Intro

Definition
What we call "Melo-Rhythm" is the series of note-values of a melody, as if we were tapping the rhythm of a melody with a pencil on a table, rather than singing it with the pitch of each note. There is a popular parlor game in which one player does just this and the others must guess the name of the melody.

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Here is an example of an empty "Melo-rhythmic Box", which delimits the "space" of the "compartment" which each note of a specific melody occupies, and you might enjoy (as in the pencil-on-the-table game) trying to guess the name of the song.
The compartments of this box do not simply delimit the length of each note, but also specify its Alternation quality.
     The two first compartments of each line are shaded light-blue because the notes are pick-ups.
     The next six compartments are shaded darker-blue because they represent the Off-beat of the cell.
     The rest of the line is of various shades of red because it represents the Beat of the cell,
          the shade becoming darker as the levels grow.
     In this box, there is one cell (at Level 0) per row.

These Boxes will be used for the entire section. Melo-rhythmic structure is not just ajusted to fit any arbitrary set of words. A well structured song always follows defined forms to produce a satisfactory result, a song which can be easily learned and memorized. The complaint often heard concerning musical comedies, where the audience comes out "singing the scenery", is frequently the result of improper Melo-Rhythm. We hope to be able to establish the same quality of structure as has been done for Harmony.

Length of Box-compartments

In order to facilitate the description of Melo-rhythmic Patterns, we will start with the nitty-gritty of symbols and abbreviations, very much as we did with for chord symbols in Harmony.

Note-values
In the text, each Note-value (normally placed in a Box-compartment)
     will be represented by the conventional notation:
     , Whole-note,
     , Half-note,
     , Quarter-note,
     , Eight-note,
     , Sixteenth-note,
      possibly , Thirty-second-note.
Examples - a 4/4 bar could consist of , , , , , etc ...

Abbreviation for Rhythmic Levels
Each level will be represented uniquely by its number.
     Example: -4 will mean Level -4.
          Isolated numerals will not be used with any other connotation.
Ternary levels will be represented by the two binary levels used to produce it.
     Examples: in bars of 3/4 the ternary level will be at -2-1, in bars of 6/8 at -3-2.

As is our habit (an arbitrary choice),
      will always be the default value of both beats and off-beats at 0,
      at -1,
      at -2,
      at -3, and
      at -4.

At the large levels,
     0 will consist of one cell,
     +1 will consist of two cells,
     +2 of four cells,
     +3 of eight cells,
     +4 of sixteen cells.
          Unless otherwise stated, a cell will always be at 0

Larger Note-values (of several bars)
     will be represented by the number of bars involved followed by ,
          now colored like the large rhythmic levels:
     2 for a note-value of 2-bar length,
     4 for a note-value of 4-bar length,
     8 for a note-value of 8-bar length, and so on.

Breaths
Breaths are indicated by the apostrophy sign " ' ".

Bar-lines
The slash " / " will represent bar-lines at 0, and
     the back-slash " \ " will represent bar-lines at -1.

Repeated Sections
Sections which appear several times
          might be indicated in ( ) preceded by the number of times.
     Examples
          - 6x ( / ' \ / ' ) in Twinkle, Twinkle,
          - 4x ( / ' \ / ' ) in Love Me Tender.

Displacing off-beats

     This is such a common performance practice that it hardly deserves to be considered a change of rhythmic level. Everyone is familiar with what is usually called "swing phrasing" in which the off-beat is played a little late, almost like playing a triplet, with the off-beat given only a third of the time of the whole beat. Played still shorter, the off-beat is only given a quarter of the time, played like a with a preceding . and usually written as such for the sake of clarity. In all our analysis and generation, these deviations will not be considered an integral part of the principles but rather a performance preference. Note will be taken of this performance deviation, but it will not be an integral part of the theoretical approach.
     1. The most common practice is the one presented above, shortening the second half of a subdivision, playing the off-beat later, which we will call a "spread" practice, the 2 notes being farther apart (we hesitate to use the word "swing", which we admit would be more colorful, because it is already used for Harmony progressions).
     2. However, the second half of a beat is occasionally played sooner, which we will call a "snap" practice, a favorite of the Scots which other ethnic groups have also adopted. We will come back to spreads and snaps (even double snaps) as we examine Feminine rhymes a little later.
     3. Syncopations are usually anticipations, at different small rhythmic levels (-2, -3, -4) which add to the tension of the phrase and can be applied to both Beats and Off-beats. As in snaps (which could be considered a form of syncopation), we will first examine the Melo-rhythm of a syncopated passage in its basic un-syncopated form and then add the syncopation as a performance practice.

