Chinese · Pronunciation Guide
dee-YEE: a hard-falling first syllable then a high level second. Note that 一 keeps its plain first tone here — the usual alternation does not apply in ordinals.
dìyī
This is the one environment where 一 refuses to change. Its famous alternation — rising before a fourth tone, falling before everything else — applies when it functions as a number in front of a measure word. In ordinals with 第, and when counting or reciting digits, it keeps its plain high level tone regardless of what follows.
Listen: 第一
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今天是我的第一天。
Jīntiān shì wǒ de dìyī tiān.
It's my first day.
Listen: 今天是我的第一天。
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今天是我的第一天。 puts yī directly before tiān, a first tone, and yet it does not become yì. If this were the counting number rather than an ordinal, the sandhi would fire and you would say yì tiān. The presence of 第 is what protects it, which makes this sentence a very clear illustration of the rule's boundary.
Learners who have drilled the 一 alternation over-apply it here and say dì yì tiān, converting the ordinal as if it were a count. That is wrong, and it happens precisely because the rule has been learned well. The other habitual slip is aspirating the d into tì. Keep the release silent and the second syllable flat.