Laminated to thin-bedded siltstones directly overlie Carboniferous coals at several localities in the Eastern Interior Coal Basin. Because lamina thicknesses show cyclical variations, the siltstones have been termed "tidal rhythmites". The rhythmites commonly show a repetitive thick-thin pairing of the laminae, and these two-lamina rhythmites have been interpreted as the result of the asymmetry of flood and ebb velocities that affected sedimentation in a diurnal paleotidal system. Alternatively, the pairing has been interpreted to be related to a pronounced difference in height between successive high tides in a semidiurnal system. This explanation suggests deposition in a mixed, predominately semidiurnal system with a marked diurnal inequality. In addition to the two-lamina rhythmites described originally, subsequent examination of drill cores indicates the occurrence of relatively rare, more complex three- and four-lamina rhythmites. A variety of mathematical techniques are used herein to analyze lamina thickness data extracted from these rhythmites. Processing techniques include: (1) comparing the linear relationship between the thicknesses of the thinner and thicker laminae and comparing these relationships to modern tidal systems; (2) analyses of thickness periodicities and comparison with modern neap-spring tidal cycles; and (3) extraction of lamina thickness inequalities and comparison to the diurnal inequalities that occur in semidiurnal tidal systems. These tests indicate that reasonable conclusions can be made for the type of originating paleotidal system. For the cases analyzed herein, the paleotidal signature suggests a mixed, predominantly semidiurnal system with a marked diurnal inequality.