Potential contrast is typically used as an image quality measure and quantifies the maximal possible contrast between samples from two classes of pixels in an image after an arbitrary grayscale transformation. It has been applied in cultural heritage to evaluate multispectral images using a small number of labeled pixels. In this work, we introduce a normalized version of potential contrast that removes dependence on image format and also prove equalities that enable generalization to more than two classes and to continuous settings. Finally, we exemplify the utility of multi-class normalized potential contrast through an application to a medieval music manuscript with visible bleedthrough from the back of the page. We share our implementations, based on both original algorithms and our new equalities, including generalization to multiple classes, at https://github.com/wallacepeaslee/Multiple-Class-Normalized-Potential-Contrast.