Structure of Time/Unknown Container/1960

The Problem

In a very specialized work dealing with the rhythmic structure of music,
          in which it is deplored that
               "There are many textbooks on harmony and counterpoint but none on rhythm",
     it is only about three-quarters of the way through the book
     that the authors decide to examine the Beats and Off-Beats of Au clair de la lune at all levels,
          which they label "accented", with "-" (for Beat) and "un-accented", with "u" (for Off-beat).


Let's examine this analysis one level at a time, starting with the smallest -
1. At Level -2, where we find Quarter notes,
     the answer is correct and evident : Beat - Off-beat, Beat - Off-beat,
          indicated "| - u | - u |".
1. At Level -1, where we find Half notes,
     again, the answer is correct and evident :
               Beat - Off-beat, Beat - Off-beat, Beat - Off-beat, Beat - Off-beat,
          indicated "| - u | - u | - u | - u |".
2. At Level 0, where we find Whole notes (bars), once again,
     the answer is correct though far less evident : Off-beat - Beat, Off-beat - Beat,
          indicated "| u - | u - |".
3. At Level +1, where find 2Whole notes (2-bar note-values), here,
     the answer is faulty because each large 2-bar note-value is composed of Off-beat - Beat
          indicated "| u - |",
      rather than Beat - Off-beat ("| - u |"), as was the case for Half notes and Whole notes.
By using the terms "accented" and "un-accented" rather than the terms "Beat" and "Off-beat",
     it was not possible (or at least not evident) to establish a consistent structure at all levels.
Had the large 2-bar note-value been placed correctly as Beat - Offbeat ("| - u |"), with bars 2 and 3,
     bar 1 would have immediately been perceived as the pick-up which it really is at this large level,
          but such a large pick-up does not seem possible in the academic outlook,
               even if there is a 3-bar pick-up at Level +2 and a 7-bar pick-up at Level +3.
4. At Level +2, with 4Whole notes (4-bar note-values)
      the alternating of Beats and Off-beats is totally abandoned, with 2 Off-beats in a row ("| - u | u - |").
At Level +3, with 8Whole notes (8-bar note-values), the analysis is not even attempted.
The pages of conjecture which follow this example are not even pertinent after this faulty exposé,
     and this volume does not seem to have been much help to future authors as we will soon see.
Are form and phrasing part of rhythm ?
     Of course they are, but they cannot be clearly explained without a consistent structure.

The Solution

By singing this song with the footsies, every single level will fall into place simply and automatically (it is very much like Polly, Put The Kettle On). We started with a relatively benign example. The melody was faultless, perfectly composed, and well written with bar-lines correctly placed. The bars were possibly a little small, at Level -1 rather than at Level 0, but this is such current practice that it certainly does not merit reproach of any kind. The only weakness here was in the analysis of the larger levels and this seems to demonstrate quite clearly the limits of current academic knowledge in dealing with such a simple, completely binary, tune.

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