In this paper, we demonstrate this technique using two systems, a basic stringency system (BSS), and a complex stringency system (CSS). We show how a complete analysis of BSS, using Property Theory, provides fundamental insights into the more complicated CSS which BSS is a simplification of. A property analysis is a set of properties that divide the languages of the typology in such a way that each language and its grammar can be identified uniquely by its property values. Such an analysis identifies the crucial rankings among constraints that distinguish all grammars of the typology so that languages that share property values share extensional traits.

BSS generalizes systems in which there is one stringency hierarchy (e.g. de Lacy 2006’s typology of sonority-driven unstressed vowel reduction or Alderete’s (2008) analysis of stress in the Pama-Nyungan language family). The constraints of BSS consist of four markedness constraints and one faithfulness constraint. The markedness constraints form a stringency hierarchy in which each markedness constraint is in a stringency relationship with every other markedness constraint. For constraints X and Y to be in a stringency relationship we mean X(cand) ? Y(cand) for all candidates, cand, of the system. This stringency hierarchy imposes a markedness hierarchy on the forms of the system in which every form of the system has a unique position on the markedness hierarchy. This yields a total order on the forms. We then show, using Property Analysis, that each grammar in the typology is completely determined by the lowest unfaithfully mapped form on the markedness hierarchy. This result applies to all stringency systems in which there is one stringency hierarchy.

CSS is an analysis of the system presented in Krämer & Zec (2017)’s typology of manners in the syllable coda. There are seven constraints in the system, one faithfulness constraint and two stringently ordered sets of markedness constraints, an F-scale set and a P-scale set, each comprised of three constraints. The F-scale consists of a constraint against fricatives, one against fricatives and liquids, and one against fricatives, liquids and nasals. The P-scale follows the same building principle based on the category of stops. Each of the stringency hierarchies imposes an independent markedness hierarchy on the forms of the system. We give a property analysis of CSS in which the properties are organized in a parallel manner to the properties of BSS. The basic system embeds in CSS in that each stringency hierarchy in CSS has a set of properties associated with it that are structurally identical to the properties of BSS. As in BSS, a grammar’s mappings in CSS are determined by where on each of the markedness hierarchies the language is first unfaithful. This shared extensional trait in BSS and CSS manifests as structurally identical properties.

Stringency systems vary in their complexity from the number of classes they refer to, to how they interact, either with another orthogonal and conflicting stringency set (e.g., Alber 2001’s analysis of regional variation in glottal stop insertion in German), with one conflicting constraint (e.g., the vowel reduction patterns alluded to above) or another parallel stringency set and a conflicting constraint (e.g., the coda manner typology). In this paper we show how the structure of a maximally reduced stringency system is reproduced using the holographic principle in the more complex system via its properties. Understanding the relations that inhere between the simple and the complex is central to explicating larger typologies that defy easy analysis.