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The description in the introduction shows how to draw the scale staff lines, compared with the way the 5-lines staff is drawn.
Thus the scale staff is not restricted to the C-major key (of course) and generalizes to arbitrary modes or chromatic music using the modern system of key signatures and accidentals.
Moreover, the scale staff is adapted to any clef (Treble, Bass or other Clefs), simply drawing the Clef to set the reference note :
The standard 5-line staff is especially at its limit when going far up or down the scale :
Two remarks :
- The scale staff allows for fast reading of notes in this situation
- The thing is not that the scale staff "is right", but that the 5-line staff has a problem.
The standard 5 line staff has lines on regular two-notes intervals. Because the standard score is made for heptatonic scales, the next octave is found after seven intervals, so drawing lines at regular two-notes intervals (for the major scale : C, then E, then G, etc.) leads to C's alternating on and off the line accross different octaves :
- the C4 is on a line
- the C5 is between two lines
- the C6 is again on a line, etc.
To my knowledge, there is no argument, in terms of music theory, to give any significance to this "even/odd" effect. It is pure noise for identifying notes and is just a consequence of regular two-notes intervals.
This even/odd alternation appears very early in the learning of music, when one learns notes on the Treble Clef : the notes C4 and C5 must be learned one after the other, and the octave interval, which is very meaningful musically, is not at all visible in the music notation.
This is why learning notes in the 5-lines staff is a long process : because there is no repeating pattern accross the octaves.
To be fair, one thing that is maybe simpler in the standard notation is the reading of intervals for chords. I think that some experimentation is needed to decide whether chords are harder to read on the staff or not. In any case, choosing the standard staff or the scale staff is going to be a tradeoff, between one with easier chord reading and one with much easier note reading.
This pitch staff notation applies to any score, for any instrument. With this, learning notes on the different clefs is not needed anymore, and musicians don't need to specialize in reading on treble, alto, tenor and bass clefs : all scores look alike.