One shape, a moving key
The arpeggio never changes — 1 3 5 8, a major shape. What moves is the
root, and the root is its own line:
arp: 1 3 5 8 # the shape, repeated every bar
key-line: 0 5 7 0 # the root, one per bar: C F G C
Each bar, the root is read from key-line (0 = C, 5 = F, 7 = G) and the
shape is transposed to sit on it. Same figure, four keys — modulation as a
line sampled over time.
It’s the companion to the moving scale: one moves the scale under a fixed phrase, this moves the key. Both are the same mechanism — a value paired with a context that is itself changing over time.