Already Quantified

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

The parameters

First a slight simplification of definition -
  • 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

Our principal tools of On/Off and Kinetic/Static identification would be -
  • 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 4 Quarter notes, habitually numbered beats 1, 2, 3, 4, are now numbered 0, 1, 2, 3
          (.00, .01, .10, .11 in the Rcode)
     with the first numeral (after the dot) denoting the On/Off of each Half note, and
     with the second numeral (after the dot) denoting the On/Off of each Quarter note,
          "0" for On, "1" for Off.
The first Quarter note, with the Half note and the Quarter note both On,
     is evidently the most On.
The fourth Quarter note, with the Half note and the Quarter note both Off,
     is evidently the most Off.
But what about the second Quarter note with the Half note On and the Quarter note Off,
     and the third Quarter note with the Half note Off and the Quarter note On ?
          Which is the more On and which the more Off ?
     That depends on the association of the second Quarter note (a small level Off-beat) -
          if it rebounds from the first Quarter note it is more On than the third Quarter note,
               with the 4 Quarter notes in a rising "stair-case" pattern, but
          if it acts as pick-up to the third Quarter note it is more Off than the third Quarter note,
               with the 3 last Quarter notes acting as 2 cells with the first Quarter note of 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 the Antecedent, and
     the second, indicated "C", acts as the Consequent,
          the same shape we had in the pick-up association in the preceding paragraph.
     The second cell, the Consequent, 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 at Level 0, but
          the second cell, C, is engulfed in the larger Level +1 cell,
               in such a way that the On of A is the first half of the Off of C.
     If the On of A has a MOTRIX (a complete Tetrad or a Deceptive Triad),
          A will have less closing (with a Kinetic On)
               but the large cell will have more closing (with a totaly Kinetic Off).
     If the On of A has no MOTRIX (a Real Triad),
          A will 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 the A and 2 cells in the C,
          each cell in the A serving as either a(ntecedent) or c(onsequent) aA or cA, and
          each cell in the C serving as either a(ntecedent) or c(onsequent) aC or cC.
     In decreasing order of closing capacity required, we have -
          the very end, the fourth cell cC, with the greatest need for closing,
          then the center, the second cell cA, with a lesser need for closing,
               established at a larger level, probably Level +2, and finally
          the first and third cells, the 2 small a(ntecedents), aA and aC with the least need for closing,
               established at a smaller level, probably Level 0.
Here, considering these 4 cells independently is even more incomplete.
     The first and third cells, aA and aC, function all by themselves at Level 0, but
          the second cell, cA, is engulfed in the larger Level +1 cell, and
               the fourth cell, cC, is engulfed in the much larger Level +2 cell,
                    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 the Quantification of Harmony