But that's what it is. When Carol talks about the "chordal scale", she's simply talking about the harmonized major scale. Understanding how this works is the key to why chords work together. That whole "ii V I" thing is based on it.
Take a major scale and write it out- really, write it out on paper for yourself, I'll wait....
C D E F G A B C
then do it again starting on the third, right on top of what you started with the third (E).
E F G A B C D E
C D E F G A B C
Repeat, again moving a third to G...
G A B C D E F G
E F G A B C D E
C D E F G A B C
Those stacks are the triads that are diatonic to the key of C. So instead of memorizing that I, IV, and V are major, that ii, iii, and vi, are minor, and vii is diminished, you know exactly WHY they are, and that helps you understand instead of just memorizing and regurgitating.
Carry it out one more level for the 7th chords...
B C D E F G A B
G A B C D E F G
E F G A B C D E
C D E F G A B C
Analyze those stacks of notes to see the third relationships, and how they build the IMa7, iimin7, iiimin7, IVMa7, V7, vimin7, and viimin7b5. But also look to see how a major seventh is a major third (C to E) with a minor third stacked on (E to G), and another major third (G to B). And compare that with the major third on top to the dominant 7 which is major (C to E), then a minor (E to G) and another minor (G to Bb).
That's what most chords you'll run into in most popular musics are (as I conveniently ignore a whole spectrum of quartal harmony which isn't nearly as common as triad harmony).
John