The paper connects two notions originating from different branches of the recent mathematical music theory: the neo-Riemannian Tonnetz and the property of well-formedness from the theory of the generated scales. These notions are mathematized and their properties are rigorously investigated. As the first result, the concepts of the generalized Tonnetze and of the multidimensional (i.e. based on multiple generators) generated tone-systems (GTS) are formally defined. Secondly, we prove a theorem stating that a normal two-dimensional GTS is well-formed if and only if it is closed. This is the main mathematical result of the paper and it can be considered a generalization of Carey-Clampitt’s work on one-dimensional generated scales to GTS’s with two generators. Finally, we illustrate power of the proposed theoretical framework. It covers various theoretical concepts found in different musical contexts. Besides the neo-Riemannian Tonnetze and Carey-Clampitt’s generated scales, our examples include Mazzola’s ‘harmonic band,’ the pitch helix known from the psychology of hearing, the ancient Chinese system of lü-lü, the Arabic 24-nīm system, and the ancient Indian 22-śruti system. In particular, we give a possible explanation of the number 22 in the Indian system.