Die
A die is a kind of cutting tool. By definition, a die is a specialized cutting tool made to perform a special act or cut a specific shape for a specific application. Dies cut by pressing a solid, positive shape through an inverse, negative shape, shearing whatever material is placed between the two as they are pressed together. A paper punch is a die. Dies can also punch sheet metal fender blanks, washers and an endless variety of complex shapes.
Shearing Action
Tool and die makers, or other machinists, use many types of specialized cutting tools from ultra-hard cobalt machine heads to diamond burs. Most of these cutting heads shave metal away like a block plane shaves wood. Dies don't cut like that. They use shear pressure: two concentrated forces in opposite directions along the same plane to shear through material. This may be combined with a slicing motion. Scissors, for example, use shearing action and the angle of the scissors to create a slicing action.
Pitch Dies
Pitch dies are used primarily in paper binding --- industrial-duty paper punches. They borrow a concept from the musical world, pitch pipes or the keys of a piano. Pitch patterns in music are like stair-steps, one after the other. Pitch dies use a row of contiguous dies or hole punches, although not all of the dies are pressed down at once. They are tunable, so the operator can mechanically choose a pattern. For example, starting with the nearest die, pressing the die might shear a hole with every third, fifth or sixth die.
Noncontiguous Pitch Dies
Conceptually, a pitch die can have one die sitting next to another in a row, just like the keys of a piano; they are capable of pressing all at once or in any mechanical sequence or pattern the die is designed for. However, not all pitch dies have contiguous cutting dies. Some may have fewer cutting dies and express their pitch ratio by comparing the width of the die to the gaps between the die. So, a 3-inch gap and a 1-inch die width has a 3-to-1 pitch ratio. These noncontiguous pitch dies may have dies that are moveable along a track so their ratio can be changed.