I know it sounds like a cheap b thriller, but bear with me :-)
As mentioned in the previous post the catena will usually determine to the hue of your tie. That being the case it should govern what it can comfortably pair with.
In the case of
this purple tie the black catena gave the purple a blackish slant, making it ideal IMO for a black or charcoal suit, and not the best for a brown one.
Here are all three suits, First the Black, then the charcoal finally the brown again: For a close up high res of the black suit with the tie
click here. Some may not like the fact that the
square I used has similar shapes to the tie but as they are not the same size it didnt bother me.
[caption id="" align="alignnone" width="460" caption="Black Suit"]

[/caption]
Swapped out the square for the naysayers for
this one.
[caption id="" align="alignnone" width="460" caption="Charcoal Suit"]

[/caption]
[caption id="" align="alignnone" width="460" caption="The Brown Suit"]

[/caption]
Finally, once we had the charcoal suit out I brought back the tie we had out from yesterday, illustrating a nice combo, Charcoal Grey and the lilac/purple family.

As always, what you have read here is just one man's opinion :-) , and I would love to hear yours!