John Lightfoot on Matthew 26:34

[Before the cock crow, thou shalt deny me thrice.] The same also he had said, John 13:38, "The cock shall not crow till thou hast denied me thrice." Therefore some say, that that was the same supper with this of the Passover. Very right indeed, if [it] ought to be rendered, the cock shall not crow once, or the cock shall not crow at all. But it is not so; but it amounts to this sense, "Within the time of cockcrowing" thou shalt deny me thrice; for Peter had denied him but once before the first crowing of the cock, and thrice before the second, Mark 14:68,72. From hence, therefore, we may easily observe in what sense those words are to be understood, which were spoken to Peter two days before the Passover, John 13:38, "The cock shall not crow," &c.: not that the cock should not crow at all between that time and Peter's denying; but as if our Saviour had said, "Are you so secure of yourself, O Peter? Verily, I say unto you, the time shall be, and that shortly, when you shall deny me thrice within the time of cockcrowing." At cockcrowing, Mark 13:35. At the Paschal supper it is said, "This night, before the cock crow," &c. Matt 26:34; Mark 14:30; Luke 22:34. But there is nothing of this said in that supper, John 13.

Concerning the cockcrowing, thus the masters: "R. Shilla saith, Whosoever begins his journey before cockcrowing, his blood be upon his head. R. Josia saith, If before the second crowing: but some say, Before the third. But of what kind of cock is this spoken?" Of a middling cock; that is, as the Gloss explains it, "a cock that doth not crow too soon nor too late." The Misna on which this Gloss is hath these words; "Every day they remove the ashes from the altar about cockcrowing; but on the day of atonement at midnight," &c.

You may wonder that a dunghill cock should be found at Jerusalem, when it is forbid by the canons that any cocks should be kept there: "They do not keep cocks at Jerusalem, upon account of the holy things; nor do the priests keep them throughout all the land of Israel." The Gloss gives the reason; "Even Israelites are forbid to keep cocks at Jerusalem, because of the holy things: for Israelites have eaten there peace offerings and thank offerings: but now it is the custom of dunghill cocks to turn over dunghills, where perhaps they might find creeping things that might pollute those holy things that are to be eaten." By what means, and under what pretence, the canon was dispensed with, we do not dispute. It is certain there were cocks at Jerusalem, as well as at other places. And memorable is the story of a cock which was stoned by the sentence of the council for having killed a little child.