Babylonian mathematical astronomy appears founded on an understanding of repeated procedures – a technology utilized by modern methods of nonlinear dynamics capable of describing deterministic chaos. The repeated procedures (known as iterated maps because they repeatedly provide a mathematical mapping from a current value to a next value) appear to model visibility phenomena such as first or last appearance using Poincaré sections describing close recurrence in position among the stars in terms of sidereal ecliptic longitude. Babylonian astronomers were careful to define stable one-dimensional periodic iterated maps addressed by terminating sexagesimal fractions and partitioned according to resonances. This strongly suggests at least empirical knowledge from music of the entrainment of nonlinear oscillators, termed mode-locking, for which the simplest rational periods correspond to the largest steps in rotation of the phenomena through the ecliptic. Although the “music of the spheres” is widely associated with Kepler’s musical expression of planetary angular velocities in Harmonices Mundi and Plato’s cosmic harmony in Timaeus, musical intervals based on 5-limit just intonation appear throughout Babylonian mathematical astronomy, whose cuneiform texts comprise predictions for the years SE 15-150 with few exceptions (c. 295/396 BCE–160/161 BCE according to the Seleucid empire). The longitudes of Babylonian Normal Stars appear well described by a mathematical model in which the ratio of successive longitudes is either 16/15 (minor second) or 8/5 (perfect fifth plus a minor second). As noted by Aaboe, for System A models, there is a zone whose elementary steps bear a superparticular ratio to the other zones i.e., whose angular frequencies are related by regular 5-limit fractions (first order resonances.) The just intervals expressed in Babylonian astronomy include minor semitone, minor whole tone, major whole tone, minor third, major third, perfect fourth, perfect fifth, and diapason.