p3Mp3F- as in Tres Palabras, using only the antecedent of 2.3.4.

The FF cell
With or without pick-up, the FF cell is by far the most popular,
     used extensively as the fusion between cells or sections
2.3.6. without pick-up, as in Jingle Bells, Mary Had A Little Lamb, London Bridge
2.3.7. with pick-up as in Voyage au Canada (Charles Trenet).

Never On Sunday (chorus)
Most a- ny
day You can be my
guest A- ny day you
say But my day of
rest Just name the
day That you like the
best On- ly stay a-
way From my day of
rest

Here is the complete 4-cell chorus of Never On Sunday
     4x (p3Mp3M) - 2x (Eight noteEight noteEight note \ Half note_Eight note Sixteenth noteSixteenth noteEight noteEight note / Half note_Eight note ' Sixteenth noteSixteenth noteEight noteEight note \ Half note_Eight note Sixteenth noteSixteenth noteEight noteEight note / Half note_Eight note ')
          with two rows for each cell (eight complete rows in all).
     Only the first and fifth ps remain undivided into Sixteenth noteSixteenth note
          Still no Fusion, only an uninterupted succession of M rhymes.

2.4 Fusion

2.4.0. The fourth transformation is that of Fusion,
     where, after Multiplication, two or more cells are tied together
          to form a larger Melo-rhythmic Entity.

Joining the two cells of +1 (KM KM),
     with a reduction of the static inertia of the Beat of the first cell,
2.4.1. by placing a Feminine Rhyme in the middle (KF= KM, possibly KF- KM), or
2.4.2. by placing a Pick-up in the middle (KM pKM), or, on occasion,
2.4.3. by using both means (KF= pKM or KF- pKM).
     This is what we call a Langer Hinge, in the middle of a 2-cell Melo-rhythmic Entity

Twinkle, Twinkle, Little Star - Fusion
How I won- der
What you are'

Here are the last two cells of Twinkle, Twinkle, Little Star
     { K1F= K1M } - { Half noteHalf note / Half noteHalf note ' \ Half noteHalf note / Whole note ' }
          with a cell in each row.
     These cells were originally
          K1M K1M - Half noteHalf note / Whole note ' \ Half noteHalf note / Whole note '
     Fusion was achieved by placing a Feminine Rhyme F= on the first cell,
          thereby reducing the breath and tying the two cells together into one Rhymic Entity.

Joining four cells of +2,
2.4.4. by applying the feminine rhyme (or the pick-up)
     on the Beat of the second cell (in the middle).
There are numerous examples in the following Generation section.

Fusion is normally applied at the end of a pattern,
          as in the MI-MI-MA
     contrary to Fission which is normally applied at the beginning,
          as in Jingle Bells.

3. Symmetry

3.1 Once procedures have been applied, the next step is to observe the Symmetry
     which exists between different elements of the pattern,
     and which is essential to the equilibrium of the pattern.
3.2. If the symmetry is insufficient (less than two, in other words, none at all),
          then a repeat will be required.

Jingle Bells - Symmetry
Jin- gle bells' Jin- gle bells'
Jin- gle all the way'

Example - with a cell in each row (two rows in all).
     The first two cells of Jingle Bells were originally identical.
          K2M - Quarter noteQuarter noteQuarter noteQuarter note / Whole note (as in the last cell).
     - Once Fusion had changed the Beat of the first cell
          from Masculine M - Whole note to Feminine F= - Quarter noteQuarter noteHalf note ' ,
     - and Fission had changed its Off-beat,
          from Kinetic K - Quarter noteQuarter noteQuarter noteQuarter note to Feminine F= - Quarter noteQuarter noteHalf note ',
     there was increased Symmetry within the first cell F=F= - Quarter noteQuarter noteHalf note ' / Quarter noteQuarter noteHalf note ' but
           there was no symmetry left between the two cells.
     Repetition was by the fact obligatory.

3.3. If the symmetry is excessive (more than three, in most cases everywhere),
          then a change is required, usually in the Off-beat of the last cell.
     Examples include Polly Put The Kettle On.

Three types of Symmetry
3.4. There are three types of symmetry
     3.4.1. Between the Off-beats of different cells (indicated "ObOb")
               resulting from Fusion at +1.
          Example
               - In Twinkle, Twinkle, with the pattern K1F= K1M - Half noteHalf note / Half noteHalf note ' \ Half noteHalf note / Whole note '
                    the Off-beats (Half noteHalf note) have the same Melo-rhythm.
               - In Aura Lee, with the pattern K2F= K2M - Quarter noteQuarter noteQuarter noteQuarter note / Quarter noteQuarter noteHalf note ' \ Quarter noteQuarter noteQuarter noteQuarter note / Whole note '
                    the Off-beats (Quarter noteQuarter noteQuarter noteQuarter note) have the same Melo-rhythm.
               - In Red River Valley, with the pattern p2K3F-- p2K3M -
                         Eight noteEight note \ Quarter noteEight noteEight note Quarter noteEight noteEight note / Eight noteQuarter note._Quarter note' Eight noteEight note \ Quarter noteEight noteEight note Quarter noteEight noteEight note / Half note. '
                    the Off-beats (Quarter noteEight noteEight note Quarter noteEight noteEight note) have the same Melo-rhythm.
     3.4.2. Between complete cells, with Off-beats the same and Beats the same (indicated "cell")
               resulting from Fusion at +2.
          Examples include Mary Had A Little Lamb, between the first and third cells.
     3.4.3. Between the Off-Beat and the Beat of the same cell (indicated "ObB")
               resulting from Fission of a cell.
          Example
               - In Jingle Bells, with the pattern F=F= - Quarter noteQuarter noteHalf note ' / Quarter noteQuarter noteHalf note '
                    both the Off-beat and the Beat ( Quarter noteQuarter noteHalf note ') had the same Melo-rhythm.
3.5. Another important element in the equilibrium of the pattern is the process of increasing level size.
     This consists of a gradual evolution, during a Melo-rhythmic Pattern,
          passing from smaller to larger levels.
     The main actor in this progressive operation seems to be the breath,
          its depth and the frequency of its occurence.
     Although the levels do not actually change, the breaths draw the attention of the listener
          from 0 (which has a breath after the beat of each cell) the normal point of focus,
          to -1 (with a breath after the Off-beat as well as one after the Beat of a split cell)
               at the beginning of the song, and eventually
          to +1 (with two cells tied together and the breath only after the second cell)
               at the very end of the song.

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