Why majors are major

The seven chords of C major again, labeled by quality this time. Tap around and listen: bright on 1, 4, 5; shadowed on 2, 3, 6; tense on 7.

The numeral already told you: uppercase major, lowercase minor, ° diminished. This pattern, M m m M M m °, holds in all twelve major keys.

Remember the recipe from 3.2: 4 then 3 is major, 3 then 4 is minor. Tap each numeral and read its stack. Nobody tuned these chords one by one. The counting just comes out this way.

The major scale has two half steps in it, between rungs 3-4 and 7-8. Each third in a stack spans two rungs: dodge the half steps and it measures 4 semitones; catch one and it shrinks to 3. Rungs 1, 4, and 5 open with a clean 4. Only vii° catches both: 3 + 3.