ΔE 26.7, loose: different enough that you should pick on purpose. Arcane Purple is noticeably darker, more muted, warmer than Beowulf Blue.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 27). Arcane Purple is noticeably darker, more muted, warmer than Beowulf Blue.
The same difference applies the other way round: Beowulf Blue is noticeably lighter, more saturated, cooler.
ΔE is the colour difference between our two swatch estimates: under about 6 is close, over about 15 is loose. Real paints also differ in finish, coverage and how they thin, so test before you commit.
See Beowulf Blue on the colour wheel See Arcane Purple on the colour wheel
All matches: Beowulf Blue equivalents · Arcane Purple equivalents