In a large bowl, mix together flours, salt, cayenne, and black pepper.
Make a well in the center and crack in eggs. Mix them gently but thoroughly into flour by scooping up handfuls and rubbing between your palms. Sprinkle in about 1/3 cup water and work it into flour mixture, then press dough into a rough ball. If ball doesn't come together, add more water, 1 tbsp. at a time, until it does (it should feel a little dry).
Turn dough out onto a work surface and knead it until fairly smooth and no longer sticky, about 2 minutes.
Set a pasta machine to the widest setting. Cut dough into thirds. Working with 1 dough piece at a time (keep others covered with a dampened kitchen towel), pat into a 1/2-in.-thick oval and feed through machine.
Fold dough into thirds crosswise and feed through again, starting with an unfolded edge. Fold and feed once more the same way. Sprinkle dough with flour if it feels sticky. Repeat folding and feeding, progressing through 2 or 3 successively narrower settings and rolling dough at least twice on each setting, until dough is as thin as you like (fettuccine is usually 1/16-inch thick). If dough sheet gets too long, cut it in half and roll each half separately.
Repeat with remaining 2 dough pieces, setting sheets to the side when done and covering with a kitchen towel (dampened if the weather is dry).
Cut each sheet to about 12 in. long and cover with the towel. Pass each dough sheet, dusted with flour if needed to keep from sticking, through the machine's fettuccine cutter. Lay fettuccine on a baking pan and dust with flour. If it's humid outside, let dry for about 1/2 hour to help keep it from sticking as it cooks.
To cook, bring a large pot of well-salted water to a boil. Add fettuccine and cook until barely tender, about 2 to 3 minutes.
Make ahead: Through step 7, up to 2 days, wrapped airtight and chilled; up to 2 months, frozen.