Your comparison to musical notation is insightful. I think that I can expand upon it a bit. I can read both western notation and Byzantine notation. Byzantine notation is very different from western notation: it describes a melody using symbols indicating how many steps to take from the current pitch in a given scale. There are also rhythmic symbols added to the notes that generally require reading ahead of what you are currently singing.

For people interested in Byzantine music, the notation can seem imposing at first -- especially to people who already know western notation. Much effort has gone into translating Byzantine music into western notation, but some problems arise. First, some Byzantine scales use very different pitches compared to a western equal tempered scale. Second, the rhythms in Byzantine music can involve syncopation or other rhythms that can be difficult to notate using western rhythmic symbols. Finally, Byzantine notation is optimized for depicting melody, while western notation is focused on harmony. There is simply more unnecessary visual noise in writing Byzantine music in western notation.

That last point resonates with your talk of idioms. While Byzantine music may seem to have many neumes for a given musical phrase, there are many idiomatic combinations of pitch-changing and rhythmic neumes together. As such, what would be read in Western notation with many individual notes and rhythmic markings, becomes in Byzantine notation a single "word".

If you're interested in seeing how these systems of notation compare, look at the following hymn: http://www.cappellaromana.org/wp-content/uploads/2014/04/Che... The neumes are in red at the top, with a simple western interpretation on the first western music staff and an ornamented interpretation on the bottom staff. Comparing the neumes to ornamented western interpretation (which represents the full Byzantine ethos, or style), we can see that significantly more information is contained in the sparser Byzantine neumes.

Anyway, you've convinced me to learn APL because I now see how similar the arguments for this notation are to my own arguments for using Byzantine notation. Thank you for your insight.