Tonogenesis-the historical process by which segmental contrasts evolve into lexical tone-has traditionally been studied through comparative reconstruction and acoustic phonetics. We introduce a computational approach that quantifies the functional role of pitch at different stages of this sound change by measuring how pitch manipulation affects automatic speech recognition (ASR) performance. Through analysis on the sensitivity to pitch-flattening from a set of closely related Tibetan languages, we find evidence of a tonogenesis continuum: atonal Amdo dialects tolerate pitch removal the most, while fully tonal U-Tsang varieties show severe degradation, and intermediate Kham dialects fall measurably between these extremes. These gradient effects demonstrate how ASR models implicitly learn the shifting functional load of pitch as languages transition from consonant-based to tone-based lexical contrasts. Our findings show that computational methods can capture fine-grained stages of sound change and suggest that traditional functional load metrics, based solely on minimal pairs, may overestimate pitch dependence in transitional systems where segmental and suprasegmental cues remain phonetically intertwined.