By listening (you could try listening too or doing frequency measurements) it seems to me that good singers build to correct intonation of a note while the note is sung.
Even good singers, it seems to me cannot get it right at the attack of the note which is almost always flat. The reason seems to be that the hearing mechanism hears flat, a lower pitch when a frequency (orchestra instruments one hears for example in the backing track) is at a normal or loud sound pressure level. Only at very low SPL do pitch and frequency seem to coincide. This is described in the Chapter called Influence of the Mind in the great book by Stevens and Warshofsky, Sound and Hearing.
Good singers seem to increase frequency after the attack until the end of the note so that it sounds correct.
It does not seem to matter that the attack is low in pitch. According to the Heisenberg Uncertainty Principle in music the less the duration of a tone the higher the uncertainty of the pitch! There is simply not enough time to measure frequency right. This is described in the great book Waves - Berkeley Physics course by Frank S. Crawford Jr.
Here is an example of what I hear as increase in pitch at middle and ending of notes so that it sounds correct to the brain of good singer and the brain of a listener. Paroles Dalida, Delon.
A good test for this could be for example to freeze a good singer's pitch by granular synthesis and measure by beat elimination comparison with a sinewave signal generator.
Summary: When I try to sing I do not care about nailing the note right at the beginning of its life but I care about nailing it after its birth. For every note. Like humans do. None is born perfect, but we do try to improve ourselves.
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