I don't think you can explain it to someone who can't play music, because it's a notation for music. You could teach someone to play an instrument the old-fashioned way, person-to-person without any sheets, and once they understood music (i.e. what patterns of notes sound good or don't) ask them to come up with a way to write it down, and they'd come up with something much like staff notation. But that's a very labour-intensive way to learn.

Hunt-and-peck is always going to be hard on an instrument that supports multiple modes, because each mode only uses some of the modes. At my school music classes were taught on the xylophone/glockenspiel, which you configure for your piece at the start (putting the correct bars on for the mode/key you're working in), which is probably easier for beginners, but it's not a popular instrument (and nor is the harp, which is the only other example I can think of of that approach).

I think a lot of the favoring of staff notation comes down to what the instrument does well. A majority of acoustic instruments are monophonic(voice, wind, brass, many strings) and have some form of linearity in pitch, and the staff accommodates them optimally - the beginner's sheet music always starts out by accompanying the staff with fingerings for each note, to help you get some confidence that you are actually playing right notes, and then after that it's pretty straightforward to extend your knowlege to read more notes.

Chord structure just isn't even touched in most of these instruments, at least in classical performance, because they aren't capable of polyphony! That only becomes a topic as one starts moving into, e.g., jazz improvisation, where knowing how to recognize and play around a root is critical. Piano is exceptional here, since finger independence and chording practically define that instrument.

On the other hand, guitar tabs are a Big Thing in part because guitar chords transpose very well, so you don't have to learn too many unique fingerings to start accessing the others - and then if the song is defined as a sung melody plus rhythmic chord backing, as a lot of popular songs are, you don't need more than a tab and hearing the tune once to have a shot at covering it competently.

Guitar's 2D layout favors isomorphism - this is what gives it this extra power to transpose. Guitar is conventionally not tuned isomorphically, but some forms of accordion like bayan, and alternative keyboard layouts such as Wicki-Hayden, Harmonic Table or Janko, are fully isomorphic. In that case, you don't have to mode set or learn any unique scales or chord fingering per key: Learn any set of intervals(chords or scales) and you can reuse them in every key by moving your fingers over. This is wonderful for learning theory and doing composition, but it doesn't make the instruments a 1-to-1 replacement for similar instruments as in performance the distances are usually much smaller, fingerings can get tangled, it can be harder to find your place or maintain tempo, etc.

> Can the beginner's question be answered, except by saying, "uh, trust me, it's great, just keep practicing"?

Basically: not really.

Musical notation... notates a bunch of stuff, not only pitches.

Unless you have a basic understanding of all the factors involved in reading and writing music, you won't be able to understand the choices fully, and you'll have to accept them.

TLDR: music notation needs to express the five qualities of sound: pitch, duration, loudness, intention and timbre. You can't just look at pitch.

The way to learn the logic behind the scales in my opinion is to learn the theory of the early Western music, up to the Baroque era, that was around while the staff was being developed. That is: learn the seven modes of Western music (https://en.wikipedia.org/wiki/Mode_(music)).

Each mode is a diatonic scale (https://en.wikipedia.org/wiki/Diatonic_scale). Each mode has a particular combination of whole steps and half steps. Each mode has a "natural" key which can be represented in modern staff notation by all white keys.

In Gregorian chant, there are rarely any accidentals. Even by the Baroque era, while there are more accidentals, I would say the music is still very diatonic in nature.

Early music was more oriented towards just intonation (the whole integer ratio harmony mentioned in the article, which is what I would consider the more "natural" way of harmony). With just intonation, however, you can't just shift to any random key on the fly. Some keys sound nice and related. Some keys sound awful and horrible.

The article author made a statement: "If your music mostly relies on the seven notes from a particular scale, then it’s more compact to only have room for seven notes in your sheet music, and adjust the meaning of those notes when necessary… right?" I think that's an absolutely a correct way of framing early Western classical music, yes.

What makes staff notation harder probably is the corresponding rise in chromatic music.

The rise of 12TET instruments (equal temperament) like the piano, and the corresponding development of chromatic instruments (compare: the natural horn used in the Baroque era vs. the modern valved horn) allows for this sort of modulation at the cost of some chords being slightly out of tune. Modulating key signature all over the place is now possible. Yes, the author should realize that some composers do change the key in the middle of a song to change the mood. (For a nice pop example, here's the Temptations' "My Girl", which changes keys midway through -- https://www.youtube.com/watch?v=6IUG-9jZD-g)

Incidentally, the diatonic nature of pre-19th century classical music is the answer to the author's sharp / flat question as well. (http://jtauber.com/blog/2006/11/17/why_a-sharp_is_not_b-flat...)

This shift to chromaticism really isn't reflected in staff notation. In fact, I'm aware that some 20th century composers abandoned the use of key notation, ledger lines, etc. altogether, perhaps in part for this sort of reason.

Yes, I almost mentioned this point about A# and Bb on his blog but didn't. He gives an example of an A# major scale and it becomes immediately obvious that something's wrong. In order to write such a scale you either have to skip named notes (A#, C, D.. what happened to B?) or have a key signature that contains double sharps. That would be the "theoretically correct" way to do it but there are no key signatures with double sharps. So the correct name for the scale is B flat, which follows the diatonic major scale pattern of "wwhwwwh" and does not skip named notes.

But from his point of view (as any beginner) this is very confusing. They sound the same and they use the same physical keys on the keyboard, so what's the difference? There is no good answer to that except it satisfies the theory (the musical "rules") of western music.

I'm working on a blog post now which I hope will answer that question (at least, in very general terms).