Spreads and Snaps
Comin' Through The Rye, shown above as
          2x ( ' / ' \ / ' )
     is, in reality, a veritable orgy of spreads and snaps, as Scottish as you can get.
          There is one cell per row of this box.
A more detailed version, given below,
     uses the -3s constantly,
          but they are used, one at a time, uniquely for spreads and snaps, never two s in the same

Changing Meters

     The processes of Meter Change permit us to see all Melo-rhythmic Patterns evolve from their basic binary form (cells composed of 2 bars of 4/4, / ). All the other generating processes will be applied first and the meter will be changed at the very end, enabling us, at each stage of the generation, to follow a well trodden path down "binary road".
     There are several forms of meter change,
          depending on the adjacent binary levels chosen which will be fused together into a more complex level.

From 4/4 To 3/4

In the fusion of -2 and -1,
          the second of each group of four (in each ) technically disappears.
     However, to save the melodic material which it contains,
          the process of "squeezing" the first down to half-size is the most efficient.
     This process consists in reducing all the values contained in the first half () of the bar ( )
          down to the next smaller size (half of the original value).
     Examples of these reductions
          - to . ,
          - to ,
          - . to ,
          - to ,
          - to , etc...

In this Box of Rock-A-Bye Baby
     there is one cell in each row - eight cells, eight rows, in all,
          no evident pick-ups, though some creep in through scansion irregularity
               at the end of the third and fifth rows.
     Note the removed second in each bar .

From 4/4 To 6/8

(b) From 4/4 to 6/8 (by fusing -3 and -2),
          the second in each group of four (in each ) technically disappears.
     However, the process of "squeezing" the first and third down to half-size is the most efficient.
     This process consists in reducing the values contained in the first and third of each bar
          down to the next smaller size (half of the original value).
     Examples of these reductions
          - to . ,
          - to ,
          - . to ,
          - to ,
          - to , etc...

In this Box of Oh Where, Oh Where Is My Little Dog Gone?
     there is a cell in each row - four cells, four rows, in all,
          a one-note pick-up in each line
               (though a second note creeps in before the third cell, at the end of the second row).
     Note the removed second in each .

From 4/4 To 9/16

(c) From 4/4 to 9/16
     by fusing -2 and -1,
          the second in each group of four (in each ) technically disappears
               changing the meter to 3/4 as in Rock-A-Bye Baby
     by fusing -4 and -3,
          the second in each group of four (in each ) technically disappears
               changing the meter to 9/16.
     The process of "squeezing" will be applied at each ternary level.

In this Box of Down In The Valley
     there are two rows for each cell - four rows, two cells, in all,
          a three-note pick-up in each row
     NOTE -
     the removed second in each , and
     the removed second in each remaining .

Those on a Guided tour should click on in the Navigation Bar below.

From 4/4 To 5/8

The ablations of the clip Red River Limp 2
Using the process of maximum ablation,
     the Fibonacci value 3 comes from the Binary value 4,
     the Fibonacci value 5 comes from the Binary value 8.
The 5/8 bar is the result of maximum ablation in the 8 s of a 4/4 bar
     fusing quinternary -3-2-1
          in which we have the ablation for a 3/4 bar, fusing ternary -2-1,
          and the ablations for a 6/8 bar, fusing ternary -3-2.

What is removed ?
In the fusion of -2-1, the second and third s will be removed, and
in the fusion of -3-2, the second and the sixth s will be removed,
     the second being removed twice.

What remains ?
In each bar, we have left -
     the first and fourth s of the first , and
     the first, third, and fourth s of the second ,
          which gives us 2 beats in each bar of 5/8 (2+3).
Note that the words have been slightly altered to remove one syllable in each bar.

For the 5/8 bar, you might be interested in seeing
the footsies, the graphics, and
Changing Meters for Red River Valley and Where, Oh Where, Is My Little Dog Gone in 5/8 time.

