The paper offers a new concept of studying abrupt chest-falsetto register transitions (jumps) based on the theory of nonlinear dynamics. The jumps were studied in an excised human larynx and in three living subjects (one female and two male). Data from the excised larynx revealed that a small and gradual change in tension of the vocal folds can cause an abrupt change of register and pitch. This gives evidence that the register jumps are manifestations of bifurcations in the vocal-fold vibratory mechanism. A hysteresis was observed; the upward register jump occurred at higher pitches and tensions than the downward jump. Due to the hysteresis, the chest and falsetto registers can be produced with practically identical laryngeal adjustments within a certain range of longitudinal tensions. The magnitude of the frequency jump was measured as the "leap ratio" F0F:F0C (fundamental frequency of the falsetto related to that of the chest register) and alternatively expressed as a corresponding musical interval, termed the "leap interval." Ranges of this leap interval were found to be different for the three living subjects (0-5 semitones for the female, 5-10 and 10-17 for the two males, respectively). These differences are considered to reflect different biomechanical properties of the vocal folds of the examined subjects. A small magnitude of the leap interval was associated with a smooth chest-falsetto transition in the female subject.