Pass formula
A pass formula (also paramodal formula, hypermodal formula, hypermodal key) is a parameter in hypermodal systems that determines the arrangement of paramodes. It's derived from the paramode of the first mode - if it's, for instance, the 3rd in it's own modal system, the pass formula of the hypermodal system would be I:III, or III2:I1.
Pass formulae are expressed through a ratio of roman numerals which are the orders of both scales in their own modal system. The first numeral is usually I. If it's not, an arabic numeral is added after both roman numerals to distinguish the original modal system (1) and the paramodal system (2). It doesn't matter at all though, as anyone can understand.
The paramodal system is always upside down (ascending from the top to the first mode), which is why it's called a "pass" formula - the modes are passing by in parallels.