Nesting
Every noteset sits inside the next — the clean structure behind the curriculum
Music's most useful structures nest inside one another: root & 5th ⊂ triad ⊂ pentatonic ⊂ major mode, each step adding only one or two notes to the one before. The root & 5th sit at the core of them all — every triad, pentatonic, and mode is built outward from it — so nothing is learned in isolation, and each layer reinforces the ones inside it.
The nesting is richer than these chains. A major mode holds a balanced set of triads — three major and three minor triads, and each is accompanied by its pentatonic. Each pentatonic in turn contains a major and a minor triad, and each major pentatonic comes with its relative minor.
The major modes are unmatched in terms of functionality, but amazingly, they are also unmatched in terms of consonance. The root & 5th are the most consonant pairing of notes and are ever-present. The major triad is the most consonant chord, effectively ringing every time any note plays, and the minor triad the next most consonant chord. The pentatonics are built from 5 steps along the circle of 5ths, and the major modes from 7.
Finally, this sequencing of music's structures introduces you to each of them by order of importance. In any melody you pick you want to be aware of the chord that is currently playing and what its notes are, as those will serve as safe havens over the chord. Using the corresponding pentatonic extends the chord tones with the two best possible other notes, that will work in any key. One triad with one pentatonic gives you melody over harmony but keeps you relatively limited — the major modes are the final key, providing a system of triads to recombine freely.