Talk about progressions and you get numerals instead of chord names. It exists so that the same conversation works in any key.
Names like "the four-chord loop" or "the Canon progression" do not refer to specific chords. They refer to a sequence of positions inside a key, and numerals are how those positions get written.
Number the scale degrees
Take the seven chords from last chapter in C major and number them. The numeral just says which scale note you stacked from.
- I = C (first)
- ii = Dm (second)
- iii = Em (third)
- IV = F (fourth)
- V = G (fifth)
- vi = Am (sixth)
- vii° = Bdim (seventh)
Naming a chord by its position in the key. G in the key of C is V; A in the key of D is also V. Same number, same job.
The same shape in any key
Here is I-V-vi-IV in three keys. Every chord is different; the shape you hear is the same.
- Key of C (C, G, Am, F)
C | G | Am | F
- Key of D (D, A, Bm, G)
D | A | Bm | G
- Key of F (F, C, Dm, B♭)
F | C | Dm | Bb
Changing key to suit a singer's range is routine. If you remember "I-V-vi-IV", you can rebuild the same progression in the new key immediately. Remember it as chord names and you have to relearn it key by key.
Generate over I-V-vi-IV in D. Compare it with the C version from chapter one: same shape, different height.
Generate over I-V-vi-IV in DA numeral is not a chord name; it is a position in the key. That is why moving the key does not rename the progression.