Large-level Fibonacci Structures

From 64 Bars to 21

The ablations of the clip Bonnie Circle
Using the process of maximum ablation,
     the Fibonacci value 3 comes from the Binary value 4,
     the Fibonacci value 5 comes from the Binary value 8,
     the Fibonacci value 8 comes from the Binary value 16,
     the Fibonacci value 13 comes from the Binary value 32,
     the Fibonacci value 21 comes from the Binary value 64.
The ABA form of the clip Bonnie Circle
     is really a ternary version of the AABA form.
The complete Bonnie Circle has 21 bars (8+5+8)
     and will therefore come from a 64-bar Binary original.
          A quarter of this original (16 bars) is twice the length of the original My Bonnie chorus (or verse).
               We will have 2 choruses in each original A and 2 verses in the original B.
          With two bars (one cell) in each line of the Melo-rhythmic box,
               we will have 32 lines in the box (for the original 64 bars).

What is removed ?
Anything removed which has already been removed by a larger ablation, will be indicated in parentheses.
     In the fusion of +4+5, Lines 1-8 will be removed
          the first quarter of the whole piece.
     In the fusion of +3+4, Lines (1-4) and 17-20 will be removed
          the first quarter of each half of the piece.
     In the fusion of +2+3, Lines (1-2), 9-10, (17-18), and 25-26 will be removed
          the first quarter of each quarter of the piece.
     In the fusion of +1+2, Lines (1, 5, 9), 13, (17), 21, (25), and 29 will be removed
          the first quarter of each eighth the piece.
     In the fusion of 0+1, the first half of Lines
               (1, 3, 5, 7, 9),11, (13), 15, (17, 19, 21), 23, (25), 27, (29), and 31 will be removed
          the first quarter of each sixteenth of the piece.

What remains ?
1. Only ABA remains of the original AABA.
2. In the remaining A section at the beginning, we find
     the second half of a chorus (half of Line 11 and Line 12)
     the second quarter of a chorus (Line 14), and
     the second half of a chorus (half of Line 15 and Line 16).
3. In the B section, we find
     the second quarter of a verse (Line 22), and
     the second half of a verse (half of Line 23 and Line 24).
4. The last A section is like the first,
     the second half of a chorus (half of Line 27 and Line 28)
     the second quarter of a chorus (Line 30), and
     the second half of a chorus (half of Line 31 and Line 32).
Which gives us 8 bars (3+2+3) in each A section and 5 bars (2+3) in the B section.

Don't forget the 6/8
So far we have only spoken of the large levels with the fusion of 0+1+2+3+4+5,
     reducing 64 bars to 21.
But we must remember that in My Bonnie we have bars of 6/8
     which are reduced from 4/4 at the Ternary -3-2.
We will find here the same shape of bars that we had in Where, Oh, Where Is My Little Dog Gone ?.

Those on a Guided tour should click on in the Navigation Bar below.

Those browsing might wish to see the footsies and the graphics of the Fibonacci 8 grouping.

Content of Box-compartments

Scansion

What will we place in the Box-compartments of each Melo-rhythmic Pattern? Many options were available: using the traditional notation of music note-values; using the MRC elaborated above; using the words of the song, with a syllable in each compartment. This last option was the one we chose. Before proceeding with its application, it seems advisable to examine the specific rhythmical structure of words which is called "scansion".

Definition
"The metrical analysis of verse in which the syllables are defined
          as either short (unaccented) or long (accented)."
     This traditional definition classifies syllables according to the Quantitative Dimension of Time
          (Duration, short or long)
     or according to the Quantitative Dimension of Energy
          (Volume, unaccented or accented)

We will define syllables according to the Qualitative Dimension of Time,
          (Alternation of Beat and Off-beat),
     a syllable being placed either on a Beat or on an Off-beat.

     The are 2 possibilities for 2-syllable words
          - the iamb (Ex- the word "today") consisting of Off-beat/Beat
          - the trochee (Ex- the word "morning") consisting of Beat/Off-beat.

     The are 3 possibilities for 3-syllable words
          - the anapest (Ex- the word "afternoon") consisting of Off-beat/Off-beat/Beat
          - the amphibrach (Ex- the word "tomorrow") consisting of Off-beat/Beat/Off-beat
          - the dactyl (Ex- the word "yesterday") consisting of Beat/Off-beat/Off-beat.

     When there are 2 Off-beats in a row, the second is always "more Off-beat" than the first
          (higher in the Rhythmic Graphics).

