Enrique,
After a few readings, I think I understand your approach.
You're assuming each measure is divided into 3 or 4 counts (quarter notes)
and each of those can be conceptually divided into 12 smaller intervals,
so you can describe the timing of any count as a series of integers summing to 12.
Or, you can divide it with appropriate-length line segments,
using occasional numbers to clarify the length when it can't be accurately estimated visually.
This seems to work well for normal rhythms, but the real challenge is handling syncopation.
The RHN traces depict this quite well, with the traces crossing the bar and count lines.
But the numeric representation is a bit messier--the parentheses alert the reader to ties,
but if there is syncopation across several counts in a row--a common situation--one could lose track of the beat.
I seemed to have a similar problem just eliminating ties--even though the note-starts or IOIs are correct,
I think the performer also needs to understand how the note-starts relate to the fundamental beat.
A simple sequence of durations doesn't do that.
I suppose that's why TN breaks beams at counts and ties across count boundaries.
[One of my timing examples used full-count beams to represent counts but attached noteheads only at the start ticks.]
Now it may be that we perceive rhythms as a pattern of durations, and that works OK for solos,
but when you have two or more syncopated "duration patterns" progressing simultaneously, (e.g. left-hand right-hand parts,
or separate choir voices)
it seems to become more important to relate the note-starts to the beat than to the previous note in your part.
So I'm beginning to believe that "syncopation" is not actually a property of a single sequence of tones,
but it more analogous to a "chord", in that it relates to the simultaneous progression of two (or more) different timing sequences.
If that is true, syncopation could not be adequately represented by a "lead sheet" or any single sequence.
In practice, the melody is heard relative to a drum or bass track which keeps a steadier beat,
but not necessarily all evenly-spaced intervals.
That's why I think that TN is fundamentally challenged in representing contemporary rhythms.
In terms of your RHN, I suppose that could mean the "count lines" (the quarter-note intervals)
might not always be a quarter-note apart.
Joe Austin
DrTechDaddy.com