ΔE 17.3, loose: different enough that you should pick on purpose. Purple is a little lighter, much more muted than Dioxazine Violet.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 17). Purple is a little lighter, much more muted than Dioxazine Violet.
The same difference applies the other way round: Dioxazine Violet is a little darker, much more saturated.
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 Dioxazine Violet on the colour wheel See Purple on the colour wheel
All matches: Dioxazine Violet equivalents · Purple equivalents