Already Quantified

Rhythm does not require additional Quantification. It is already quantified with its well-defined Quantitative Dimension of Note-length (with itsnote-values) and its equally well-defined Qualititative Dimension ofAlternation(with its multi-level Beats and Off-beats), both combined in theRCode. As a stable container, Rhythm embraces all kinds of variable contents which must submit to its exigencies.

The parameters

• At all levels we use the terms "Beat" and "Off-beat" to define rhythmic quality. In current usage, the terms "On the beat" and "Off the beat" are often used for the same purpose, and, whenever it is clear that Rhythm is involved, "On" and "Off" would suffice, serving as both adjectives and nouns. Besides this On/Off parameter of Alternation, there will be 2 other parameters involved here.
• TheKinetic/Staticparameter, in which movement (or rest) is generated by the Harmonic and Melodic contents of the music. This movement (or rest) may be either On or Off within any given cell (at any given level).
• A new "Opening/Closing" parameter denoting the level of cadential "strength" of any given cell, in which Off movement will increase the Closing level of the cell, but On movement will decrease the Closing level of the cell, a Kinetic Off and a Static On generating the most Closing.

The available tools

• TheRhythm Graphics, both with individual and combined levels, which clearly identify both On/Off and Kinetic/Static parameters.
• TheRcodewith "0" denoting On and "1" denoting Off at all levels, but without identifying the Kinetic/Static parameter with its specific Off-beat Association.
• The 2-cell concept ofAntecedent/Consequent, with its 4-cellaA / cA, aC / cCextension, in whichaArepresents the smalla(ntecedent) of the largeA(ntecedent),cArepresents the smallc(onsequent) of the largeA(ntecedent),aCrepresents the smalla(ntecedent) of the largeC(onsequent), andcCrepresents the smallc(onsequent) of the largeC(onsequent), with the Antecedents being Off and the Consequents being On (at different levels).
• The important element of breaths and how they affect theAssociation of Off-beats, with Rebounds, usually found in smaller levels, reversing the normal Kinetic-Off/Static-On affinity of the Pick-up Association, found in larger levels. These 4 tools will be constantly combined and the results compared.

Quaternary Groupings

The 4/4 Bar

The 4s, habitually numbered beats 1, 2, 3, 4, are now numbered 0, 1, 2, 3
          (.00, .01, .10, .11in the Rcode)
     with the first numeral (after the dot) denoting the On/Off of each, and
     with the second numeral (after the dot) denoting the On/Off of each,
          "0" for On, "1" for Off.
The first, with theand theboth On,
     is evidently the most On.
The fourth, with theand theboth Off,
     is evidently the most Off.
But what about the secondwith theOn and theOff,
     and the thirdwith theOff and theOn ?
          Which is the more On and which the more Off ?
     That depends on the association of the second(a small level Off-beat) -
          if itreboundsfrom the firstit is more On than the third,
               with the 4s in a rising "stair-case" pattern, but
          if it acts aspick-upto the thirdit is more Off than the third,
               with the 3 lasts acting as 2 cells with the firstof the next bar.
     This choice of association will be clearly visible and evident in the Graphics,
          but will not be present in the Rcode with the second beat of the bar always indicated.01
               regardless of the association.
     In a piece of music, one will occasionally find both associations at the same time, usually
          with one as a Pick-up (in the Melo-harmony with a breath before the second beat), and
          another as a Rebound (in the Melo-rhythm with a breath after the second beat),
               a very striking effect.

2 Cells - AC

When we have only 2 cells,
     the first, indicated "A", acts as theAntecedent, and
     the second, indicated "C", acts as theConsequent,
          the same shape we had in thepick-upassociation in the preceding paragraph.
     The second cell, theConsequent, must evidently be at least as closing and final as the first.
However, it does not seem wise to consider these 2 cells independently, as if only their order was pertinent.
     The first cell,A, functions all by itself atLevel 0, but
          the second cell,C, is engulfed in the largerLevel +1cell,
               in such a way that the On ofAis the first half of the Off ofC.
     If the On ofAhas aMOTRIX(a complete Tetrad or a Deceptive Triad),
           Awill have less closing (with a Kinetic On)
               but the large cell will have more closing (with a totaly Kinetic Off).
     If the On ofAhas noMOTRIX(a Real Triad),
           Awill have more closing (with a Static On)
               but the large cell will have less closing (with a breath in the middle of its Off).

4 Cells - aA / cA, aC / cC

When we have 4 cells, we have, evidently, 2 groups of 2 cells each -
     2 cells in theAand 2 cells in theC,
          each cell in theAserving as eithera(ntecedent) orc(onsequent)aAorcA, and
          each cell in theCserving as eithera(ntecedent) orc(onsequent)aCorcC.
     In decreasing order of closing capacity required, we have -
          the very end, the fourth cellcC, with the greatest need for closing,
          then the center, the second cellcA, with a lesser need for closing,
               established at a larger level, probablyLevel +2, and finally
          the first and third cells, the 2 smalla(ntecedents),aAandaCwith the least need for closing,
               established at a smaller level, probablyLevel 0.
Here, considering these 4 cells independently is even more incomplete.
     The first and third cells,aAandaC, function all by themselves atLevel 0, but
          the second cell,cA, is engulfed in the largerLevel +1cell, and
               the fourth cell,cC, is engulfed in the much largerLevel +2cell,
                    with, in its Off, the On of the second cell and the complete third cell.
     We will be obliged to deal with these Rhythmic structures very carefully.

On to theQuantification of Harmony