In this paper, we have considered a new contextualization of the Gini index, giving a particular interpretation of inequality. The Gini index is the most widely used measure of inequality in the world, however, this index does not meet some desirable properties of an inequality indicator, even so, as it is a measure adopted by most countries through the years, makes it a valuable statistical input; which requires adjustments that provide information, making the study of inequality more robust by adding different indicators that can account for their economic, political, and social environment. This article provides a variation of the Gini index with the purpose of compare and classify different territories (the States of Mexico, as well as some countries) with similar Gini index. The classification is carried out into groups (called turbines) with either positive equality, negative equality, positive inequality or negative inequality. The main contribution of this paper lies on distinguish territories with similar Gini index but different in how privileges and facilities are distributed into them.