Rhymes

Two Kinds
1. "Agreement in the terminal sounds of lines of verse (or words)"
2. (a) "Masculine rhyme - of but a single stressed syllable",
     (b) "Feminine rhyme - of two syllables of which the second is unstressed"

We have here two quite different definitions of the word "rhyme",
     1. the first concerning the terminal sound of words
          as with the words "mor-ning", "eve-ning", "bring-ing", "long-ing",
               which all end with the sound "ing", with no reference to Beat or Off-beat
     2. the second concerning the scansion of the words.

We will, from time to time, draw your attention to the terminal sounds,
     but our main interest is in the scansion of the words.

Kinetic - Static
Before defining and cataloguing Masculine and Feminine Rhymes,
     it might be a good idea to examine the concepts of "kinetic" and "static".

A kinetic note-value is one which is in movement, and
     a static note-value is one which is at rest.
A breath ( ' ) will normally follow a static note-value.

Kinetic Off-beat
The Off-beat is essentially kinetic (in movement)
     and will be indicated "K".

Scansion Rhymes on the Beat
Rhymes apply essentially to the Beat of a cell
          are always followed by a breath, and may be either
     Masculine (indicated M), in which case the Beat consists of
           ', undivided, completely static (without movement) , or
     Feminine (indicated F), in which case the Beat consists of
          - ' or ' (indicated F=) a normal Feminine (perfectly binary) rhyme
               with the first kinetic, and the second static,
          - . ' or ', or ' (indicated F+) a "dotted" Feminine rhyme
               with the first three kinetic and the last static,
          - . ' (indicated F-), a "snap" Feminine rhyme
               with the first kinetic and the last three static,
          - ._ ' (indicated F--), a "double-snap" Feminine rhyme
               with the first kinetic and the last seven static (almost a M).

As we will later see, the most "normal", conclusive, final cell will be the KM cell.

Pick-ups
Pick-ups (anacruses) are placed before an Off-beat,
     take their "allotted time" from the end of the preceding Beat
          (the pick-up of the first cell, from the Beat at the end),
     and will be indicated "p".

In the Box of Oh Where, Oh Where Is My Little Dog Gone?
     Note the one-note pick-up before each cell, at the beginning of each line,
          and the added pick-up note before the third cell, at the end of the second line.
     Note that all the Off-beats are kinetic K.
     Note that the Beat of the first cell is Feminine F=, '
          the words "lit-tle dog gone".
     Note that the Beat of the second cell is Masculine M, ._ '
          the word "be".
     Note that the Beat of the third cell is Feminine F=, '
          the words "tail cut long".
     Note that the Beat of the fourth cell is Masculine M, ._ '
          the word "he".

Grouping of Box-compartments

Cell description
Each cell at 0 (colored accordingly)
     will be represented by two upper-case letters,
          one for the Off-beat and one for the Beat of the cell,
     an Abbreviated Melo-Rhythmic code (MRA) with
          K for Kinetic (in constant movement), for Off-beats,
          M for Masculine rhymes, mostly for Beats, but occasionally for Off-beats
          F for Feminine rhymes, mostly for Beats, but occasionally for Off-beats
          p for pick-ups
     More details of this to follow.

Melo-rhythmic Entities
What we call "melo-rhythmic entities",
          which end with on the beat (a Masculine Rhyme), and
               which have a Langer Hinge in the center (a Feminine Rhyme),
     will be placed between { and } .

The MI-MI-MA
From the Latin words "major" (large) and "minor" (small), we have devised the expression "MI-MI-MA" to convey the concept of a structure composed of two small entities followed by one twice as large. The most current application of the "MI-MI-MA" is the AABA form, the BA linked together into the "MA".

     A classical example of MI-MI-MA is found in Happy Birthday in which
          (a) the first two cells (first two rows of this Box),
                    composed of { pKM } - { \ / ' }
               are short entities, ending on a M Beat
                    with a breath attracting attention to 0, then
          (b) the third and fourth cells (third and fourth rows of this Box),
                    composed of { pKF= pKM } - { \ / ' \ / ' },
               are tied together by the F=, attracting attention to +1.

In Melo-harmonic Patterns
It will be interesting to note that, in the generation of Melo-harmonic (chord) Patterns, the opposite evolution takes place. The focus is on the larger levels at the beginning (with fewer chord changes) and on the smaller levels at the end (often with tenant chords).

Those on a Guided tour should click on in the Navigation Bar below.

Those browsing might wish to see the Procedures
of the Generation of Melo-rhythmic Patterns
before seeing the Generation itself.