A Binary Bottle for Binary Wine

We will present here a new Rhythmic Code (Rcode for short)
     which applies to each note of a piece of music,
     and which defines, clearly and accurately,
          the exact position of the note,
          the precise length of the note
               (its Duration, the Quantitative Dimension of TIME), and
          the quality of Beat/Offbeat of the note at all levels
               (its Alternation, the Qualitative Dimension of TIME).

Fractions in the Binary Code
To assure precise and abbreviated identification of these three parameters
          (position, duration, and alternation)
     we will use the binary system of numerical notation (with only "0"s and "1"s).
This is common practice for units -
     1=1, 10=2, 11=3, 100=4, and so on,
          each column representing an exponential of 2,
               as they do for exponentials of 10 in the decimal system.
We will "extend" the system to include fractions,
     with numerals ("0" or "1") which will follow the "binary point"
          as we commonly do with the decimal point -
     .1=1/2, .01=1/4, .11=3/4, and so on,
          each column now representing a negative exponential of 2,
               as they do for the negative exponentials of 10 in the decimal system,
          and, above all, a specific rhythmic level.

Coding Note-values
The choice of note-values is evidently arbitrary, and this Rcode could be adjusted to any choice.
However, we will remain here in the choice which is the most convenient
     - the complete bar of Level -1 will be composed of a whole-note ("")
               and will be placed just before the binary point:
          1. will represent the complete first bar,
          10. will represent the complete second bar,
          11. will represent the complete third bar,
          100. will represent the complete fourth bar, and so on...
     For bars of larger size, the "*" will be used to include both 0 and 1 at that level.
          1*. will represent the first bar of Level 0
               which includes both the second (10.) and third (11.) bars of Level -1
          The same will apply to 1**. and 1***.
               for the first bar of Level +1 and Level +2.
     Note values within a bar will be placed just after the binary point:
          1.0 will represent the first half-note ("") of the first bar,
          1.1 will represent the second of the first bar,
          1.00 will represent the first quarter-note ("") of the first bar (the first in the first ),
          1.01 will represent the second of the first bar (the second in the first ),
          1.10 will represent the third in the first bar (the first in the second ) and
          1.11 will represent the fourth in the first bar (the second in the second ).
     And so on for eighth-notes (), sixteenth-notes () ...
For all levels, "0" will represent a Beat and "1" will represent an Off-beat.

Examples

We will use the same melodies which are used on the site,
     first for "Footsies" and then for Graphics.

Twinkle, Twinkle, Little Star
Here is the Rcode for the first part of the song
     (the first four bars at Level -1)
Note the divided bars (.0 and .1)
     for all the bars except the fourth (100.).
In the first example, the Rcode has been squeezed into one line
     containing the two cells (four bars).
In the second example, the Rcode has been spread over two lines
     one cell (two bars) per line.

Twinkle, Twinkle, Little Star - Complete
Here is the Rcode for the complete song
     (twenty-four bars at Level -1).
Note that it starts at the ninth (1001.) bar,
     the first eight having been removed by the Transformation of Ablation to produce the ternary ABA form.
The rest is repetitious, only the bar numbers gradually increasing to end at the thirty-second (100000.) bar.

Polly, Put the Kettle On
Here is the Rcode for the whole song (eight bars at Level -1)
     spread over four lines, one cell (two bars) per line
Note the bars (.00, .01, .10, .11)
     for the first (1.), third (11.), fifth (101.), and sixth (110.) bars.
Note the breath ( ' ) in the sixth (110.) bar.
Note the bars (.00, .01, .1)
     for the second (10.) and fourth (100.) bars.
Note the bar (.0, .1)
     for the seventh (111.) bar.
Note the bar (1000.)
     for the eighth (1000.) and last bar.

Red River Valley
Here is the Rcode for the whole song (eight bars at Level -1),
     spread over eight lines, one bar per line, one cell every two lines.
Note the pick-up notes (.110, .111)
     at the end of the first line, in bar 0..
Note the syncopation at 10.001 and 110.001,
     the "- -" indicate that the note lasts until the beginning of the next note;
Note the dotted (.) at 100.0,
     the "-" indicates that the note lasts until the beginning of the next note.

Happy Birthday
Here is the Rcode for the complete song
     (eight bars at Level -1), one bar per line.
Note the pick-up notes .110, .111
     at the end of the first line, as in Red River Valley,
The shaded column indicates second beats which have been removed by the Transformation of Ablation.

Never OnSunday
Here is the Rcode for the complete verse
     (four bars at Level -1), one bar every two lines.
Note the pick-up notes
     .1001, .1010, .1011, .1100, .1101, .1110, .1111
          at the end of the first line, as in Red River Valley,