ΔE 14.7, fair: the same colour family, but not a straight swap. Gloomy Violet is a little lighter, much more muted, cooler than Dark Purple.
Only where an exact match doesn’t matter, such as a new unit or a highlight. Fair match (ΔE 15). Gloomy Violet is a little lighter, much more muted, cooler than Dark Purple.
The same difference applies the other way round: Dark Purple is a little darker, much more saturated, warmer.
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 Dark Purple on the colour wheel See Gloomy Violet on the colour wheel
All matches: Dark Purple equivalents · Gloomy Violet equivalents