Three pronunciations can be found in Modern Standard Mandarin:
Modern dà, from Middle Chinese dɑH, from Old Chinese *lˤaːts. The phonological development from Old Chinese to Middle Chinese is irregular. Original sense: "big" (Shijing). Derived senses: "size" (Mozi), "thick" (Zhuangzi), "to respect" (Mengzi), "to respect" (Xunzi), "to extol" (Gongyang Zhuan), "to exaggerate" (Classic of Rites), "arrogant" (Guoyu), "good" (I Ching), "(of time) long" (Erya), "senior" (Shijing).
Modern dài, from Middle Chinese dɑiH, from Old Chinese *lˤaːts. This Middle Chinese pronunciation-preserving (i.e. literary) pronunciation occurs only in compounds such as 大夫 (dàifu, “doctor”) and 大王 (dàiwang, “(in operas, old novels) king; ringleader”).
Modern tài, from Middle Chinese tʰɑiH, from Old Chinese *l̥ˤaːts. This is the ancient form of 太 (tài, “too, excessively”) and this orthographical usage is obsolete in modern languages.
Pronunciation 2), the diphthong reading, is traditionally regarded as the correct one. However, the monophthong reading 1) has been recorded as early as Han Dynasty, and Sui-Tang rhyme books record both. Both readings are reflected in Sino-xenic readings in non-Sinitic languages, although the diphthong readings dominate in compounds. Axel Schüssler postulates that all pronunciations can eventually be traced back to liquid initials, i.e. 1,2) **laːts, 3) **hlaːts.
The three pronunciations are cognate. Within Chinese, they are cognate with 太 (OC *tʰaːds, “too, excessively”), 泰 (OC *tʰaːds, “big”), 誕 (OC *l'aːnʔ, “big, magniloquent, ridiculous”). There are no unambiguous Tibeto-Burman cognates. Proto-Tibeto-Burman *taj(“big”), from which came Written Tibetan མཐེ་བོ(mthe bo, “thumb”), Anongtʰɛ(“big; large; great”), Mikir tʰè, ketʰè ("id."), Burmeseတယ်(tai, “very”), is often compared with. There is no final –s in the Tibeto-Burman words, but a –y, which, according to James Matisoff, "indicates emergent quality in stative verbs". Also compare Chinese 多 (OC *ʔl'aːl, “many, much”), 都 (OC *taː, “all”).