(Susan M. Pigott is a fountain pen collector, pen and paperholic, photographer, and professor. You can find more from Susan on her blog Scribalishess.)
Tyrian Purple is named after a reddish-purple dye made in Tyre, Phoenicia, from sea snails. Huge numbers of snails were collected and boiled in lead vats. The smell, apparently, was quite memorable. The dye was meant to mimic clotted blood, and it was restricted to the rich, because of its limited availability. (Source: The New York Times; see also Wikipedia).
Diamine's version certainly evokes the ancient color with both red and purple tones. It reminds me a little of Noodler's Black Swan in Australian Roses (original formulation), though that ink has more shading. Nevertheless, Diamine's color exhibits good shading with a flex or broad nib. With a finer nib, you won't notice the shading at all.
The ink flows well, has no distinctive odor, and dries relatively quickly depending on the paper. On the Rhodia dot pad, it takes a bit more time to dry than on more absorbent paper.
This is not a highly saturated, deep purple. It leans more toward magenta. But it is beautiful, and if you want a purple that looks more like wine than grape juice, Tyrian Purple is a good choice. If you prefer a purer purple color, Diamine Imperial Purple might suit you better.
A comparison of several purple inks is below. Unfortunately, I sold my bottle of Black Swan in Australian Roses, so I couldn't include it in the comparison.
Tyrian Purple will work well for journaling and personal correspondence. I wouldn't use it in a business setting, though for grading papers it would be a happy medium between red and purple.
You can purchase Diamine Tyrian Purple at JetPens for $14.50 (80ml).