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On the basis of recent work by Cardin and Teixeira on ordinary differential equations with more than two time scales, we devise a coordinate-independent reduction for systems with three time scales; thus no a priori separation of variables into fast, slow etc. is required. Moreover we consider arbitrary parameter dependent systems and extend earlier work on Tikhonov-Fenichel parameter values -i.e. parameter values from which singularly perturbed systems emanate upon small perturbationsto thedoi:10.18154/rwth-2019-06677 fatcat:krm3tjw75bajthyh64hgqimjie