Regarding the amount of "heat" in the recipe, I'd agree with @justkt that you'd want to go with 1/8 to 1/4 (at most) of the specified amount of black pepper if substituting cayenne. I like spicy food and go through a lot of cayenne (and other) chile pepper preparations, and they can vary a lot in terms of strength even within the same variety. So, I'd start on the light end and add more to taste if it's not spicy enough for you.
My wholly unscientific opinion is that when a recipe calls for black pepper in any significant quantity it's for the flavor as much or more than the spicy heat. If you have any ground cardamom on hand you might could toss a pinch of that in as well to replace some of the resinous flavor that black pepper has and cayenne lacks.
Props to Magnus for his excellent and botanically accurate answer.
Your mix is just a chili powder with a fruity flair.
As a rule of thumb, chili powder contains large amounts of chilis, cumin, and either garlic or onion. Other flavors come and go and appear in varying quantities. The ingredients in your mix that are not typical are the amchur, coriander, and cinnamon. Cinnamon with chili powder is not unheard of and results in familiar flavors but it isn't often included in standard recipes.
The amchur, dried and powdered unripe mango, and the coriander would impart fresh, fruity notes that are not typical but sound delightful!
AB's is a decent standard chili powder recipe:
- 3 ancho chiles, stemmed, seeded and sliced
- 3 cascabel chiles, stemmed, seeded and sliced
- 3 dried arbol chiles, stemmed, seeded and sliced
- 2 tablespoons whole cumin seeds
- 2 tablespoons garlic powder
- 1 tablespoon dried oregano
- 1 teaspoon smoked paprika
I was able to find a recipe that looked more similar to yours- that is with coriander and cinnamon:
- 5 dried Guajillo chilies
- 2 dried Chipotle chiles
- 4 Arbol chiles (or other thin red spicy chiles)
- 1 Tbs paprika
- 1 Tbs coriander seed
- 1 Tbs cumin seed
- 1 cinnamon stick
- 2 tsp Mexican oregano
- 1 tsp onion powder
- 1 tsp black peppercorns
Start with this recipe and modify it to your taste. For example I would probably double the cumin and leave out the black pepper as I don't think it fits here. If the flavor of the mango was distinctive in your mix it could be added to taste without adversely affecting the mix. If you don't want your mix to be too spicy then you should stick with milder dried peppers. Many dried peppers are surprisingly mild and fruity. Don't just leave them out because they do make up a bulk of the flavor and the magic.
Notice that both recipes call for no salt. Commercial spice mixes include a lot of salt as cheap filler. You should salt your dish to taste and not add it in your spice mix.
By mixing this yourself you will also be able to use freshly toasted and ground spices which will taste much better.
Best Answer
They don't taste identical at all, and even more important, they don't smell the same. White pepper has a distinct "barnyard" odor. People do indeed use them when black flecks might be unpleasant, but in most cases I'd rather go pepperless or just live with the color.